摘要:

DISCUSSIONS OF THE FARADAY SOCIETY No. 30, 1968 THE FARADAY SOCIETY Agents for the Society’s Publications : The Aberdeen Universitv Press Ltd. 6 Upper Kirkgate, Aberdeen Scotland@ The Faraday Society and Contributors, 1960 PUBLISHED 0 . . 1961 PRINTED IN GREAT BRITAIN AT THE UNIVERSITY PRESS ABERDEENA GENERAL DISCUSSION ON THE PHYSIC CHEMISTRY QF AERQSOLS 13th-15th September, 1960 A GENERAL DISCUSSION on The Physical Chemistry of Aerosols was held in the Chemistry Lecture Theatre, Queen’s Building, Bristol University, on the 13th, 14th and 15th September, 1908. The President, Sir Harry Melville, K.C.B., F.R.S., was in the Chair, and over 100 members and guests were present. Among the distinguished overseas members and guests were the following : Prof. F. P. Buff (University of Rochester), Dr.and Mrs. R. D. Cadle (Stanford Research Institute), Prof. and Mrs. S . W. Churchill (University of Michigan), Prof. and Mrs. F. T. Gucker (Indiana University), Prof, Charles L. Hosler (Pennsylvania State University), Dr. Claude Kaziz (Pechiney- Centre de Recherches), Prof. and Mrs. Milton Kerker (Clarkson College of Technology), Dr. A. Reuter (Germany), Dr. Bernard R. Stein (European Research Office, Frankfurt/Main), Prof. V. B. Vouk (Yugoslav Acad. Sci. Arts, Zagreb).A GENERAL DISCUSSION ON THE PHYSIC CHEMISTRY QF AERQSOLS 13th-15th September, 1960 A GENERAL DISCUSSION on The Physical Chemistry of Aerosols was held in the Chemistry Lecture Theatre, Queen’s Building, Bristol University, on the 13th, 14th and 15th September, 1908. The President, Sir Harry Melville, K.C.B., F.R.S., was in the Chair, and over 100 members and guests were present.Among the distinguished overseas members and guests were the following : Prof. F. P. Buff (University of Rochester), Dr. and Mrs. R. D. Cadle (Stanford Research Institute), Prof. and Mrs. S . W. Churchill (University of Michigan), Prof. and Mrs. F. T. Gucker (Indiana University), Prof, Charles L. Hosler (Pennsylvania State University), Dr. Claude Kaziz (Pechiney- Centre de Recherches), Prof. and Mrs. Milton Kerker (Clarkson College of Technology), Dr. A. Reuter (Germany), Dr. Bernard R. Stein (European Research Office, Frankfurt/Main), Prof. V. B. Vouk (Yugoslav Acad. Sci. Arts, Zagreb).CONTENTS PAGE INTRODUCTORY NO~E- Aerosol Pollutants of the Atmosphere. By R.Lessing . . 7 Nucleation Processes and Aerosol Formation. Nucleation Processes and Aerosol Formation. By W. J. Dunning . * 9 Nucleation of Water Aerosols. By B. J. Mason . . 20 Ice Crystal Nucleation by Aerosol Particles. By N. H. Fletcher . . 39 Phase Changes in Salt Vapours. By E. R. Buckle . . 46 The Molecular Hydrostatic Analysis of Gibbs’ Theory of Capillarity. By Frank P. Buff . . 52 GENERAL DIscvssIoN.-Dr. B. J. Mason, Dr. W. J. Dunning, Dr. E. R. Buckle, Dr. N. H. Fletcher, Dr. H. Wilman, Mr. W. R. Lane 59 I. NUCLEATION : ]HOMOGENEOUS AND HETEROGENEOUS- 11. GROWTH OF PARTICLES- Droplet Interaction in Aqueous-Disperse Aerosols. By D. P. Benton and G. A. H. Elton . . 68 Experimental Results Relating to the Coalescence of Water Drops with Water Surfaces. By R.M. Schotland . . 72 The Growth of Hygroscopic Drops in a Humid Air Stream. By W. L. Dennis . . 78 The Stabilization of Water Mists by Insoluble Monolayers. By H. S. Eisner, 33. W. Quince and C. Slack . . 86 The Influence of a Foreign Film on Evaporation of Liquid Drops. By €3. V. Derjaguin, S. P. Bakanov and I. S. Kurghin . . 96 On the Discontinuity Involved in Diffusion Across an Interface (the A of Fuchs). By P. G. Wright . . 100 Crystal Structure and Growth of Metallic or Metallic-Oxide Smoke Particles produced by Electric Arcs. By J. Harvey, H. I. Matthews and P-I. Wilman . . 113 Investigation of Long-Range Diffusion Forces between Water Droplets and Non-Volatile Particles. By P. S. Prokhorov and L. F. Leonov 124 The Motion of a Small Particle in a Non-Uniform Gas Mixture.By S . P. Bakanov and €3. V. Derjaguin . . 130 GENERAL DIscussIoN.-Dr. R. G Picknett, Prof. N. Fuchs, Dr. B. J. Mason, Dr. G. A. H. Elton, Dr. G. S. Hartley, Prof. R. M. Schot- land, Dr. D. J. Ryley, Dr. W. Smith, Dr. R. H. Essenhigh, Dr. W. L. Dennis, Dr. C. N. Davies, Dr. E. R. Buckle, Mr. H. S. Eisner, Dr. P. G. Wright, Prof. P. S. Prokhsrov and Dr. E. F. Eeonov, Dr. R. D. Cadle . . 139 111. PHYSICAL AND CHEMICAL PROPERTIES- Kinetics of Atmospheric Chemical Reactions involving Aerosols. By Behaviour of Iodine Vapour in Air. By A. C. Chamberlain, A. E. J. 5 R. D. Cadle and R. C. Robbins. . . 155 Eggleton, W. J. Megaw and J. B. Morris . . 1626 CONTENTS Dispersed Carbon Formation in Acetylene Self-Combustion. By P. A. Light Scattering of Coated Aerosols. Tesner . Part 1.-Scattering by the AgCl Cores. By E. Matijevik, M. Kerker and K. F. Schulz . The Angular Variation of Light Scattered by Single Dioctyl Phthalate Aerosol Droplets. By Frank T. Gucker and Robert L. Rowel1 . Light-Scattering by Very Dense Monodispersions of Latex Particles. By S. W. Churchill, G. C. Clark and C. M. Sliepcevich The Aggregation of Small Ice Crystals. By C. L. Hosler and R. E. Hallgren . . Combustion of Liquid and Solid Aerosols. By R. H. Essenhigh and Ian Fells . GENERAL DrscussIoN.-Dr. R. D. Cadle, Dr. P. G. Wright, Prof. Milton Kerker, Dr. W. Smith, Dr. G. A, H. Elton, Prof. Frank T. Gucker, Prof. S. W. Churchill, Dr. B. J. Mason, Prof. C. L, Hosler . Author Index . 170 178 185 192 200 208 222 229

ISSN:0366-9033    

DOI:10.1039/DF9603000001

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

Introductory Note BY R. LESSING In the Faraday Society’s General Discussion on ‘‘ Disperse Systems in Gases : Dust, Smoke and Fog ” at Eeeds in 1936, the opening sentence of my introductory paper on the industrial aspects read : “ Disperse systems in gases in their relation to the problems of industry and the amenities of life have not yet received the close study which their ubiquity and practical importance demand.” Whilst much research has been done since then, largely stimulated by the fog disasters in the Meusc Valley in 1930, at Donora, Pennsylvania, in 1948, by the great London fog in December, 1952, and the continuing smog nuisance of Los Angeles, many problems of air pollution still remain unsolved. As far as fog formation and the dispersion of air masses containing natural nuclei such as salt spray from the oceans or dust from volcanic eruptions, or man- made pollutants from the combustion of fuels are concerned, much closer co- operation between meteorologist and physical chemist is needed in the future.In this brief note I will only refer to what I consider the most pressing among the many complex problems of air pollution still awaiting intensive study by the physical chemist, that of sulphur. Great Britain discharges into the atmosphcre a sulphuric acid equivalent of about 12 million tons a year derived from the combustion of coal and oil and their products, the bulk in form of sulphur dioxide with a small proportion about 2-4 % of sulphur trioxide formed-by a still unexplained mechanism-in high- temperature firing.Relatively small quantities of hydrogen sulphide are emitted in the inefficient burning of coal in domestic grates and old boiler plants. In addition an unknown quantity of sulphur compounds, perhaps hydrogen sulphide, arises from decaying vegetation. Some of the sulphur dioxide is blown out to sea and, incidentally, is identifiable in the western part of Scandinavia, but the majority reaches the ground, being deposited in combination with particulate matter or being washed out by rain. Ths vast quantity of acidic material is the main contributor to the damage caused by air pollution assessed by the Beaver Committee 1 at &250 million a year-probably an under-estimate. Whilst the final effects of the reactions of suiphur dioxide with metals, stones, textiles, vegetation and the human and animal body are well known, it is by no means clear whether they or some of them are caused by direct reaction or through the medium of sulphuric acid.Eventually the end products of the attack by atmospheric sulphur oxides are sulphates, but the mechanisms of the oxidation of sulphur dioxide or its salts still require elucidation. Practical experience shows that the interaction of sulphur oxides with dusts and liquid aerosols begins in the air. I venture to present a picture of the com- plex phenomena involved suggesting pointers for future individual researches rather than to record achievements attained. Much, if not most, of the dust in the air over Britain is part o€ the ash emitted from coal-fired furnaces. The particles vary widely in chemical composition.:! They may be oxides or carbonates of bases, silicates, occasionally fused to spheres, free silica, or carbonaceous matter ranging from tarry or oily soot to coke.They 78 AEROSOL POLLUTANTS OF THE ATMOSPHERE vary in shape, structure, surface, porosity and size distribution. They will there- fore differ in their capacity of adsorbing and concentrating sulphur dioxide molec- ules. When the particle is in collision with pre-existing SO3 or H2SO4, the acid film formed tends to collect more S02. On deposition, such acid-coated particles have bcen found to initiate severe corrosion of metals. Whether the oxidation of sulphur dioxide, with or without the intervention of pre-formcd sulphuric acid, is promoted by catalysis and to what extent, will require the examination of different types of dust particles.These might be separated from the mixed ash dust from pulverized coal.2 The acid boundary layer adsorbed on particulates is affected in its reactivity, hygroscopicity and resistance to diffusion by the presence in the air of minor quantities of ammonia liberated in the carbonization stage of the inefficient burning of coal or derived from animal and vegetable sources. The behaviour of sulphur oxides in combination with organic aerosols calls for special and urgent study in view of the increasing rate of pollution by the exhaust from motor vehicles and the emission from oil-fired furnaces. Although the sulphur content of petrol and diesel oil is relatively low, the discharged mixture of hydrocarbons and aldehydes in the former and of oily soot in the latter also contains oxides of sulphur and nitrogen which affect the stability of the aerosols formed.To what extent they are affected by collision with SO;! and SO3 after discharge is an open question. The formation of acid " smuts " when burning fuel oil still remains unexplained. Their corrosive and soiling effect is particularly harmful as shown by deposits on motor cars standing in the lee of oil-fired installations. The reactions involved in the oxidation of sulphur dioxide and leading to its final and stable form of sulphuric acid and sulphates may be pronioted by catalysis as suggested. At the same time the photo-chemical effects of sunlight must also be considered. The indication that olefines under the influence of irradiation are more liable to aerosol formation 3 than other hydrocarbons suggests that sulphur dioxide adsorbed by solids may exhibit similar differences. I submit this note, being convinced that the problem of the pollution of the air with its dire consequences can only find a practical solution when the physical chemist can satisfactorily explain the fundamental reactions involved and give a lead to the chemical engineer to devise appropriate remedial measures. 1 Report of Committee on Air Pollution (H. M. Stationery Office), Cmd. 0 322, 1954. 2 Lessing, 2nd World Power Con$ Trans., 1930, 4, 174 ; Fuel in Science and Practice, 3 Renzetti and Doyle, Int. J. Air Pollution, 1960, 2, 327. Prager, Stephens and Scott 1930, 9, 348. Ind. Eng. Chem. 1960, 52, 521.

ISSN:0366-9033    

DOI:10.1039/DF9603000007

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

I. NUCLEATION ; HOMOGENEOUS AND HETEROGENEOUS NUCLEATION PROCESSES AND AEROSOL FORMATION BY W. J. DUNNING Dept. of Chemistry, University of Bristol Received 22nd July, 1960 The Volmer-Weber-Becker-Doring theory of homogeneous and heterogeneous nuclea- tion of liquid and solid particles from a supersaturated vapour phase is summarized briefly. The predictions of the theory are compared with the experimental results obtained by various authors using the cloud chamber method, the method of isentropic expansion through nozzles and the method in which a jet of vapour on issuing into a cool atmosphere becomes supersaturated. It is concluded that the theory is in fair agreement with the experiments and that supercooling by isentropic expansion through nozzles offers the most complete test of the theory.This method appears to have potentialities which would permit detailed analysis of nucleation and growth processes at high supersaturation. Aerosols may be formed by condensation from material molecularly dispersed in the gaseous form. The particle size distribution of the aerosol will depend upon the rate of formation of nuclei, the rate of growth of those nuclei and of the resulting particles and the rate of coagulation of the particles. This paper will discuss mainly nucleation from a supersaturated gaseous phase. In the absence of nucleation catalysts, a vapour can be compressed beyond its saturation pressure to a supersaturated metastable state from which the separation of the stable phase requires a finite time. Aggregates (or embryos) containing various numbers of molecules are formed within the supersaturated vapour as a result of statistical fluctuations, the process of aggregation taking place by the progressive accretion of single vapour molecules A, thus, A+A+A, A, +A+A, .. . . . . . . Ai-1 +A+Ai. For a liquid as the stable phase, these embryos may be considered as minute droplets and their vapour pressures will depend upon their sizes in accordance with the Gibbs-Thomson equation, where pi is the vapour pressure of a droplet of radius ri containing i molecules, plco is the saturation vapour pressure, 0 the surface tension and 011 the volume of a molecule in the liquid. The smaller the embryo the greater is its tendency to redisperse. However, there will be a certain sized embryo (i = k ) the vapour pressure of which is just equal to the vapour pressure of the supersaturated vapour.Embryos smaller than this critical size tend to redisperse, those larger tend to grow. Once embryos reach this critical size they grow reZativeZy unimpeded into macroscopic droplets. This critical size is the bottleneck of the process and 910 NUCLEATION PROCESSES corresponds to the activated state in ordinary chemical kinetics. The rate of nucleation is the rate of passage through this bottle-neck. Calculation of the rate of nucleation J is complicated; the method of Zeldovich 5 as given by Frenkel6 leads to the expression where nz is the mass of a molecule and AGk is the free energy of formation of a critical nucleus of k molecules : The form of eqn. (2) was first given by Volmer and Weber,l and later by Farkas,2 and by Kaischew and Stranski; 3 the calculation has been improved by Becker and Doring,4 Zeldovich 5 and by Kuhrt.7 The rate of nucleation J is positive for all values of the supersaturation ratio p1/p1 greater than unity but is negligibly small until the supersaturation ratio reaches some critical value (pl/pl a)crit above which the rate increases extremely rapidly.EXPERIMENTAL INVESTIGATIONS WITH TIPE CLOUD CHAMBER Wilson 8 produced condensation by expanding adiabatically a volume of gas (assumed to be inert) saturated with condensable water vapour, cooling the vapour below its saturation temperature. Preliminary expansions caused condensation to take place on '' dust " particles which could then be removed by allowing the condensate to settle.If this cleaned system were subjected to expansions of gradually increasing magnitude it was found that no condensation in the vapour phase resulted so long as the supersaturation ratio S(= p1/pI a) was less than about 4. Between supersaturation ratio of 4 and 8 a relatively small number of heavy drops formed as a result of condensation on ions. At and beyond the super- saturation ratio of 7.9 the water vapour condensed as a persistent cloud or fog of small water droplets. The number of drops increases rapidly with increasing supersaturation ratio, the drops becoming progressively smaller since the amount of water condensing at each expansion is almost constant. As the drops become smaller, diffraction colours begin to border the image of a source of light viewed through the cloud and when the size of the drops becomes comparable with the wavelength of light, the diffraction system expands.The initiation of the condensation at a supersaturation ratio of 7.9 was inter- preted by Wilson as due to homogeneous nucleation. From his experimental results, it is found that, for a supersaturation ratio S = 7.9 at a temperature of T = 253°K and a pressure p1 = 8.1 mm, a critical nucleus has a radius rk of 6 . 4 5 ~ 10-8 cm, and contains 48 molecules of water; the rate of nucleation according to (2) is about lOS/crn3 sec. A thorough test of the equation for the rate of nucleation would require experimental evaluation of the dependence of the droplet size and droplet con- centration on the time, the supersaturation ratio and the temperature.The droplets seen as fog are, of course, much larger than the original nuclei and have presumably developed in size by further condensation of vapour and possibly by coagulation. The equation for the nucleation rate can be tested (to someW. J . DUNNING 11 extent) by assuming after Volmer and Flood 9 that at the critical expansion for the onset of homogeneous nucleation, the rate of nucleation J reaches a certain critical value Jcrit, then The first term on the right-hand side depends but weakly on the supersaturation ratio, hence (T/0)3/2 log &it should be essentially constant. Farley 10 has cal- culated (af/a)3/2 log Sc,t from Powell's 11 data, which gives as a function of the final temperature 2') after expansion ; he found that for 7 ) ranging from 247" to 320"K, this quantity was reasonably constant, decreasing a little with increasing Tj.However, Sander and Damkijhler 12 found that log & . i t varied linearly with T-1; this behaviour they ascribe to the variation of 0, the surface tension, with temperature. Another way of testing the nucleation rate constant is to insert a likely value for Jcrit ; Volmer and Flood 9 assumed Jcrit-l/cm3 sec, and find the value of S,,i, for comparison with the experimental value. Volmer and Flood found for water vapour that, when the final temperature a f was 244.3", the cal- culated was 4-16 in cornparison with an experimental value of 4-21. Here it will be noticed that the critical supersaturations obtained by Voher and Flood are close to 4, at which Wilson considered condensation to take place on ions.In fig. 1, the results of Powell, of Wilson, and of Volmer and Flood, are shown; the results of Sander and Damkohler are similar to those of Volmer and 'Flood. In discussing Wilson's results, Volmer suggested that the rate of growth of the droplets is not as small as Wilson assumed and that the heat liberated by the con- 10 2 0 2 2 2.6 2.8 T+X 104 FIG. 1 .-Log S&t against T-3/2 for water vapour. 0 Powell, x Volmer and Flood, @ Wilson, + Amelin densation would render difficult the evaluation of the true supersaturation. How- ever, more recent work by Clarke and Rodebush 13 and by Pound 14 are reported to vindicate Wilson's interpretation. Volmer and Flood also studied the con- densation of a number of organic compounds and found satisfactory agreement with the theory in all cases except methyl alcohol.EXPERIMENTAL INVESTIGATIONS WITH EXPANSION NOZZLES An alternative experimental procedure which offers some advantages over the cloud chamber method is the expansion of a vapour flowing through a nozzle. In this the history of the condensation process is spread out spatially instead of12 NUCLEATION PROCESSES events following one another in a rapid time sequence. The conditions prevailing along the nozzle and across the condensation zone can be explored in detail. This additional information, though it requires lengthy mathematical computation, does provide a greater insight into the processes taking place than does a cloud chamber experiment.If an unsaturated vapour flows through a suitably designed nozzle, e.g. a Lava1 nozzle (fig. 2), it undergoes an isentropic expansion, decreasing in static pressure and static temperature ; '' static " pressures and temperatures are those which P 1 I I 0 008 0 I I 1 0 2 4 cm FIG. 2.-Static pressure (mm Hg) against distance along nozzle. 0, @ experimental results of Yellott, would be measured by instruments moving with the stream at the velocity of the stream. The relation between the isentropic change in the pressure of a vapour with temperature and the change in the saturation vapour pressure p a with tem- perature is given by - theoretical calculations of Oswatitsch. AH (7) For many substances of low molecular weight, the right-hand side is greater than unity and the static pressure of the vapour decreases less rapidly with decreasing temperature than does the saturation pressure ; if the temperature drop is sufficient, the expanded vapour will become saturated or supersaturated and condensation may occur.von Helmholtz 15 in 1887 noted that steam, when expanded through a nozzle, became supersaturated before condensing and the phenomenon was investigated further by Stodola,l6 Yellott 17 and Binnie and Woods.18 A similar phenomenon was found when humid air is expanded in supersonic wind tunnels and in 1942 Wagner 19 showed that dry air, at room temperature and atmospheric pressure, after expansion in a hypersonic wind tunnel would reach a supersaturated state for the nitrogen and oxygen when the Mach number approached five.The aeronautical literature is summarized by Stever 20 and by Wegener and Mack.21W. J . DUNNING 1 3 The experimental procedure is to measure the static pressure at stations in the wall of the nozzle or by a search tube traversing the axis of the nozzle; the con- densation may also be revealed by light scattering, schlieren or other optical effects. It is found (see fig. 2) that the static pressure, plotted against the distance along the nozzle, follows fairly closely the line for isentropic expansion until it reaches a narrow region in which the supersaturation collapses. From this region down- stream a blue mist is visible 17 and Keenan 22 explained the pressure disturbance as being due to the heat of condensation. Oswatitsch 23 applied nucleation theory to this problem of condensation in supersonic nozzles, incorporating the kinetics of nucleation and droplet growth with the thermodynamics of flow.In addition to the three conservation equations of mass, momentum and energy, the equation of state requires a knowledge of the amount of condensation which has occurred at each point along the nozzle. The amount of condensate G(x) at a point x results from all the nuclei born up- stream from this point and the amount of growth each has sustained in travelling to the position x from its birthplace. If we designate the birthplace XI, the number of nuclei born per unit of time in the region x' to xf + dx' is J(x') f (x')dx', wheref(x') is the nozzle area at XI. Such nuclei when they reach position x have acquired the mass M(x', x), hence the total mass of condensate at x is r x G(x) = J M(x', x)J(x') f (x')dx! -03 The rate of growth of a droplet of radius r was calculated with the result (9) where TT is the temperature of the droplet, T that of the vapour, p the density of the wet vapour and u the translation velocity. Since the pressure follows the isentropic line fairly closely until the condensation process sets in, Qswatitsch chooses a point x1 just upstream from the beginning of the condensation region and calculates the state, the velocity, the supercooling, etc., of the vapour at that point.With this information he calculates the rate-of nucleation at x1 using the Becker-Doring equation, then the amount of condensed vapour at XI. This is used to compute the parameters of state at XI+ dxl, amount of growth of old nuclei and rate of nucleation of new nuclei, etc., and so he solved the problem stepwise.In fig. 2 the computations of Qswatitsch for the pressure distribution along the nozzle are shown in comparison with two series of experimental points by Yellott and it is seen that there is agreement within the accuracy of the experiments; the experimental points towards the right-hand side of fig. 2 results from shock following recompression and need not be considered here. In fig. 3 are shown for these two experiments, the calculated rate of nucleation, the total number of droplets and the amount of condensation as functions of x, the position along the line of flow. From this it is seen that nucleation is confined to a small segment of the nozzle in which the supersaturation collapses.Downstream from this segment the number of droplets remains constant though they undergo further growth under conditions close to saturation. Oswatitsch calculated a droplet size of about r = 0.5 x 10-6 cm as the mean of a wide range. Yellott had estimated, from the visibility of the mist by scattered light, that the size was much less than the wavelength of blue light (-40 x 10-6 cm) whilst Durbin,l9 using light-scattering techniques, found a size of 5 x 10-6 cm in similar experiments involving super- cooled hypersonic flow. In fig. 4 the calculations of Qswatitsch for the experiments of Binnie and Woods are shown in comparison with the experimental points. The black points are those for an experiment in which conditions were chosen so that no condensationc_<-..--------- ----.cm FIG. 3.-DetaiIed calculations of Oswatitsch. - rate of nucleation, --- total number of droplets, -.--.-- amount of condensate. All against distance along nozzle. PIP0 0.6 0 5 04 0 3 I I 1 - - - - - “O t 0 0 + 9 h =- .- . ’8.. t I I I 2 4 6 8 10 12 14 cm FIG. 4.-Ratio of static pressure p to stagnation pressure PO. 0, 0 experimental results of Binnie and Woods, - theoretical calculations of Oswatitsch. and an intricate theory, in which the kinetic problems of nucleation and growth have been integrated with those of ffuid mechanics, is very satisfactory. Owing to the lengthy computations involved and some difliculties in achieving precision experimentally, it is not easy to judge how delicate a test of the details of nucleation theory this method is.It does seem to offer greater potentialities than the cloud chamber method .15 In the expansion of purified nitrogen, Willmarth and Nagamatsu 25 observed supercoolings of about 15°K. The results have not been treated with the detail of Oswatitsch’s method though the critical supersaturation p / p a at which the static W. J . DUNNING FIG. 5.-Critical supersaturation for condensation of nitrogen as a function of the percentage by weight of carbon dioxide. 8 critical supersaturation given by Volmer theory with In J = 7. pressure first noticeably deviates from the isentropic curve was determined. This supersaturation is much higher than that which would correspond to J = 107 in eqn.(2) (see fig. 5) ; there are some indications in the results that the nucleation may be of solid nitrogen. NUCLEATION OF CRYSTALS FROM THE VAPOUR The theory of the rate of nucleation of crystals 49 26327 from the vapour rests on concepts closely similar to those for the nucleation of droplets. The resulting equation is similar to eqn. (2), though the pre-exponential factor now involves the rate of growth of a crystalline nucleus. From their results using the cloud chamber method, Sander and Damkobler 12 considered that there was some evidence of crystalline ice nucleating below -662°C. Oswatitsch23 expanded humid air through a nozzle and, in order to reconcile the results with his theory, had to assume that ice crystals nucleated. Wegener 28 also found that in the expansion of humid air through a nozzle there was evidence for the nucleation of crystalline ice.TIME LAG IN NUCLEATION In the derivation of the rate of nucleation it was assumed that there is a steady- state distribution of embryos, but under conditions of rapidly increasing super- saturation there will be a time lag during which the initial distribution of embryos adjusts itself to the distribution characteristic of the new conditions.29 The rate of nucleation J(t) depends upon the time which has elapsed and an approximate calculation 303 31 gives J(t) = J exp [ - (k2/gt)] (11)16 NUCLEATION PROCESSES where g is the rate of growth of the nucleus and k is again the number of molecules in the critical nucleus. Kantrowitz 30 and Probstein 31 related this theory to the transit time before condensation for a supercooling vapour expanding through a nozzle.However, calculations by Wakeshima 32 suggest that the major part of the delay in the appearance of condensation can be explained by the Becker- Doring theory without appealing to the theory of time-lag. FOREIGN NUCLEATION Wilson 8 observed that condensation in the cloud chamber took place on dust particles at low supersaturations. In his investigations on the expansion of steam through nozzles, Stodola 16 found that, when the expansion rate was slow (-0.05 sec duration), the condensation took place on the dust particles present in the steam, but when the expansion was rapid (-10-4 sec duration), the transport of vapour to the relatively few and widely separated dust particles was too slow to establish equilibrium and supersaturation appeared.In the expansion of air through nozzles, the degree of supersaturation achieved is usually small and shows wide deviations in the experiments of different investigators. It is considered by Stever 20 and by Wegener and Mack 21 that here the role of impurities is dominant, the degree of supersaturation attained depending in particular on the presence of vapours such as water and carbon dioxide which are more readily condensable than oxygen and nitrogen. This is borne out by the experiments of Willmarth and Nagamatsu 25 who determined the effect of traces of C02 added to purified nitrogen and found that the supersaturation achieved before the nitrogen con- densed was markedly reduced as shown in fig.5 ; further work by these authors showed that larger amounts of C02 eliminate completely the nitrogen supersatur- ation. The carbon dioxide condenses upstream and particles which presumably act as centres of condensation are produced in numbers large enough that, despite the rapidity of the expansion, the supersaturation collapses. For the iiucleation of liquids on a surface, Volmer26 has shown that AGlCs, the free energy of formation of such a nucleus, is a fractionf(0) of the free energy AGk of the spherical nucleus in equilibrium with the same parent phase, i.e., with where 0 is the angle of contact. The smaller the value of 8 the smaller the value of Ae;l,,. The rate of nucleation per unit area of surface is given by AGh = f (6)AGk (12) (13) f ( e ) = (I - cos ~ ~ ( 2 - cos ey4, where o k s is the area of the spherical surface of the nucleus, v the frequency of vibration of an adsorbed molecule perpendicular to the surface and A G A ~ is the free energy of adsorption. If there are present no foreign nuclei each of area A, the number which have become condensation centres at time t is The results of Willmarth and Nagamatsu may be examined from this point of view.If we make the assumption that the C02 particles all have approximately the same size, then eqn. (15) leads to an expression between the amount w of C02 added and the critical supersaturation B In fig. 6, log w is plotted against the reciprocal of T3 log2(pl/pl derived from these experiments and it is seen that four points lie close to a straight line.The position of the fifth point suggests that concentrations of C02 up to about 0.007 % produceW. J . DUNNING i;i too few nuclei to catalyze the condensation and that nitrogeri containing less than this amount of C02 nucleates homogeneously. This is in agreement with the results of Stodola in steam condensation. When the foreign particle is below the critical size of the liquid nucleus, it must condense vapour around itself by fluctuations until the composite system reaches the dimensions of a critical nucleus. Reiss 33 has considered this situation and treated the kinetics in some detail. -log w FIG. 6. If the foreign nuclei are crystalline and the nuclei precipitating on them are themselves crystalline then the process of nucleation is one of crystalline over- growth.The efficiency will depend on the structure and properties of the substance catalyzing the nucleation. The more closely its crystal structure resembles that of the crystalline precipitate, the more readily will it be covered with new lattice planes of the precipitate. Turnbull and Vonnegut 34 have adapted the Volmer theory (ref. (26), p. 104) of crystal growth by surface nucleation to obtain for the critical supersaturation ratio S, where OAV is surface free energy of the interface nucleus vapour, h is the height of the island nucleus, 0 the area per molecule and II (the " spreading pressure ") is given by where CTFV and QFA are the surface free energies of the interfaces foreign particle- vapour and foreign particle-nucleus respectively.From this it is seen that the larger 11 is, the smaller the critical supersaturation ratio and the more efficient the catalysis. The surface free energy of the foreign particle-nucleus interface will depend on the intermolecular attractive forces between them and the degree of misfit of the lattice planes in contact. The minimum supercoolings of water on silver iodide,34 quartz,35 and other materials 36 have been discussed from this point of view. The efficiency of a foreign particle may depend upon the imper- fection of its surfaces; Schaefer 37 found that imperfect lead iodide crystals are more effective in nucleating ice than apparently more perfect crystals. II = GFV-CJFA-~AV, (18)18 NUCLEATION PROCESSES SUPERCOOLING PRODUCED BY MIXING THE VAPOUR WITH A COOL GAS Amelin 38 studied the cloud formed when a jet of water vapour issued into a cold atmosphere. By varying the temperature of this atmosphere until the cloud appeared or disappeared, he was able to obtain the critical supersaturation and the corresponding temperature; this point is shown in fig.7 and appears to be in agreement with the other measurements shown there. In later work, Amelin and Belyakov 39 studied the particle sizes of glycerol fogs produced by forcing air at 311°C and saturated with glycerol vapour through a nozzle into a cool atmos- phere. Amelin’s analysis of the state of the turbulent jet has been extended and improved by Higuchi and O’Konski.40 Using the Becker-Doring theory they developed an expression for the nucleation rate as a function of the co-ordinates of the jet and hence were able to calculate the total nucleation rate in the jet.A comparison of the theoretical rate with the rate measured by counting the particles enabled the exponential and pre-exponential factors (cf. eqn. (2)) to be determined. Good agreement with the Becker-Doring theory was obtained for dibutyl phthalate nucleation. The experimental results for octadecane were less precise but still satisfactory ; the nucleation rates for triethylene glycol were anomalous and the authors suggest that the hydrogen bonding may be influential here. CONCLUSION The theory of nucleation due mainly to Volmer and Weber and Becker and Doring seems to be in fair agreement with the results of experiments, especially those concerned with the nucleation of liquids, since experimental information where crystals are nucleated from the vapour is rather meagre.Most of the comparisons between the theory and experiment test the form of the theoretical expression and not the absolute rate of nucleation which it predicts. Here the central problem in the theory is to evaluate the standard free energy of formation of an i-embryo from the vapour; in the theory this is approximated by the free energy ikTlog(pl/pco)+aOi, of forming a droplet from the vapour (0’ is the surface area of the droplet). A further approximation is made in assuming that CT is the macroscopic surface free energy. Kirkwood and Buff 41 have considered the question of the dependence of CT on the size of the droplet. Such considerations are important if the theory is to be used for predicting absolute rates since Q occurs as its cube in the exponential term. 1 Volmer and Weber, 2.physik. Chem., 1925,119,277. 2 Farkas, 2. physik. Chem., 1927,125,236. 3 Maischew and Stranski, 2. physik. Chem. B, 1934, 26, 317. 4 Becker and Doring, Ann. Physik, 1935, 24, 732. 5 Zeldovich, J . Expt. Theor. Physics (Moscow), 1942, 12, 525. 6 Frenkel, Kinetic Theory of Liquids (Oxford, 1946), p. 381. 7 Kuhrt, 2. Physik, 1952, 131, 185. 8 Wilson, Phil. Trans. A, 1897, 189,265 ; 1900, 183, 289. 9 Volmer and Flood, 2. physik. Chem. A, 1934, 170,273. 10 Farley, Proc. Roy. Soc. A , 1952, 212, 530. 11 Powell, Proc. Roy. SOC. A, 1928, 119, 553. 12 Sander and Damkohler, Naturwiss., 1943, 39/40, 460. 13 Clarke and Rodebush, quoted in Solid State Physics (ed.Turnbull et al., Academic Press, New York, 1956), vol. 111, p. 264. 14 Pound, quoted in Solid State Physics ; see ref. (13). 15 von Helmholtz, Ann. Physik, 1887, 32, 1. 16 Stodola, Steam and Gas Turbines (McGraw Hill, New York, 1927). 17 Yellott, Engineering, 1934, 137, 303, 333. Yellott and Holland, Engineering, 1937, 18 Einnie and Woods, Proc. Inst. Mech. Eng., 1938, 138, 229. 143, 647.W. J . DUNNING 19 19 Wagner, WVA Archiv. No. A3 Kochel (Darmstadt, 1942, mentioned in Stever (ref. (20)). 20 Stever, Fundamentals of Gas Dynamics (ed. Emmons, Oxford Univ. Press, 1958), p. 526. 21 Wegener and Mack, Advances in Applied Mechanics (ed. Dry den and Karman, Academic Press, New York, 1958), p. 307. 22 Keenan, discussion following ref. (17), 1934. Thermodynamics (Wiley, New York, 1941), p. 442. 23 Oswatitsch, 2. angew. Math. Mechanik, 1942, 22, 1. 24 Durbin, NACA Tech. note 2441, 1951, mentioned in Stever, ref. (20). 25 Willmarth and Nagamatsu, J. Appl. Physics, 1952, 23, 1089. 26 Volrner, Kinetik der Phasenbildung (Steinkopff, Dresden and Leipzig, 1939). 27 Dunning, Chemistry ofthe Solid State (ed. Garner, Butterworths, 1955), p. 159. 28 Wegener, J. Appl. Physics, 1954, 25, 1485. 29 Frenkel, J. Chem. Physics, 1939, 7, 200, 538. 30 Kantrowitz, J. Chem. Physics, 1951, 19, 1097. 31 Probstein, J. Chem. Physics, 1951, 19, 619. 32 Wakeshima, J. Physic. Soc., Japan, 1955, 10, 141. 33 Reiss, J. Chem. Physics, 1950, 18, 529. 34 Turnbull and Vonnegut, Ind. Eng. Chem., 1952,44, 1292. 35 Turnbull, Proc. Woods Hole Conf. Cloud Physics (American Geophysical Union, 36 MOSSO~, €‘roc. Physic. Soc. B, 1956, 69, 165. 37 Schaefer, J. Meteorology, 1954, PI, 417. 38 Amelin, Koll. Zhu~., 1948, 18, 169. 39 Amelin and Belyakov, Koll. Zhur., 1955, 17, 10. 40 Higuchi and B’Konski, J. Colloid Sci., 1960, 15, 14. 41 Kirkwood and Buff, J. Chem. Physics, 1949,17, 338. Buff and Kirkwood, J. Chem. Washington, 1956). Physics, 1950, 18, 991. Buff, J. Chem. Physics, 1955, 23, 419.

ISSN:0366-9033    

DOI:10.1039/DF9603000009

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

NUCLEATION OF WATER AEROSOLS BY B. J. MASON Imperial College of Science and Technology, London Received 7th July, 1960 This paper reviews recent studies of homogeneous and heterogeneous nucleation of water aerosols involving vapour-to-liquid, supercooled liquid-to-solid and vapour-to-solid transitions with particular reference to recent investigations in the author’s laboratory. THE HOMOGENEOUS CONDENSATION OF WATER DROPLETS FROM THE VAPOUR In a gas entirely free of all foreign particles and ions condensation of water vapour can occur only as the result of chance collisions of molecules. Small molecular aggregates (embryos) are continually formed and disrupted because of microscopic thermal and density fluctuations in the vapour, but only if they surpass a certain critical radius r, given by where M, OLV, PL, are respectively the molecular weight, surface tension, and density of the liquid, R the gas constant, p the pressure of the supersaturated vapour and p a the equilibrium vapour pressure at temperature T over a plane surface of the liquid, can they survive and continue to grow to become nuclei for the development of the liquid phase.The probability of formation of such a nucleus of critical size increases as the saturation ratio, S = p/pco, of the vapour increases according to the formula rc = 2M%v/P,RT In (PIP,)? (1) where 1 is the number of nuclei formed per cm3/sec, a is the accommodation coefficient of the droplet surface, N Avogadro’s number and k Boltzmann’s con- stant. This may be derived from the kinetic treatments of the condensation process given by Becker and Diiring 1 and Zeldovich.2 Fig.1 shows a plot of log I against the saturation ratio S = P/Pm for water vapour with T = 260”K, a = 1, and OLV taking the bulk value of 77.5 erg cm-2. The nucleation rate increases rapidly with increasing values of S and attains a detectable value of 1 cm-3 sec-1 only when S+5. The formulation of the theory is, however, unsatisfactory in that it treats small molecular aggregates of the condensed phase as well-defined spherical “ droplets ” having the thermodynamic and physical properties of the bulk liquid. The macro- scopic concepts of surface tension and bulk free energy become rather vague when the aggregates contain as few as 20 molecules, and are probably meaningless when applied to embryos of sub-critical size which are not in phase equilibrium with the vapour.In particular, the surface tension, to the assumed magnitude of which the calculated value of I is very sensitive, cannot be precisely defined for very small aggregates of molecules. The early stages of embryo formation need to be considered in terms of successive attachments of vapour molecules to a small existing aggregate and the probability of capture assessed in terms of intermolecular force fields, the relative orientations of molecules: etc., rather than in terms of macroscopic concepts. A quantitative theory on these lines seems remote especi- ally for a complex polar molecule like water. 20B . J . MASON 21 Despite these weaknesses, the theory, culminating in eqn. (2), has formed the basis for discussion of the condensation process and its predictions have been tested with a variety of vapours and carrier gases.With water vapour, experiments have been made by several 9 A .b ' ' I 10 ' ' 12 ' I 14 ' ' s = PlPco FIG. 1.-The rate of nucleation 1 as a function of the saturation ratio S calculated from eqn. (2). different workers in which very clean, water-saturated air has been subjected to rapid expansion in a cloud chamber and the minimum supersaturation required to produce a detectable droplet concentration determined. The results are summarized in table 1. In the literature there has been a tendency to underline an apparent good agreement between the experimental results and the predictions of eqn. (2), but these claims merit a more critical examination. TABLE 1 .-EXPERIMENTAL AND OBSERVED RATES OF HOMOGENEOUS NUCLEATION IN WATER VAPOUR author Wilson 3 Powell 4 Voliner and Hood 5 Frey 6 Sander and Damkohler 7 Barnard * 293 257 291 256.6 261 263 261 293.7 261 261 238 S Obs.droplet concn. I obs. 7-90 " cloud limit " 9 106 7-80) probably >lo3 5.03 -1 -1 02 4.36 1 102 6.60 103 106 (cm-3) 5.0 10 105 5-70 10 103 6.40 10 103 theor. > 7.0 5-42 5.90 5.42 6.40 5-68 9-50 It is rather difficult to compare the experiments of Wilson and of Powell with the theory since the rates of droplet formation corresponding to their reported appearance of a " cloud " as distinct from sparse " rain-like " condensation are uncertain. If, however, we assume that the droplet Concentration must have exceeded 103 cm-3 in order to be detected above the background condensation on ions (which were not removed) and, furthermore, that the effective sensitive time of the chamber was about 10-3 sec, we arrive at a minimum value of I = 106 cm-3 sec-1.Substitution of this value in eqn. (2) gives a lower limit for the theoretical saturation ratio of S = 7.0 to be compared with the measured value of 7.8 or 7.9. Part of this discrepancy may be accounted for by the fact that, with such high concentrations of droplets, the actual saturation ratio achieved in the cloud chamber must have been less than that calculated on the basis of a perfectly adiabatic expansion due to the abstraction of water vapour and release of latent heat by the growing droplets (see Mason 10).22 NUCLEATION OF WATER AEROSOLS Volmer and Flood, who removed foreign particles from the air by repeated expansions and ions by a strong electric field, determined a critical expansion ratio which just produced a noticeable increase in the number of droplets above the background. They estimated the minimum observable increase in droplet density to correspond to I = 1 cm-3 sec-1 for which the corresponding theoretical value of S, at a final temperature of 261"K, was 4.96 according to Volmer and Flood and 5-05 according to eqn.(2) ; these are to be compared with their measured value of 5-03. Similar good agreement was obtained for a number of other pure vapours and consequently this work became accepted as a verification of the theory and as a basis for much subsequent work in the general field of nucleation pheno- mena.However, it is very doubtful whether Volmer and Flood could have detected such a small increase in the number of droplets in a chamber whose sensitive time was only about 10-2 sec. An increase of one droplet/cm3 is just about detectable by careful visual observation ; this would correspond to I = 102 cm-3 sec-1, for which eqn. (2) gives S = 5.42. It is accordingly doubtful whether Volmer and Hood obtained such good agreement between experiment and theory as they believed. Frey 6 attempted to determine the droplet concentration more accurately by photo- graphing the transient cloud. The minimum detectable concentration was 10 droplets/cm3 and the effective sensitive time of the chamber probably not much in excess of 10-4 sec.This minimum concentration of droplets was observed at a final temperature of 261 "K and saturation ratio of 5.0; the corresponding theoretical value of S is 5.90. But Frey's method of cleaning his chamber before each experiment appears inadequate and it seems highly probable that the initial condensation which he observed occurred upon foreign nuclei or upon ions. A similar criticism may be made of Sander and Damkohler.7 In some more recent and very careful experiments by Barnard,s who was well aware of the difficulty of removing all foreign nuclei and of preventing their formation by rubber and mctal surfaces under the influence of ultra-violet light, the concentration of droplets was photographed as the expansion ratio was increased in very small steps.It was found that the increase of droplet concentration with increasing supersaturation was systematically less than that predicted by the theory. Thus if a figure for the sensitive time of the chamber (and hence for the nucleation rate I ) was chosen to make theory and observation agree for an observed droplet concentration of 1 cm-3 and S = 5-20, a droplet concentration of 103 cm-3 occurred at S = 6.60 instead of at the theoretical value of 640. However, the agreement here is quite good and probably part of the discrepancy may be attributed to the actual supersaturation being rather less than the nominal adiabatic value. The most recent work is that by Pound et aZ.9 who used purified and filtered nitrogen as a carrier gas and an electric field to remove the ions.Working with a minimum detectable droplet concentration of 10 cm-3, these authors obtained good apparent agreement between the experimental and theoretical values of the critical supersaturation when the final temperatures at the end of the expansion were only a few degrees below 0°C (see table 1). However, much larger discrepancies occurred at lower temperatures, droplets now appear- ing at much lower supersaturations than are indicated by the theory. This led Pound et al. to conclude that, unless the surface tension of water decreases rather than increases as the temperature is lowered below about -25°C (measurements show it to increase smoothly down to -23"C), these serious discrepancies at low temperatures suggest that the agreement obtained at higher temperatures may have been fortuitous ; indeed the condensation may not have been homogeneous but have occurred on nuclei produced, perhaps, by chemical reactions between the water vapour, the carrier gas and small irremoveable traces of impurities under the influence of ultra-violet light.In conclusion, it may be said that a critical analysis of the various experimental results, summarized in table 1, indicates that the Becker-Doring theory of homo- geneous condensation has not been satisfactorily verified by experiment. There are certainly unsatisfactory and unconvincing €eatures of the theory, but the dis- crepancies between the theory and the experimental results of different authors are not of a systematic nature which might be reconciled by inserting different values for such parameters as the accommodation coefficient and surface tension in eqn.(2). Much of the trouble probably lies in the experiments where there are great difficulties in excluding entirely small traces of contamination and sources of foreign nuclei, in determining accurately the droplet concentration, and the sensitive time of the chamber and hence the nucleation rate. There remainsa need for an experimentum crucis in which one can be certain of observing homo- geneous nucleation in the absence of foreign particles and in which the dropletB . J . MASON 23 concentration will be sufficiently low to ensure that the peak supersaturation can be accurately computed in terms of the expansion ratio and initial temperature for a truly adiabatic system. The experiment should probably be carried out in all-glass apparatus, with a number of highly-purified carrier gases and over a fairly wide range of temperature. CONDENSATION OF WATER VAPOUR ON FOREIGN NUCLEI (a) CONDENSATION ON IONS Homogeneous condensation of water vapour occurs only if the supersaturation reaches several 180 %; the presence of impurities in the vapour may greatly facilitate condensation.In the atmosphere there is an abundance of particles having a wide variety of size and constitution, their size and number concentration usually being such that even the most rapid cloud formation is associated with very small supersaturations, usually less than 1 %. The first experiments to demonstrate condensation of water vapour on foreign nuclei were carried out by Coulier 11 and by Aitken ;I2 they were also able to remove most of the nuclei from the air by filtration, sedimentation, and repeated cloud formation and show that the resulting clean air could sustain an appreciable supersaturation without droplets appearing in the body of the gas.Later, Wilson 13 discovered that if, after removing the nuclei in this way, the air was expanded by increasing amounts, no droplets appeared until the expansion ratjo reached a value of about 1.25, corresponding to a saturation ratio of about 4. The nuclei responsible for these droplets could not be removed by successive expansions nor by filtration through cotton wool. The fact that condensation occurred at similar supersaturations when the air was irradiated with X-rays suggested that the respon- sible nuclei were small ions.Wilson 3 therefore investigated the relative efficiencies of positive and negative ions as centres of condensation. By ionizing the air in his chamber by a very short exposure to X-rays and by application of electric fields of the appropriate polarity, Wilson was able to ensure an excess of ions of either sign. He then found that expansion from an initial temperature of 293 "I< produced condensation or some negative ions with an expansion ratio of 1.25, for which S = 4, that practically all the negative ions were involved when the ratio exceeded 1 *28 but that to effect condensation on positive ions, the expansion ratio had to exceed 1-31 ( S E ~ ) . Wilson's results have been confirmed by several Iater workers, a representative sample of results being given in table 2.TABLE 2.-sATURATION RATIOS AT WHICH CONDENSATION OCCURS ON SMALL IONS ion sign Tl('K) * TZ Vzl VI S - 293 267-8 1.252 4.2 + 293 1.31 6.0 - 293 1.236 3-7 + 293 1.31 6.0 - 267.6 1.256 4.2 - 267.8 1-253 4.1 - 291 266.5 1.245 3.98 Flood 17 - 265 1.252 4.1 Wilson 3 Przibram 14 Laby 1s Andr6n 16 Powell 4 Loeb, Kip and Einarsson 18 { i 295 1.25 1.31 295 292 1.25 414 1.28 4.87 265 3-9 Scharrer 19 {T 292 Sander and Damkohler 7 - * TI and V1 are respectively the initial temperature and volume of the air, while T,, VL refer to the values at the end of the expansion. The conditions under which condensation occurs upon ions seem to be more sharply defined and more reproducible than is the case for homogeneous nucleation ; the results obtained by different workers are in good agreement.It is interesting to compare these results with the predictions of theory.24 NUCLEATION OF WATER AEROSOLS The condition for equilibrium to exist between a supersaturated vapour and a spherical droplet of radius r, surface tension CLV, carrying a charge q in an external medium of dielectric constant E, is If daLv/dr = 0, S has a maximum value when if the embryo radius exceeds r’, it will continue to grow with a decrease of free energy as long as the supersaturation is maintained and become a droplet. If the embryo carries a single electronic charge (q = 4.8 x 10-10 e.s.u.), and we assume E = 1 for air, T = 265”K, GLV to take the bulk value of 77 erg cm-2, the value of r’ is calculated to be 6 .2 ~ 10-8 cm, the corresponding value of S is 4.59, which may be compared with the experimental value of 4.1 for the critical saturation ratio required to produce visible droplets around negative ions. If one includes the doLv/dr term which, according to Tolman,20 would have a value of about 2 x 108 erg cm-2, the calculated critical value of S would be 3-90. However, this simple treatment ignores polarization of the droplet by the ion. In water, where strongly polar molecules form an oriented surface layer, the surface energy of the droplet will probably be modified to an extent depending not only on the magnitude of the charge as indicated by eqn. (3), but also on its polarity. Therein may lie the explanation of negative ions being able to promote condensation at lower supersaturations than can positive ions.Loeb, Kip and Einarsson,l8 who obtained experimental confirmation of this sign preference, argue that small ions cannot grow into water droplets by successive attachments of water vapour molecules, but rather that an ion is captured by a molecular aggregate or embryo, which is not yet large enough to possess a regular surface layer and a statistically conditioned electrical double layer which are characteristic of a true droplet. The molecules in the surface layer of the embryo are imagined to be oriented with the oxygen atoms directed outwards ; the surface force field will then tend to orient approaching vapour molecules with their protons towards the surface, so favouring H-bond linkages and propagation of the surface structure.The capture of a negative ion by the aggregate will enhance the surface force field and so favour the capture of further molecules in the correct orientation, while molecules striking a positively charged embryo would have to rearrange themselves before becoming bound. Thus, condensation may be expected to occur more readily on negative ions than on positive ions. Again, it appears that eqn. (3), which is derived in terms of macroscopic con- cepts, cannot apply to the pseudo-crystalline embryo droplets just discussed ; indeed, the existence of sign preference, which is not predicted by eqn. (3), is evidence of the breakdown of this equation in the very early stages of the con- densation process. r = r ’ = ~1~14n0,4+ ; (b) CONDENSATION ON HYGROSCOPIC, NON-HYGROSCOPIC AND MIXED NUCLEI In the presence of solid, insoluble, wettable particles, droplet formation will be much facilitated, since these particles are ready-prepared aggregates to serve as nuclei €or condensation at supersaturations which diminish with their increasing size.Eqn. (l), which is plotted in fig. 2, gives the supersaturation necessary for continued condensation to occur on pure water droplets. The degree of super- saturation required is higher the smaller the drop, some typical values being given in table 3(b). Thus a droplet of radius 10-7 cm requires a saturation ratio of 3-23 or a supersaturation of 223 % to persist, while droplets of radius greater than 10-5 cm require supersaturations of less than 1 %. For insoluble, wettable particles of the same size, the supersaturations required will be slightly less, while those required for the activation of hydrophobic particles will be higher.B .J . MASON 25 If, however, the droplet is formed on a wholly or partially soluble nucleus, the equilibrium vapour pressure at its surface is reduced by an amount depending on the nature and concentration of the solute, which means that condensation is able to set in at lower supersaturations than those required for an insoluble nucleus of the same size. This is a fact of considerable importance in cloud and fog form- ation because a high proportion of atmospheric nuclei are composed wholly or partly of soluble matter. look 95 f droplet radius (cm) FIG. 2.-The equilibrium relative humidity (or supersaturation) as a function of droplet radius for solution droplets containing the indicated masses of sodium chloride.The equilibrium vapour pressure p i over a droplet of pure aqueous solution of radius r is given by the equation (see Mason 21), - (PLIPD Pto ~ ( $ n r ~ p t imM - m> 1 ’ (4) where the primed symbols refer to the solution rather than to pure water, m is the mass and W the molecular weight of the dissolved salt, and i is van’t Hoff’s factor which depends upon the nature and concentration of the solute. Eqn. (4) can be used to calculate the relative humidity H which the air must have to remain in equilibrium with nucleus droplets of a given radius containing a specified mass of a particular salt or, conversely, to compute the radius of drops which will be in equilibrium with an atmosphere of a given humidity. We have, then, p:/pco = H/lOO, and if the humidity is nearly 100 %, eqn.(4) may be written more simply and with little loss of accuracy asTABLE 3.-cRmICAL RADJI AND SUPERSATUXATIONS FCR NUCLEI OF VARIOUS SIZES, T = 273'K (a) HYGROSCOPIC NUCLEI OF NaCl - 13 - 12 - 11 - 10 ~ ( p ) at H = 78 % 0.039 0.084 0.185 0.39 0.88 1-85 4.1 - 16 - 15 - 14 Iogm (g) yc&)* 0.20 0.62 2.0 6-2 20 62 200 r(of crystal)&) 0.022 0.048 0.103 0.22 0.48 1 4 3 2.2 Nc-lOO(= supersat. %>.F 042 0.13 4.2 X 1W2 1.3 X 10-2 4.2 x 10-3 2.3 X 10-3 4.2 x 10-4 Y at H = 100 % is approx. rc/d3. * For other nuclear substances of rnolecdar weight W, multiply by (585/ W)*. -f For other nuclear substances of molecular weight W, multiply by (W/SS.S)&.(b) INSOLUBLE WETTABLE NUCLEI log z(m) - 7 - 6 - 5 - 4 - 3 10Q)prlpco 323 112*5 101.2 100.12 100*01 - 9 8.8 620 1.3 x 10-4 4.8 2 C c, r M > C-I 0 0 - 8 18.5 '..I 2,000 4.2 x 10-5 Z 10.3 w e 4 cl M w 3 R id 0 M 0 r MB. J . MASON 27 Graphs showing how the equilibrium radii of drogdets containing specified masses of sodium chloride vary with the relative humidity are shown in fig. 2. Some growth of these hygroscopic nuclei occurs before the air becomes saturated and indeed they become droplets of saturated sodium chloride solution at 78 % relative humidity. The equilibrium radius of the droplet increases with increasing humidity until the air becomes supersaturated by a critical amount corresponding to the maximum of the relevant curve in fig.2. At this stage the solution is quite dilute, and if the droplet exceeds this critical radius given by the supersaturation required to maintain equilibrium thereafter decreases with increasing droplet size. If the supersaturation were maintained, transition from a nucleus droplet (r<rc) to a fully developed cloud droplet of r>rc would now occur very rapidly and, in theory, the droplet would grow without limit. In a cloud we are not concerned with a droplet growing in isolation under a steady supersaturation, but rather with a whole population of droplets competing for the water vapour being released in a cooling air mass. In this case, the supersaturation will not remain steady; when the vapour is being extracted at a faster rate than it is being released, the supersaturation is forced to retreat and so growth of the droplets is restricted.Table 3 shows the critical radii and critical sapersaturations calculated from eqn. (4) for sodium chloride nuclei with masses ranging from 10-16 g to 10-8 g. We notice, for example, that nuclei of 10-15 g achieve radii of 0.62 p at a critical supersaturation of 0.13 % beyond which they may act as centres of continued condensation. The very large salt particles, of mass greater than 10-11 g, will usually not remain in the atmosphere long enough to attain their critical size. So far, we have discussed the behaviour of completely insoluble particles and of hygroscopic, soluble particles as potential condensation nuclei. But atmos- pheric aerosols are often partly soluble, partly insoluble; over the continents there is an abundance of insoluble particles coated with a thin layer of hygroscopic substance.At high humidities, these mixed nuclei react to humidity changes like wholly soluble particles of equivalent size but, at humidities below about 70 % the solution coat shrinks until the particle becomes almost completely solid. (c) THE NUCLEI OF ATMOSPHERIC CONDENSATION Atmospheric aerosols cover a wide range of particle sizes from about lQ-7 cm for the small ions consisting of a few neutral air molecules clustered around a charged molecule, to more than 10 (u (10-7 cm) for the largest salt and dust particles. Their concentrations, expressed as the number of particles per a n 3 of air, also cover an enormous range, and may exceed lO6/cm3 in the highly polluted air of an industrial city.The small, ubiquitous ions play no role in atmospheric con- densation because of the very high supersaturations (e.g. 300 %) required for their activation, while the largest particles remain airborne for only a limited time. The size distribution of aerosols measured over land is, on average, as shown in fig. 3. It is convenient to divide the particles into 3 size groups : (i) nuclei having radii between 5 x 10-7 cm and 2 x 10-5 cm (0.2~) which are called Aitken nuclei in recognition of the fact that particles of this size, but not the small ions, are detected in the Aitlcen " dust " counter ; (ii) Zarge nucZei with radii between 0 . 2 ~ and l p ; and (iii), giant nucZei with radii greater than lp.A comprehensive review of the techniques employed in determining the size, con- centration and identity of the particles and of the results obtained, is given by Mason.21 The lower limit of the size distribution is set by the fact that the smaller nuclei coagulate under the influence of Brownian motion. The upper limit is determined by the balance between the rate of production of large particles at the earth's surface, their upward transport and the rate at which they are removed by sedimentation, by precipitation, etc. The number concentration of Aitken nuclei may vary from only a few per cm3 over the oceans and in the upper air to, perhaps, a million or more per cm3 in industrial cities.28 NUCLEATION OF WATER AEROSOLS Over the continents, the size distribution of large and giant nuclei obeys a law of the form IZ = A/m = B/r3, where n js the concentration of particles of mass greater than m or radius greater than r.Typically, the concentrations of particles o€ radius greater than O.lp, l p and l o p are respectively 103/cm3, 1 /cm3 and l/litre, compared with averagc Aitken-nucleus counts of about 40,00O/cm3. Over the oceans, the abundance of large nuclei, which originate in the foam of breaking waves, increases with increasing wind speed and roughness of the sea surface. In winds just strong enough to produce " white horses 'I, sea-salt particles of m> lO-I4g (about 0 . 2 ~ radius at 78 % humidity)occurinconcentrations of about 10/cm3, the numbers falling as the particle size increases, to reach about l/litre for nuclei larger than 10-9 g.In winds of hurricane force, the numbers of giant nuclei may increase IOO-fold, while over a calm sea they may be only one hundredth of these quoted figures. FIG. 3.-A Aitken nuclei - 2 10' I 0 -5 10 -6 10 + iclei zr itme . radius (cm) generalized representation of the size distribution of natural aerosols polluted air over land. in heavily In the absence of rain, which washes out the larger particles, appreciable concentrations of sea-salt nuclei may be carried some hundreds of miles inland and, conversely, nuclei of land origin are carried out to sea. The fact that the Aitken-nucleus counts over the oceans do not change appreciably with windspeed and the state of the sea surface indicates that they are not mainly of maritime origin but that they have been transported from land sources.Their mean life in the atmosphere is several days. Atmospheric aerosol originates in three ways : (i) by condensation and sublimation of vapours during the formation of smokes and in reactions between trace gases through the action of heat, radiation, or humidity. (ii) the mechanical disruption and dispersal of matter at the earth's surface, either as sea-spray over the oceans, or as salt and mineral dusts over the continents. (iii) by coagulation of nuclei which tends to produce larger particles of mixed constitution. Typical substances formed in large quantities by condensation following combustion include ashes, soot, tar products, oils, as well as sulphuric acid and sulphates in cases where the fuel contains sulphur.A great variety of particles is formed in this way by industrial operations and by domestic fires. The sizes of these particles cover a wide range, but are primarily within that of the Aitken nuclei.B . J . MASON 29 Chemical reactions between the nitrogen, oxygen and water vapour of the air and various trace gases, for example, sulphur dioxide, chlorine, ammonia, ozone and oxides of nitrogen, are also important sources of nuclei ; here solid particles may play an important role by adsorbing the gases and water vapour and thereby concentrating the substance-perhaps in solution. Examples are : the formation of NH4Cl in the presence of HN3 and HCl vapours ; the oxidation of SO2 to SO3 and the conversion of the latter to H2S04 in the presence of water vapour and, more important, the oxidation of SO2 by sunlight in the liquid water of cloud and fog droplets to form HzSO4 ; the reaction of sulphuric acid and ammonia to produce ammonium sulphate ; and the production of the higher oxides of nitrogen by the action of heat, ozone, or ultra-violet radiation.The mechanical disintegration, by wind and water, of rocks and soil produces particles mostly of radius greater than 0.1~. Rather little is known about the role which soil and mineral-dust particles play in atmosphere condensation but Twomey 22 suggests that the rupture of crusts of salt adhering to the surfaces of soil particles is an important continental source of cloud nuclei. Until recently it was generally assumed that wind-borne sea-spray was the main source of sea-salt nuclei.But Woodcock et al.,23 using high-speed photography, have shown that the numerous small air bubbles bursting in the foam of waves each produce a small water jet which shoots into the air and breaks up in 5 or so droplets of diameter about one-tenth that of the air bubble and that this is a much more effective source of nuclei. Furthermore, Mason 24 discovered that, besides the large salt nuclei produced by the breaking jet, about oiie hundred much smaller particles, as small as 10-15 g, are formed by the rupture of the bubble cap and believes that this is the main source of the more numerous, smaller salt nuclei. The most important feature of the coagulation process is probably the capture of small hygroscopic nuclei by larger insoluble particles to form mixed nuclei.It seems likely that, during cloud formation in the atmosphere, all the available large and giant nuclei become centres of condensation together with a proportion of the Aitken nuclei which will vary with the particular circumstances. The more efficient, hygroscopic nuclei may originate from the sea, or result from combustion, or from chemical reactions in the atmosphere. Clouds formed over the middle of large oceans usually have rather low concentrations of droplets whose formation may be accounted for by condensation of the available sea-salt nuclei. Over the continents, the droplet concentrations are generally 10 times larger so the majority of the nuclei must be supplied either by natural and man-made combustion or by particles originating from the land surface.( d ) DROPLET GROWTH BY CONDENSATION We shall discuss the growth of a small isolated single droplet about a hygro- scopic nucleus in a n infinite atmosphere maintained at constant temperature and supersaturation. The rate of mass increase of a droplet of radius r is given by dmldt = 4nrD(p -pr>, (6) where D is the diffusion coefficient of water vapour in a i q p is the vapour density at distances remote from the droplet andp, the corresponding value at the surface of the droplet. Since dm/dt = 4nr2p~dr/dt and p = pM/RT, where p~ is the density of the droplet, p the vapour pressure, M the molecular weight of water, R the gas constant and T the temperature of the air, eqn. (6) may be rewritten as dr DM DM 1 r- = - ( p -pi) = - (Sp - p:>, dt pLRT PLRT (7) where p i is the vapour pressure at the droplet surface, p a the saturation vapour pressure at air temperature T, and S = p/pa the saturation ratio of the environ- ment.The growth rate of the droplet is controlled not only by the rate at which water vapour can diffuse to its surface, but by the rate of condensation? which is limited by the rate at which the liberated heat of condensation can be dissipated. Nearly all this heat is lost from the drbplet surface by conduction through the air according to the equation30 NUCLEATION OF WATER AEROSOLS K being the thermal conductivity of the air, L the latent heat of condensation and T, the surface temperature of the droplet which is higher than that of its surround- ings.We also have eqn. (5) for the equilibrium vapour pressure p: over the surface of a dilute solution droplet and the Clausius-Clapeyron equation for the variation of the saturation vapour pressure with temperature l d p LM pdT ==z* By making only slight approximations, the last four equations may be combined to give dr dt r- = [(S-l)----] 2oLVM 8*6m p,RTr Wr3 which shows how the growth rate of the droplet is determined by the size and nature of the nucleus ; the supersaturation of the air, the rate of diffusion of water vapour to, and the conduction of heat from, the droplet. The times taken from droplets arising on sodium chloride nuclei of various masses to grow to specified radii may be calculated from eqn. (10) ; some specimen results are given in table 4.TABLE 4.-RATE OF GROWTH OF DROPLETS BY CONDENSATION ON SALT NUCLEI temp. T = 273'K pressure = 900 mbar nucleus mass 10-14 g 10-13 g 10-12 g supersaturation = lOO(S- 1) % 005 ' 0.05 0.05 radius (p) 1 2 5 10 20 30 40 time (sec) to grow from initial radius of 0 . 7 5 ~ 2.4 0.15 0.01 3 130 7.0 0.61 1,000 320 62 2,700 1,800 870 17,500 16,800 1 4,500 44,500 43,500 41,500 8,500 7,400 5,900 The formation of a cloud involves the growth, in a cooling air mass, of a population of droplets growing on condensation nuclei covering a wide range of sizes. In this case the supersaturation varies with time in a manner determined by the rate at which water vapour is released for condensation by the cooling of the air minus the rate at which it is condensed on to the droplets.The problem is now specified by dBerentia1 equations expressing the rate of cooling of the air, the time variation of the supersaturation and the equations of droplet growth for nuclei of differing sizes. A discussion of this complex problem is given by Mason.21 THE NUCLEATION AND FREEZING OF SUPERCOOLED WATER DROPS Interest in the supercooling and freezing of water, matters which have been extensively studied since the early work of Fahrenheit iu 1724, has greatly increased during the last fifteen years, nlainly because of their essential,importance in the physics of clouds and precipitation. Although large quantities of water such as lakes and ponds do not usually supercool by more than a few hundredths of a degree, the tiny droplets composing atrnos- pheric clouds may exist in the supercooled states down to temperatures as low as -40°C.In cloud physics one is concerned with the temperatures at which airborne drops, varying in diameter from a few microns to about 5 mm for the largest raindrops, will freezeB. J. MASON 31 and how the attainable degree of supercooling may depend upon the drop size, the rate of cooling and the purity of the water, Although there was some indication in the extensive writings of earlier scientists that the attainable degree of supercooling tends to increase when the volume of the water sample is reduced, there was so much variability in the results, with serious discrepancies between those of different workers, that no clear-cut relationships could be deduced. It appears that the earlier work may have failed to provide the required information for three main reasons.First, the water samples used by the different investigators varied greatly in their origin and purity; secondly, they were usually contained in glass tubes or supported as drops on variously-treated metal surfaces so that freezing may often have been initiated by the solid boundaries ; thirdly, in any one investigation, the volume of the sample was not usually varied sufficiently to establish clearly how this might be related to the degree of supercooling, particularly as there was usually a considerable spread in the freezing temperatures recorded for specimens of the same volume. For these reasons, the whole subject has recently been examined afresh. (a) THE F'REEZMG OF WATER CONTAINING FOREIGN NUCLEI-HETEROGENEOUS NUCLEATION The great majority of experiments have been concerned with the study of heterogeneous nucleation in that the water used almost certainly contained foreign particles which initiated crystallization.A considerable improvement in the technique of investigating the supercooling of such water was made in the author's laboratory by Bigg,25 who eliminated the influence of solid supporting surfaces by suspending the water drops at the boundary between two immiscible liquids having different densities, where they were also protected from infection by airborne particles. He also investigated a wide range of drop sizes-varying in diameter from about 20 p to 2 an-and thus volumes which differed by a factor of 109. The use of five pairs of supporting liquids, the members of a pair being practically immiscible with water and with each other, established that the observed freezing temperatures of the drops were a property of the water and not of the surrounding media.Bigg determined the freezing temperatures of large numbers of drops of various sizes, cooled at a constant rate. Fig. 4 shows the distribution of freezing temper- atures of more than 1000 drops each of 1 mm diam. The drops were made from distilled water from which gross impurities had been removed but which still FIG. 4.-The distribution of freezing temperatures of 1127 water drops of 1 mm diam. (after Bigg). contained very small foreign particles. The most frequent freezing temperature was -24°C with half of the drops freezing below this temperature.Thus, if a large volume of water is sub-divided into many smaller samples of equal volume, the freezing temperatures of the latter show a simple probability distribution as illustrated in fig. 4. Because of this statistical character of the nucleation events, it is necessary to determine the freezing points of large numbers of samples in order to obtain characteristic and significant relationships. Such an important relationship is revealed when one plots the median freezing temperature of a large32 NUCLEATION OF WATER AEROSOLS group of drops, i.e. the temperature below which half of the drops freeze, against the logarithm of the drop diameter (or volume). This produces the straight-line relationship shown in fig. 5 which may be represented by the equation log V = A-B(273 - T ) = A - BT,, (11) where V is the drop volume, T the freezing temperature in OK, and A and B are constants for the particular sample of water under test.Bigg's work has recently been checked and extended by Langham and Mason.26 The results obtained with water varying in purity from that of rain water to that produced by multiple distillation showed the same general trends; plots of the median freezing temperatures of groups of drops against the logarithm of their diameters produced straight lines parallel to those of Bigg, but displaced towards lower or higher temperatures depending upon whether the water used was more, or less pure than that investigated by Bigg. Although in these experiments the grosser particles were removed from the water, it still contained large numbers of small particles which can be removed only by taking extreme measures.Eqn. (1 1) therefore represents nucleation by foreign particles-heterogeneous nucleation. This relationship between droplet volume and degree of supercooling may be explained on the assumption that the water was contaminated by particles which were, at one time, airborne, and whose efficiency as freezing nuclei increased exponentially with decreasing temperature in the manner observed for atmospheric aerosols.21 ' The activity of the contained freezing nuclei may thus be represented by n = no exp (aT,), where n is the concentration of nuclei which becomes effective at temperatures be- tween 0°C and - T'"C, and no and a are constants.For drops of volume V being cooled to temperature - TsoC and containing a randomly-distributed population of nuclei, the probability P of a drop containing at least one effective nucleus on reaching the latter temperature is or Now Bigg's empirical relationship shows the value of Ts for which drops of different volumes have a 50 % probability of freezing, i.e. P = 0.5, and for these, eqn. (14) becomes P = l - exp(-Vn), (13) (14) In (1-P) = - Vn = - Vno exp (aT,). Vno exp ( a q ) = const., or In V = In C - a x , which is Bigg's relationship. The value of the constant fixes the shape of the freezing-nucleus distribution, while the value of C depends upon the total con- centration of nuclei, i.e. upon the purity of the water. (b) THE PROPERTIES OF ICE-FORMING NUCLEI In the absence of foreign surfaces, nucleation of the ice phase may occur only by the chance orientation of localized groups of water molecules into an ice-like configuration.A suitable solid particle, however, may cause water molecules to become " locked " into the ice lattice under the influence of its surface force field. Such a molecular aggregate will not only be bound to the surface of the particle, but will have only one exposed surface; on both counts it will be less vulnerable to thermal bombardment than will a spontaneously formed aggregate, and will therefore have a higher probability of attaining the critical size at which it may nucleate the ice phase. The formation of a stable ice nucleus must be largelyB . J. MASON 33 determined by the temperature of the supercooled liquid: and the configuration of the surface force field of the substrate which, in general, will not be uniform, but contain some specially favoured sites for nucleation.The ice nucleating ability of a wide variety of both natural and artificial sub- strates has been tested, usually by dispersing them as fine dusts, smokes or sprays into a cloud of supercooled water droplets, and determining the highest tem- perature at which about 1 in 1.04 of the particles produced an ice crystal. In an attempt to discover the nature and origin of the atmospheric ice nuclei responsible for initiating natural rainfall, Mason and Maybank,27 and Mason 28 tested the nucleating properties of 35 different types of soil and mineral-dust particles.Twenty-one of these, mainly silicate minerals of the clay and mica groups, were found to produce ice crystals in supercooled clouds at temperatures of - 15”C, or above, and of tb.ese, 10 were active above - 10°C (see table 5). The most abundant of these is kaolinite with a threshold temperature of - 9°C ; the kaolin minerals together with the illites and halloysite are considered to be the most important natural sources of efficient ice nuclei. The possibility of inducing rain by the introduction into clouds of artificial nuclei has stimulated many investigations of the ice-nucleating ability of a wide variety of chemical compounds, but there has been little agreement in the results published by different workers. Careful tests in the author’s laboratory indicate that many of the published results are spurious because of the presence, in the air or the chemicals, of small traces of silver or free iodine, leading to the formation of silver iodide which is the most effective of all substances which have been studied so far.If all such trace impurities are removed, many of the substances that have been suggested are found to be quite ineffective. There remain those TABLE 5.-sUBSTANCES ACTIVE AS ICE NUCLEI subs tame coveilite vaterite P-tridymite magnetite ltaolinite anauxite illite metabentonite glacial debris hematite brucite gibbsite dickite halloysite volcanic ash dolomite biotite attapulgite vermiculite phlogophite nontronite natural nuclei crystal symmetry hexagonal hexagonal hexagonal triclinic monoclinic hexagonal hexagonal monoclinic monoclinic hexagonal monoclinic monoclinic monoclinic artificial nuclei crystal threshol d temp.(“C) symmetry temp. (“C) threshold substance - 5 -7 -7 -8 -9 -9 - 10 - 10 -11 -11 - 12 - 12 -13 - 14 - 14 - 14 - 15 -15 -15 silver iodide lead iodide cupric sulphide mercuric iodide silver sulphide silver oxide ammonium fluoride cadmium iodide vanadium pentoxide iodine hexagonal hexagonal hexagonal tetragonal monoclinic cubic hexagonal hexagonal or thorhomb i c orthorhombic -4 -6 -6 -8 -8 -11 -9 - 12 - 14 - 14 listed in table 5 ; the first six, which are only slightly soluble, are active to the extent of about one particle in lo4 producing an ice crystal and the indicated threshold temperature when introduced into a supercooled cloud formed in a cloud chamber.They also cause highly purified bulk water to freeze at these same temperatures. NH4F, CdI2 and 12, being soluble in water, are inactive in a water-saturated atmosphere but produce ice crystals in an environment supersaturated relative to -34 NUCLEATION OF WATER AEROSOLS ice but sub-saturated relative to water, at the temperatures indicated. More de- tailed accounts of these experiments are given by Mason and Hallett,29* 30 Mason and van den Heuvel.31 Although there is a tendency for the more effective nucleators to be hexagondly- symmetrical crystals in which the atomic arrangement is reasonably similar to that of ice, table 5 shows that there are a number of exceptions ; but all substances which are active above - 15°C possess a low-index crystal face in which the degree of misfit between the ice and substrate lattices is less than 15 % (see Bryant, Mason and Hallett 32).However, there is not, in general, a high correlation between the threshold nucleation temperature and the degree of misfit, indicating that nucleating ability is only partly determined by geometrical factors. This is also strongly indicated by observations that epitaxial deposits of ice crystals on large single- crystalline substrates grow preferentially on the growth and cleavage steps, on etch pits, and other imperfections on the surface 32 (see fig. 6(a)). (C) ? h E i HOMOGENEOUS NUCLEATION OF SUPERCOOLED WATER A number of experiments (see Mason21) have confirmed that micron-size water droplets formed by condensation in very clean, particle-free air may be super- cooled to about -4Q"C before freezing occurs. For example, Mossop 33 reported that, in a cloud of droplets of diameter about 1 p produced in an expansion chamber, the number of ice crystals increased rapidly as the temperature fell below -4O"C, and all the droplets were estimated to have frozen after being maintained at - 41.2 f0.4"C for 0.6 sec.As solid particles are excluded from these tiny droplets formed in clean air, nucleation can occur only by small groups of water molecules becoming oriented by chance into an ice-like configuration. Such molecular aggregates will con- tinually arise and disappear as a result o€ thermal agitation but the lower the temperature, the greater will be their size and frequency of formation until, eventu- ally, they attain it critical size above which they survive and continue to grow, forming nuclei for the ice phase.An expression for the rate of formation, fcm-3 sec-1, of such nuclei has been derived by Turnbull and Fisher 34 viz. : nkT I f i ~ exp - [( U -t- Wc)/kT] ,, where n is the number of molecules per cm3 of the liquid, k is Boltzmann's constant, la Planck's constant, U the activation energy for self-diffusion of a molecule in the liquid, and Wc the work of nucleus formation. Now where OSL is the specific surface free energy of the crystalJliquid interface and A is the total surface area of the nucleus. The free energy of formation of an ice embryo containing g molecules is where ps, , u ~ are the Gibbs (or chemical) potentials per molecule in the solid and liquid phases.For (metastable) equilibrium between the embryo and supercooled liquid AG must be a maximum and d AG/dg = 0, when dA dAdV $9 SLdVdg' pL--ptJ = as,-- = B -- where Y is the volume of the nucleus. But d L -(pL-h) = - ( s L - s s ) = - dT T'B . J. MASON 35 where SLY S, are the entropies per molecule and L is the latent heat of fusion. and A4 dA TLdT osL-- - Np,dV where TO is the thermodynamic freezing point (= 273"K), My ps the molecular weight and density of the solid phase and N is Avogadro's number. If the critical nucleus is assumed to be a hexagonal prism with height = short diameter = 2rc, and where L' is now the latent heat per g. Therefore and The probability P that a droplet of volume Y will freeze within a time t is given by or Idt, and dPldt = VI, (26) 1 dPdT I =--- VdT dt' Eqn.(27) may be used to determine 1 at a given temperature from experimental data on the frequency with which a population of droplets each of volume V freezes when cooled at a constant rate. But because the parameter CTSL cannot be calculated with cogfidence, and because a 10 % error would lead to an error of 106 in the calculated value of I, it does not appear profitable to make a close comparison between the nucleation rate calculated from eqn. (25) and that which may be deduced from experimental observations of freezing drops. However, one may use the experimental data of MOSSOP,~~ Carte,35 and of Langham and Mason,26 who studied the freezing af pure water droplets in the diameter range 1-5Qpy to deduce the values of I gt different temperatures in the range - 41°C to - 35"C, substitute these in eqn.(23, and calculate the correspond- ing values of (TSL. Computed in this manner, QSL = 19.0 erg cm-2 at -41"C, 20.0 erg cq-2 at - 38"C, and 20.3 erg cm-2 at - 35°C. Using these and extra- polated values of: OSL, eqn. (25) can be used to predict the temperatures at which water drops will crystallize spontaneously in terms of their volume and the time. The lower curve of fig. 5 indicates the temperatures at wJajch drops of various diameter should freeze when held at these temperatures for a period of 1 sec. This curve,, representing hamogcneous nucleation, differs markedly from that of Bigg's line which represents heterogeneous nucleation.36 NUCLEATION OF WATER AEROSOLS Also in fig.5 are plotted the observations of a number of workers who have been able to supercool small droplets (10-3Op diam.) down to temperatures ap- proaching -4O"C, and also a few exceptional cases, recorded in the literature, of much larger volumes being supercooled to unusually low temperatures. The close grouping of these observations about the theoretical curve strongly suggests that, in most cases, the nucleation of the water samples was homogeneous and that foreign nuclei were not involved. It is not possible to make a more exact com- parison between the experimental data and the theory because the cooling rates employed are not always stated in the original papers, but they are unlikely to have differed by more than tenfold from those used by Bigg, Carte and MOSSOP, in which case, the temperature corrections would always be less than one degree.equivalent drop diameter FIG. S(a).-Bigg's relationship between the median freezing temperatures and the diameters of water drops containing foreign nuclei (heterogeneous nucleation). @).-Median freezing temperatures for groups of droplets of very pure water having diameters <500p and the lowest freezing temperatures recorded for drops of d>500p. These experimental data lie close to the curve calculated from the theory of homogeneous nudeation (eqn. (25)). An earlier analysis of this kind encouraged Langham and Mason 26 to try and produce, in appreciable quantity, water entirely free from foreign particles and to study systematically the homogeneous nucleation of large numbers of drops varying in diameter from about 10 p to 1 mm.Purification of water to this degree proved difficult but, using a multiple distillation technique in which extreme pre- cautions were taken to exclude room air, to remove particles from the inner walls of the Pyrex still, and to prevent ebullition, they produced drops of up to 2 lzlpn diam. which could be regularly supercooled to temperatures very close to limits indicated by the theory of homogeneous nucleation (see fig. 5). Altogether the agreement between the theoretical curve and the experimental data of the several different workers, who together covered a volume range of more than 1012, is rather impressive. There is, therefore, a substantial body of experi- mental evidence to suggest that Bigg's result, expressed by eqn.(11) and the line in fig. 5, represents the relationship between the volume of a water drop and the depth of supercooling for heterogeneous nucleation, and that the curve of fig. 5, which is based on eqn. (25), represents the corresponding relationship for homo- geneous nucleation.FIG. 6(a).-ice crystals growing epitaxially at growth steps on a basal surface of cadmium iodide. FIG. 6(h).-Oriented deposit of ice crystals growing on a surface of freshly-cleaved mica. [To face page 36. B . J . MASON 37 FORMATION OF ICE CRYSTALS DIRECTLY FROM THE VAPOUR There has been considerable controversy as to whether ice crystals may form by direct deposition from the vapour without the intervention of the liquid phase.In heterogeneous nucleation, Mason et aZ.31~32 have shown that, in order to form ice crystals on various crystalline substrates at temperatures only a few degrees below WC, it is necessary to cool the air to the dew point but, at lower temperatures, ice crystals appear when the air is sub-saturated relative to water but supersaturated relative to ice to a degree which is independent of the tem- perature. In this latter regime, no visible deposit of water droplets appeared and since the criterion for ice-crystal formation was the degree of supersaturation rela- tive to ice and not the relative humidity (which sometimes exceeded 95 % without ice crystal formation), it may well be that crystals were formed by a direct vapour- to-solid transition. In precipitating water vapour by rapid expansions in cloud chambers, Sander and Damkohler,7 and also Pound et aZ.9 reported that, until terminal temperatures of - 62°C to - 65°C were reached, the condensation appeared as spherical particles but, at lower temperatures, as a cloud of angular, glittering ice crystals.Sander and Damkohler suggested that either the crystals were formed by direct homo- geneous sublimation of ice from the vapour, or that - 62°C represented the crystal- lization temperature of what, at higher temperatures, had been liquid droplets. Pound et a/. suggested that because homogeneous nucleation of liquid water droplets at -40°C had been well established, the particles appearing between this temperature and - 65°C were frozen droplets which had not yet developed crystal- line faces large enough to cause specular reflection.A similar suggestion was made earlier by Mason 41 to account for the appearance of iridescent mother-of- pearl clouds at temperatures of about -80°C in the stratosphere. Certainly, substitution in eqn. (2) of the parameters which are relevant to a vapour-solid transition suggests that, during the cooling of water vapour, the first condensation product would be liquid droplets rather than ice crystals although, at temperatures below -4O"C, the droplets would freeze within a fraction of a second. At very low temperatures, around - 140"C, the condensate might be in the form of amor- phous, non-crystalline ice as observed by Blackman and Lisgarten.42 Experimentally, Maybank and Mason43 have shown that during the rapid expansion of clean, moist air, ice crystals appeared only when the saturation ratio exceeded 4 and the terminal temperature fell below - 4.O0C, suggesting a two-stage process.At lower temperatures and correspondingly higher supersaturations the numbers of ice crystals increased smoothly and no evidence was obtained for a sudden increase or change of mode of formation at any temperature down to about -100°C. Accordingly, there appears to be no convincing evidence that water molecules condense homogeneously into the ice lattice without first going through the less-ordered liquid structure. 1 Becker and Doring, Ann. Physik, 1935, 24, 719. 2 Zeldovich, J. Expt. Physics (Russ.), 1942, 12, 525. 3 Wilson, Phil. Trans. A , 1899, 193, 265. 4 Powell, Proc. Ray. SOC. A , 1928, 119, 553. 5 Volmer and Flood, 2. physik. Chem. A , 1934,170, 273. 6 Frey, 2. physik. Chem. B, 1941, 49, 83. 7 Sander and Damkohler, Naturwiss., 1943, 31, 460. * Barnard, Ph.D. Thesis (Glasgow Univ., 1954). 9 Pound, Madonna and Sciulli, Airforce Cambridge Research Centre, Geophys. Res. Pap., no. 37, 1955. 10 Mason, Proc. Physic. Sac. B, 1951,64,773. 11 Coulier, J. Pharrn. Chim. Paris, 1875,22, 165. 12 Aitken, COIL Scientijic Papers (ed. Knott) (Camb. Univ. Press, 1923). 13 Wilson, Phil. Trans. A, 1897, 189, 265.35 NUCLEATION OF WATER AEROSOLS 14 Frzibram, Sitz. Akad. Wiss. Wien, 1906, 115, 81. 15 Laby, Phil. Trans. A, 1908, 208, 445. 16 Andrkn, Ann. Physik. (Lpz.), 1917, §2, 1. 17 Flood, see Volmer, Kinetik der Phasenbildung (Steinkopff, Dresden), 1939, p. 132. 18 Eoeb, Kip and Einarsson, J. Chem. Physics, 1938, 6, 264. 19 Scharrer, Ann. Physik, 1939, 35, 619. 20 Tolman, J. Chem. Physics, 1949, 17, 333. 21 Mason, The Phy,sics of Clouds (Clarendon Press, Oxford), 1957. 22 Twomey, Bull. de I’Obs. de Puy de D h e , 1960, p. 1. 23 Woodcock, Kientzler, Arons and Blanchard, Nature, 1953, 172, 1144. 24 Mason, Nature, 1954, 174, 470. 25 Bigg, Proc. Physic. SOC. B, 1953, 66, 688. 26 Langham and Mason, Proc. Roy. SOC. A, 1958,247,493. 27 Mason and Maybank, Quart. J. Roy. Met. Soc., 1958, 84, 235. 28 Mason, Quart. J. Roy. Met. SOC., 1960, in press. 29 Mason and Hallett, Nature, 1956, 177, 681. 30 Mason and Hallett, Nature, 1957, 179, 357. 31 Mason and van den Heuvel, Proc. Physic Soc., 1959,74, 744. 32 Bryant, Hallett and Mason, J. Physic. Chem. Solidr, 1959, 12, 189. 33 MOSSOP, Proc. Physic. SOC. B, 1955, 68, 193. 34 Turnbull and Fisher, J. Chem. Physics, 1949, 17, 71. 35 Carte, Proc. Physic. SOC. B, 1956, 69, 1028. 36 Jacobi, J. Met., 1955, 12, 408. 37 Pound, Madonna and Feake, J. Colloid. Sci., 1953, 8, 187. 38 Meyer and Pfaff, 2. anorg. Chem., 1935, 224, 305. 39 Wylie, Proc. Physic. SOC. B, 1953, 66, 241. 40 Bayardelle, Compt. rend., 1954, 239, 988. 41 Mason, Quart. J. Roy. Met. Soc., 1952, 78, 22. 42 Blackman and Lisgarten, Proc. Roy. SOC. A, 1957, 239, 93. 4 3 h M ~ ~ n and Maybank, Proc. Physic. SOC., 1959,74, 11.

ISSN:0366-9033    

DOI:10.1039/DF9603000020

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

ICE CRYSTAL NUCLEATION BY AERBSQL PARTICLES BY N. H. FLETCHER Dept. of Physics, University of New England, Armidale, N.S.W., Australia Received 24th May, 1960 The action of insoluble particles as ice crystal nuclei is discussed from a molecular viewpoint, and it is concluded that though some important issues are becoming more clearly understood, the theory is not yet sufficiently developed for practical application. A non-molecular approximate theory is then developed which gives adequate treatment of the nucleation activity of aerosols and particularly of the effects of particle-size dis- tribution. The decay of nucleation activity caused by ultra-violet irradiation is also discussed. The results are illustrated with special reference to aerosols of silver iodide. 1. INTRODUCTION The nucleation of ice crystals by aerosol particles is a subject which is at present exciting considerable interest because of its importance in the natural and artifici- ally-stimulated precipitation of rain clouds.Interest has mainly been experi- mental and has concentrated on two lines of research-the nature, origin and properties of naturally occurring ice-forming nuclei, and the production and properties of aerosols of efficient nuclei of simple substances like silver iodide. The first topic belongs most properly to the fields of meteorology and cloud physics, and it is with some physical-chemical aspects of the properties of simple nuclei that we shall here be concerned. Most studies of the nucleation behaviour of aerosols have been experimental and because of the lack of a coherent body of theory their results have often been hard to interpret.It is the aim of this paper to put forward theoretical results, some rather speculative and some more soundly based, which bring a measure of order to the experimental findings, and which, it is hoped, point to some aspects worthy of further investigation. 2. CLASSICAL THEORY Classical nucleation theory 1 leads to an expression for J, the rate of formation of freely growing embryos of the new phase, of the €om, where AG* is the height of the free energy barrier which must be surmounted to form such an embryo, and K is a kinetic constant typically of order 1025 cm-2 sec-1 for the cases which we shall consider. In the classical theory, free use is made of macroscopic concepts like surface free energy, though their validity when applied to aggregates of a few hundred molecules is uncertain.Despite this fact the theory generally gives excellent agreement with experiment in cases to which it has been applied.29 3 Progress in extending the theory should ultimately lead to an expression for AG* in molecular terms, abandoning macroscopic quantities, but little progress has been yet made in this direction. Nevertheless, a recognition of the detailed molecular nature of the embryo has helped to clarify some aspects of nucleation behaviour. Postponing this molecular treatment it has been found possible, using strictly classical ideas, to extend the theory to cover a variety or more complex and practically important situations in a way which we shall discuss.39 J = K exp (- AG*/&T), (2.1)40 ICE CRYSTAL NUCLEATION 3. MOLECULAR ASPECTS In the classical theory of heterogeneous nucleation the important parameter is 8, the angle of contact between the material of the embryo (ice, in our case) and the nucleating substrate. This enters the theory in terms of its cosine which is related to properties of embryo and substrate by where yn, y and yi are respectively the surface free energy per unit area of the nucleating substrate, the embryo phase and the interface between them. As m + 1, the nucleating surface becomes " perfect " and AG* 3 0. This requires in general a close similarity between the nucleus and the embryo phase as we shall see below. From (3.1) the criterion for an efficient nucleus is that the interfacial free energy yi be as small as possible.This quantity can conveniently be divided into two parts, one chemical, involving binding energies, and one mechanical, representing dislocations and elastic strains at the interface. Binding of water molecules to a foreign surface is largely due to their dipole moments and this suggests that a good nucleating surface should have strong electric fields in its vicinity, a condition satisfied by a dipolar or ionic crystal structure. The interfacial energy is in general increased by the presence of dislocations or elastic strains,4 so that these should be minimized in an efficient nucleus. This occurs most simply if the surface structure of the nucleus is geometrically the same as that of some low index plane of ice, though the approximate coincidence of a moderate fraction of atoms of the two structures is actually sufficient.Good nucleating agents like AgI, PbI2 and CuS are found to satisfy these conditions, though for PbI2 and CuS only a fraction of the atom sites correspond to atom sites on possible surface planes of an ice crystal. In all cases the relative misfit against the ice structure is only a few percent so that elastic contributions to yi are small, and the degree of ionization of the component atoms is sufficient to ensure large electric fields at the surface. An effect has been suggested by the present author 5 which may further limit the types of surfaces which are efficient in ice nucleation. It is well known that the ice structure has a residual entropy at absolute zero which is associated with the distribution of hydrogen ions on the bonds connecting the oxygen ions.Expressing this in another way, the orientation of molecular dipoles in an ice crystal is normally random, subject only to certain limitations on the orientations of neighbouring dipoles. If, then, an ice crystal is nucleated upon a substrate for which the lowest inter- facial free energy corresponds to a parallel orientation of interfacial dipoles, then the entropy of the ice structure will be reduced and its free energy increased. This results in an overall increase in AG* and a very marked decrease in nucleating efficiency. On the other hand, if the nucleating surface contains equal numbers of positive and negative ions, the orientation of the ice dipoles is random after the first monolayer has been deposited and the effect does not occur.Applied to actual crystals this suggests that basal (0001) planes of AgI or PbI2 should not nucleate ice efficiently despite their close structural resemblance to it, since all the exposed ions are of one sign. On the other hand, prism faces suck as (1010) which have equal numbers of ions of both signs exposed should nucleate efficiently. These conclusions are consistent with the experimental evidence, 6 but as yet no precise experimental tests of the theory have been devised. rn = cos 0 = (y,-yJ/y, (3 * 1) 4. SURFACE IMPERFECTIONS In the theory of crystal growth at low supersaturations, surface imperfections, and particularly screw dislocations, play a very important part.It is natural to enquire whether such imperfectionc are equally important in heterogeneous nucleation.N. H. FLETCHER 41 Considering first the screw dislocation, its chief importance is due to the fact that it obviates the necessity for surface nucleation in crystal growth. For the nucleation problem we must balance against this the fact that a small embryo containing a screw dislocation is in a state of considerable elastic strain and hence its bulk free energy is raised. A consideration of both these effects 6 suggests that, in the case of ice, screw dislocations do not act as favoured nucleation sites. Other important imperfections are growth steps and re-entrant corners having depths greater than the dimensions of the embryo concerned.For a simple cubic crystal and substrate, particularly simple results can be obtained,6 If AG; is the free energy barrier to homogeneous nucleation then the barrier to nucleation involving n perpendicular intersecting planes, each of surface parameter m is AG: = AG: [(l - m)/2]", (4.1) where n = 0, 1, 2 or 3 corresponds to nucleation in space, on a plane, in a step or in a corner. The results for hexagonal crystals such as ice are more com- plicated 6 but show the same general features. Since - 1 <rn <l corners and steps will always be favoured nucleation sites. Whilst these considerations throw some light on molecular mechanisms of the nucleation process, it must be admitted that the position is still far from satisfactory. In particular, since screw dislocations are apparently not good nucleation sites, the problem of the energy barrier imposed by two-dimensional nucleation remains.It is possible that this barrier is lowered by the effects of the vapour molecules adsorbed on the substrate surface, but no theory of this effect has yet been proposed. In what follows we shall ignore this complication and derive a theory based on an entirely " classical " model. The justification for this procedure is found in the value of the results derived which appear to give an adequate description of many nucleation phenomena. 5. SrzE EFFECT The theory of heterogeneous nucleation as developed by Volmer and others treated only nucleation upon a plane foreign surface. Such results have little direct application to the behaviour of aerosol particles of which the average surface curvature may be very large.It has proved possible, however, to solve the nuclea- tion equations for a spherical cap embryo nucleating upon a perfect spherical particle.7 This geometrically idealized situation is actually not a bad approxima- tion to many cases of practical interest, though it is hoped to complete calculations for a more " crystalline " geometry soon. If AG; is the free energy barrier to homogeneous nucleation in a given situation, then it can be shown that the free-energy barrier to nucleation on a spherical particle of radius R and surface parameter m is where r* being the radius of curvature of the surface of a critical embryo in this situation. The form of the functionf(m, x) is shown in fig.1 from which it can be seen that values of rn close to unity and values of x greater than unity are required for efficient nucleation. This theory can be applied to many interesting nucleation processes, but for our present purposes we shall consider only the nucleation of ice crystals by particles suspended in an atmosphere at water saturation and at a temperature below 0°C. If we restrict ourselves to particles which are insoluble and which have a finite contact angle for liquid water. then ice nucleation can only proceed by a process of sublimation. There is reason to believe that this is the case for an aerosol of silver iodide particles.8 AG* = AGzf(m, x), (5.1) x = R/r*, (5.2)42 ICE CRYSTAL NUCLEATION Making the plausible assumption that the surface-free energy of ice is about 100 erg cm-2 and using eqn.(5.1) and fig. 1 we can then derive the activity curves shown in fig. 2. For a given surface parameter m these show the temperrtture at which a spherical particle of radius PS will on the average, nucleate an ice crystal from the environment in about:one second. The broken curve given for silver iodide is derived not from any precise knowledge of the appropriate value for my but rather from the experimental fact that large particles of silver iodide are active as ice-forming nuclei at a temperature of about -4°C. There is some measure of experimental verification of this curve.8 X FIG. 1.-The geometrical factor f(m, x) in terms of the ratio x = R/r*. m is shown as a parameter.’ 6. ACTIVITY OF AEROSOLS Curves such as those shown in fig.2 can now be used to derive the activity spectrum of an aerosol once its composition and size distribution are known. We shall illustrate this €or silver iodide. A convenient measure of the activity of an aerosol is the number of nuclei, per gram of suspended material, which are active in producing ice crystals above a certain temperature. A plot of this quantity as a function of temperature then characterizes the behaviour of the aerosol. At a given temperature the activity will be greatest if the aerosol is mono- disperse and has a particle size which is just active at the temperature considered. This maximum possible activity at a given temperature can easily be derived for silver iodide from the characteristic curve of fig.2, and is displayed in fig. 3. The activity spectrum of a polydisperse AgI aerosol must at all points lie below this curve, and its detailed shape will be determined by its size distribution. The size distribution of a silver iodide aerosol is typically log-normal with most probable particle radius near lOOA, though, of course, there may be wide43 variations in this parameter. In fig. 3 the broken curve gives the colllputed activity spectrum for an AgI aerosol having median particle radius lOOA and With radii distributed log-normally with standard deviation of a factor 2.5. TFS CUWe agrees very well both in general shape and also in numerical magnitude Wltb N. H. FLETCHER R FIG. 2.-Temperature Tat which sublimation occurs in one second on a spherical particle of radius R in an environment at water saturation.7 Parameter is rn = cos 8.Broken curve is for silver iodide. temp., OC. FIG. 3.Fu11 curve shows maximum number of nuclei active at a given temperature that can be produced from 1 g of AgI. Broken curve shows theoretical activity spectrum for the aerosol desciibed in the text. activity curves measured on the smoke produced from practical burners 0 The behaviour of these smokes may be complicated by the presence of materials like NaI, but the agreement of their behaviour with theoretical expectations provides gratifying support for the approximate validity of the theory.44 ICE CRYSTAL NUCLEATION 7. PHOTO-DECAY Since the nucleation behaviour of a particle depends critically upon the structure of its surface it may be expected that any agent which tends to modify the state of the surface will have an important effect upon nucleation activity.Vapours which are adsorbed on the crystal surface and gases which react chemically with it are examples of this effect. At the present time, however, experimental evidence bearing on these processes is meagre and little purpose is served by a theoretical analysis. One form of surface modification exists, however, for which there are abundant experimental results. This is the progressive modification produced by photolysis of the crystal material by ultra-violet light. For silver iodide it has been found that irradiation in the fundamental absorption band decreases the activity of the aerosol, though widely diverging figures have been quoted for the de-activation rate, ranging from a decrease of a factor 2 during 1 h irradiation to a decrease of a factor lo9 in the same time, the intensity involved being that of sunlight. With the aid of a few simple assumptions and the theory of the size effect discussed above, it is possible to treat the de-activation process equantitatively and to explain the origin of the different observed decay rates.10 The absorption of ultra-violet light by silver iodide particles depends critically upon their size, since the absorption coefficient in the fundamental absorption band is -1O5cm-1 while the radius of the particles with which we are dealing is -10-5 cm.The approximate rate of energy absorption per particle can, however, be easily evaluated. If a quantum efficiency a for the production of photolytic silver atoms by absorbed quanta is assumed, then the rate of production of these atoms can be found.The distribution of photolytic silver within the particle will depend upon the distribution of trapping centres for the photo-electrons produced by the incident radiation. If there are special surface traps associated with the outer layers of the particle, then the ratio of their concentration to that of traps in the bulk of the crystal is important, otherwise the trap density appears only through its effect on the quantum efficiency a. Only silver atoms produced at the surface of the nucleating particle have any effect on its properties, and their effect is to increase approximately linearly the value of the interfacial free energy yi.This in turn decreases the surface parameter rn linearly with time and decreases the nucleation activity. Discussion of the de-activation of an aerosol as a whole involves consideration of this process €or an appropriate distribution of particle sizes.10 We shall not go into this in detail here but simply summarize the general results obtained. (i) The decay is only roughly exponential, the decay rate varying with time. (ii) Typical decay rates in sunlight are of the order of a factor 102 per hour, to a factor 104 per hour can be (iii) In general the activity of small part cles decays at a faster rate than does Whilst these results have been applied specifically to an aerosol of silver iodide, the general approach can be used to treat the photo decay of aerosols of other materials if the relevant parameters are available. but decay rates ranging from a factor expected depending upon details of that of large particles. size distribution in the aerosol. 8. CONCLUSION The behaviour of aerosols in the nucleation of ice crystals from a supercooled vapour is fairly well described by the theory which has been outlined above. It is recognized, however, that the theory itself can only be a first approximation in its present state, and further progress should Come from a more detailed consideration of the molecular processes involved,N. H. FLETCHER 45 1 Volmer, Kinetic der Phasenbildung (Steinkopff, Dresden and Leipzig, 1939). 2 Volmer and Flood, 2. physik. Chem. A, 1934,170, 273. 3 Twomey, J. Chem. Physics, 1959, 30, 941. 4Turnbull and Vonnegut, I d . Eng. Chem., 1952,44, 1292. 5 Fletcher, J. Chem. Physics, 1959, 30, 1476. 6 Fletcher, Austral. J. Physics, 1960, 13, 408. 7 Fletcher, J. Chem. Physics, 1958, 29, 572 and 1959, 31, 1136. 8 Fletcher, J. Meteorology, 1959, 16, 173. 9 Fletcher, J. Meteorology, 1959, 16, 385. 10 Fletcher, J. Meteorology, 1959, 16, 249.

ISSN:0366-9033    

DOI:10.1039/DF9603000039

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

PHASE CHANGES IN SALT VAFOURS BY E. R. BUCKLE Dept. of Chemical Engineering and Chemical Technology, Imperial College of science and Technology, London, S.W.7 Received 20th June, 1960 A high-temperat ure cloud chamber technique devised for studying the freezing of supercooled ionic melts also provides data on phase changes involving salt vapours. Descriptions are given of the condensation, growth and evaporation of liquid and solid particles in clouds of alkali halides. Comparison is made with other work on salt aerosols and the results are examined in the light of recent knowledge of vapour constitution and the theory of nucleation in condensation and crystal growth. A method for studying the spontmeous freezing of ionic melts has recently been described.1 In this method molten salt is prepared in a state of fine sub- division by condensing the vapour.Salt vapour at the saturation pressure is generated, in the presence of argon, by heating the solid in the central chamber of a resistance furnace lined with carbon. A salt bead formed on a small platinum heater coil in the roof of the chamber functions as a supersaturating device. On passing a current of about 2 A through the coil the temperature of the bead is raised by 3QQ-4QOo@ and the vapour in its vicinity rapidly becomes supersaturated. Clouds of solid or liquid particles are formed, depending on the furnace tem- perature, and these are studied as they circulate in the supporting gas (fig. 1). Movement of individual particles is followed by examining the strongly-illuminated clouds with a telescope, the presence of crystalline particles being revealed by twinkling.By studying clouds at various furnace temperatures below the melting point Q, a point is located where twinkling first becomes apparent during the lifetime of a cloud. In this way, values are obtained for the threshold of freezing Ts and the critical supercooling 8 = Tf-.Ts. A full account of the method together with results for alkali halides will be given elsewhere? An interpretation of the observed supercoolings, based on the theory of homogeneous crystal nucleation, is also in progress.3 Certain qualitative information concerning the condensation, growth and evaporation of cloud particles was obtained during the course of these experiments which received only brief discussion in previous papers.In the present paper this is set out more fully, together with additional evidence, and compared with other work relating to alkali halide aerosols. The results are discussed with reference to recent studies on the constitution of alkali halide vapours and the theory of nucleation in condensation and crystal growth. RESULTS OF OBSERVATIONS ON CLOUDS The most profound changes in the characteristics of cloud particles for any salt were brought about by changes in the furnace temperature. This provides a convenient basis for the description of clouds, FURNACE TEMPERATURES ABOVE Ts At furnace temperatures above the freezing threshold the Airy diffraction patterns seen in the telescope consisted of a bright central disc of about 0 . 5 m diam.with occasionally a faint concentric ring separated from the disc by a dark 46E. R. BUCKLE 47 region. The patterns showed no abrupt periodic changes in intmsity and it was concluded that the particks were molten. Confirmation o€ this has now been obtained by examining fall-out from clouds with the microscope. Impingement on a glass slide placed in the cloud chamber results in spreading and co.alescence of the droplets, which thereupon freeze to a glass. For the majority of the salts studied, droplets formed rapidly on operating the supersaturator. Further growth was also rapid under continued supersaturation, droplets falling out from the cloud when their size exceeded about 4,u diam. When the initial degree of supersaturation was not maintained dxoplets quickly evaporated.Because of the rapid growth or evaporation of droplets the lifetimes of clouds were comparatively short. A lii'etirne of 5-10 sec was typical at tem- peratures within a few degrees of T , but this diminished quite sharply when the temperature was raised still further. Preferential growth of the larger droplets and their rapid precipitation on achieving a diameter of about 4 p probably explains the essentially monodisperse appearance of clouds very soon Gter their formation (fig. 1). The behaviour of sodium and lithium fluorides was rather different. Heats of evaporation are high for these compounds and more drastic use o€ the super- saturator was necessary to induce condensatlan. Droplets grew slowly under prolonged supersaturation but re-evaporated quickly when this was discontinued.Clouds had a polydisperse appearance immediately on formation and this per- sisted throughout their lives. Lifetimes €or lithium. fluoride clouds were sub- stantially longer than those for other slkali halides due to its low density. FURNACE TEMFERATUWS AT OR JUST WLOW Ts The freezing of droplets at T, was apparent in the onset of twinkling. This was visible in the telescope as flickerings of the Airy discs, the frequency of in- tensity change being always about 5 sec-1, Although the extent of intensity change could not be judged reliably by @ye, photographs showed that even where the effect was most readily seen it involved only partial extinction of the scattered light. The alkali halides so far examined may be classified into two series according to the reproducibility of their T,-values.z Critical supercoolings ("C) derived from T,-values and compiled data on melting points 4 are as follows : series A : NaCI, 168; NaBr, 166; KC1, 171; KBr2 168; KI, 159; RbCl, 156; CsF, 132.Series B : LiF, 232 ; LiCl, 190 ; LBr, 94 ; NaF, 281 ; CsCl, 152 ; CsBr, 161 ; CsI, 193. salt material was mainly of A.R. or laborqtory reagent purity and was examined without further purification. Compounds in series A showed clear twinkling and T,-values were reproducible to f3"C. As the furnace temperature was lowered the onset of twinkling ocqyrred earlier in the lifetime of a cloud until at 5-10" below T,, particles appewed to twinkle from the outset. Twiilkling was more difficult to discern for salts of series B, and the onset of twinkling was less definite.In spite of a number oE lengthy experiments with these compounds, it was not possible to obtain consistently reproducible values for T,, but in at least two experiments on each salt results were within f3" of the given values. Microscopical examination revealed that provided strict precautions were taken to exclude moisture, fall-out from cbuds of Kx or RbCl was composed, of trans- parent particks of about 5,u &am. In many preparations these were spherical and presumably glassy, although they showed no tendency to crystallize spon- taneously on keeping. Pravided, however, sufficient time was allowed for the condensate to cool before settling out on the slide particles were mainly crystalline. Crystals were often cubic, sometimes to a high degree of perfection, but mostly showed (1 1 I> facets at the cube corners.In some cases the (1 1 I} surfaces were more prominent, crystals showing various combinations of the cube and octa- hedron (fig. 2). Particles containing inclusions of lower refractive index were frequently found in RbCl fall-out. These inclusioqs disappeared readily when the48 PHASE CHANGES I N SALT VAPOURS particles were deliberately moistened. It appeared in some instances that crystal- lization of droplets was arrested at a very late stage, the last traces of melt having solidified to glass (fig. 2). A noticeable feature of all RbCl preparations was that incipient crystallization of droplets occurred at a single centre in an overwhelming majority of cases.Similarly, inclusions were usually found to occur singly, and their size was fairly uniform. The crystallinity of CsBr particles was much more difficult to discern on exam- ination with the microscope. It was apparent only in the surface roughness of the particles, which were invariably of spherical shape. Sediment from clouds formed at temperatures quite close to T, also contained many glassy particles with inclusions of lower refractive index than the matrix. The size of inclusion was much more varied than for WbCl and in some cases represented 10 % or more of the total volume of particle. Although, as with RbCl, the inclusions were apparently water-soluble the particles were non-hygroscopic. Glassy particles were evidently still fluid on hitting the microscope slide as many showed flattened surfaces. Con- glomerates of three or more glassy particles were occasionally found which showed flat interfaces.In so far as it was possible to watch droplets in clouds formed at these tem- peratures growth and evaporation appeared to take place readily, as at higher tem- peratures. Crystalline particles, however, grew more slowly, even at high super- saturation. Evaporation was also slow for crystals, and they were lost from clouds mainly by sedimentation. The marked change in the stability of clouds as the furnace temperature passed through Ts served to locate this roughly in pre- liminary experiments. As at higher temperatures, clouds of NaF and LiF were polydisperse, and the slow growth and rapid evaporation typical of droplets was also observed for crystals.FURNACE TEMPERATURES WELL BELOW T, At temperatures 50" or more below the freezing threshold the faintness of the Airy discs and their marked translational Brownian motion indicated that par- ticles of much smaller dimensions were formed. Confirmation was obtained on examining fall-out from clouds of RbCl and CsBr, which were found to consist entirely of sub-micron particles. In most cases growth of particles became in- creasingly difficult as the furnace temperature was lowered. A point was eventu- ally reached where prolonged use of the supersaturator merely resulted in multi- plication of particles, dense smokes being formed which dispersed very slowly on switching off the supersaturator. The behaviour of LiCl and LiBr was strikingly different, however.With these compounds growth and evaporation occurred readily at low temperatures, and the dense smokes observed with other salts did not form even at a temperature 400" below the melting point. DISCUSSION It is believed that for alkali halides of series A the nucleation and growth of the vast majority of cloud particles were spontaneous processes, since the general behaviour of clouds at any temperature was entirely reproducible. Any effects due to non-volatile chance impurities were either entireIy absent or confined to a very small proportion of particles. The materials responsible for inclusions in sediment particles of RbCl and CsBr have not yet been identified. Unless the inclusions were merely voids, it would seem that the impurities existed in the samples at the start and were volatilized and condensed along with pure salt.Inclusions were not visible in droplet preparations from clouds formed above T,, and their appearance at lower temperatures seemed to have no influence on the crystal habit of the pure compound.FIG. 1.-Molten salt particles in the cloud chamber (RbCl ; 1/25 sec exposure). FIG. 2.-Particles from RbCl clouds formed at furnace temperatures [To face page 48 about 15°C below the freezing threshold.E. R. BUCKLE 49 CONDENSATION AND RE-EVAPORATION OF DROPLETS The temperature and degree of supersaturation at which nucleation of droplets took place cannot be estimated very accurately. It is known 2 that temperatures in the vicinity of the supersaturator rose to levels where the saturation vapour pressure of the salt is several mm of mercury.Calculations using the Becker and Doering theory of homogeneous nucleation in vapours 5 and conservative estimates of the supersaturation predict nucleation rates adequate for the observation of clouds at temperatures above the melting point of the salt.2 As observations on the further growth of molten salt droplets and their re-evaporation were only possible over a narrow range of temperatures relatively little was learned about these processes. On comparing the behaviour of droplets with that of solid particles, however, it seems likely that for most alkali halides the condensation and evaporation of melt are non-activated changes (see also below). MECHANISM OF SOLIDIFICATION, AND THE GROWTH AND EVAPORATION OF CRYSTALS GROWTH IN THE MELT It has been shown elsewhere 2 that at furnace temperatures close to Ts crystals are formed in clouds of alkali halides by the freezing of droplets.Microscopical examination reveals that droplets of salts with the rock-salt structure crystallize to single cubes, although these later develop octahedral facets. In interpreting the critical supercoolings it is postulated 193 that the cubes grow from single three-dimensional nuclei and that the rate, and thereCore the tem- perature, of freezing is governed by the nucleation process. This implies that the time required for complete crystallization of the molten droplet following nucleation is negligible compared with the observation time.Microscopy of fall-out from RbCI. clouds might appear to contradict this assumption since cubes are occasion- ally seen which have a thin envelope of glass preserving the spherical outline of the original droplet (fig. 2). This is probably due to the sudden cooling of droplets which were swept on to the slide by convection currents. This interpretation is supported by the experiments of Jones, Burgers and Amis 6 who obtained spherical particles 70-300 ,u in diameter, and with smooth surfaces, by pouring molten NaCl on to a metal disc rotating at 4000rev/min. X-ray diffraction showed that the bulk of the material was crystalline. The formation of crystalline particles in aerosols of NaCl or KCl has been reported by a number of investigators.7-12 Correlation with present results is made difficult by lack of knowledge concerning the mechanism of solidification in these earlier experiments. The genera1 features of the products in all cases show close similarities. Where adequate precautions were taken to exclude moisture, particles usually consisted of cubic crystals of 0.01-5 p diam.9-11 Exposure to moist air resulted in rapid re-crystallization and sintering of particles,7-11 with at least partial modification of the cubic habit, although in one investigation 13 re- crystallization and growth of NaC1 particles exposed to moist air apparently pro- duced cubes of greater perfection.The degree of perfection of cubes in NaCl and KCl aerosols may vary for other reasons, however. Balk and Benson12 have observed rounding of cube corners in anhydrous preparations which they believe may be due to the presence of high-index facets.Support is given by experimental measurements on the heats of solution of the products. These lead to surface enthalpies which are anomalously high compared with theoretical estimates for { 100) surfaces. High surface energies for NaCl were also obtained by Lipsett, Johnson and Maass7 from heats of solution, and by Craig and McIntosh 9 from the pressures of water vapour in equilibrium with products.59 PHASE CHANGES IN SALT VAPOURS GROWTH IN THE VAPOUR If the theory of crystal growth developed by Burton, Cabrera and Frank for van der Waals’ crystals is applicable to ionic crystals,l4 spontaneous roughening of (100) and (111) surfaces of alkali halides with the rook-salt structure is likely to be absent at temperatures below the melting point.Growth of perfect crystals in the vapour must therefore depend on surface nucleation, which is a process requiring a high degree of supersaturation. In the experiments descyibd here crystals grew fairly easily at temperatures close to Ts. Thqs, once crystals had formed by the freezing of droplets they continued to grow in the vapour at levels of supersaturation well below that necessary for the nucleation of fresh droplets. Crystals formed from the melt may therefore hqve contained numbers of im- perfections, such as screw dislocations, which enhanced. the growth rate. The slowness of growth at furnace temperatures well b@ow the frqezipg threshold suggests that here a surface nucleation mechanism was operative.These particles were probably formed by sublimation,2 and were presumably too small to contain even a single screw dislocation. Calculations based on the translational Brownian motion were not informative as they indicated particle sizes of sub-atomic leve€,2 but the finest smokes, which gave rise to barely perceptible light scattering, possibly contained crystals little larger than three-dimensional nuclei. The preference for particle multiplication at low temperatures may be explained as follows. Three-dimensional nucleation is possible only in the region of high supersaturation in the immediate vicinity of the salt bead. These nuclei can grow very little before being transferred by convection to more remote parts of the cloud chamber where the degree of supersaturation is too low to support further growth by repeated surface nucleation.Because of the turbulence induced by the high excess temperature of the supersaturator, further exposures of particles to high supersaturations near the hot bead are infrequent and transitory. Work by various authors 15-24 on the constitution of the vapours of alkali halides has shown that most of these contain polymeric species. These might be expected to influence the rates af processes such as Condensation, growth and evaporation? In crystal growth, for example, condensation of polymeric Specks might involve dissociation to monomers or the attainment of critical orientations prior to their incorporation into a growing step. These requirements could con- ceivably result in an activation free energy not necessarily involved in the converse process of evaporation.Such considerations may explain the growth and evaporation behaviour of solid and liquid particles of LiF and NaF at high temperatures since there is an exceptionally high content of dimers in the vapours of these compounds.19, 22 Zarzycki’s studies on X-ray diffraction in molten alkali halides 25 show that the degree of short-range order is higher in fluoride melts than in the corresponding chlorides. Restrictions on the orientation of vapour molecules during condensa- tion may therefore be more severe for molten fluorides than for other alkali halides, where comparatively free interchange of small polymers would be expected between melt and vapour.26 EVAPORATION OF CRYSTALS Interesting differences in the evaporation process for various alkali halides are revealed by previous experimental studies.Bradley and Volans 27 found that evaporation in vacuo took piace at more OF less equal specific rates from (100) and (1 1 l } faces of KCl monocrystals grown from the melt. Evaporation coefficients M; of 0.5-0-7 were obtained for (loo), (110) and (1 1.1) faces. As the values were almost independent of temperature over a range of about 100°C they were thought to be due to an orientation factor28 It was later shown by Miller and Kusch 16 that the vapour of KCI contains appreciable quantities of dimers, although their experi- mental temperatures were about 200°C higher than those of Bradley and Volans.E. R. BUCKLE 51 Rotliberg, Eisenstadt and Kusch 22 observed activated evaporation from (100) faces of LiF and NaCl crystals in evacuated enclosures, a varying with temperature in the range 0.2-1.0, The vapours were shown to contain large proportions of dimers.In the same investigation it was found that the vapours of CsBr and Csl showed little or no evidence of polymers, and a was about 0-3. The orientation of the crystal faces was not known, however, and no information on the tem- perature dependence of a was obtained. In the present experiments the stability OP clouds at low temperatures indicates that evaporation of the smallest particles is an activated process. The exceptional behaviour of LiCl and LiBr is difficult to explain from considerations of the heats of sublimation or the structure of crystal and vapour since these do not differ sharply from those of most other alkali halides.No information is yet available on the crystal form of these particles. The development of octahedral facets on cubic RbCl crystals formed from the melt (fig. 2) suggests that these subsequently evaporate preferentially at { 1 1 1) planes, in contrast to the behaviour of KCl crystals of much larger size studied by Bradley and Volans.27 The rounding of cube corners in the NaCl and KCI preparations of Balk and Benson 62 may also have been due to evaporation. It is not easy on the basis of existing experimental evidence to trace any definite correlations between vapour constitution and the processes of crystal growth and evaporation of alkali halides.More data, particularly of a quantitative nature, are needed to test current theories of homogeneous nucleation in phase changes 29 and of the kinetics of growth and evaporation.26 1 Buckle and Ubbelohde, I. U.P.A. C. Symp. IFhermodynamics (Wattens, 1959). 2 Buckle and Ubbelohde, Proc. Roy. SUC. A, 1960,259,325. 3 Buckle and Ubbelohde, to be published. 4 Kubaschewski and Evans, Metallurgical Thermochemistry (Pergamon, London, 5 BwIcer and Doering, Am. Physik., 1935, 24, 719. 6 Jones, Xlurgers and h i s , 2. physik. Chem., 1955, 4, 220. 7 Liipsett, Johnson and Maass, J. Amer. Chenz. Soc., 1927, 49, 925, 1940. 8 Keenan and Holmes, J. Physic, Chem., 1949, §3, 1309. 9 Craig and McIntosh, Can. J. Chem., 1952,3Q, 448. 10 Young and Morrison, J. Sci. Instr., 1954, 31, 90. 11 Harrison, Morrison and Rose, J. Physic. Chem., 1957, 61, 1314. 12 Balk and Benson, J. Physic. Chem,, 1959,63, 1009. 13 McLauchlan, Sennett and Scott, Can. J. Res. A,. 1950, 28, 530. 14 Burton, Cabrera and Frank, Phil. Trans. A , 1951, 243, 299. 15 Friedman, J. Chem. Physics, 1955, 23, 477. 16 Miller and Kusch, J. Chem. Physics, 1956, 25, 845. 17 Pugh and Barrow, Trans. Farday SOC., 1958, 54, 671. 18 Berkowitz and Chupka, J. Chem. Physics, 1958, 254 453. 19 Eisenstadt, Rothberg and Kucb, J. Chem. Physics, 1958, 29, 797. 20 Porter and Schoonrnaker, J. Chem. Physics, 1958,29, 1070. 21 Kusch, J. Chern. Physics, 1959, 30, 52. 22 Rothberg, Eisenstadt and Kusch, J. Chem. Physics, 1959, 30, 517. 23 Schoonmaker and Porter, J. Chem. Physics, 1959,30, 283. 24 Datz and Smith, J. Physic. Chem., 1959, 63, 938, 25 Zarzycki, J. Physique Rad. (Suppl. Phys. Appl.), 1958, 19, 13A. 26 Hirth and Pound, J. Physic. €hem., 1960, 64, 619. 27 Bradley and Volans, Proc. Roy. SOC. A , 1953, 217, 508. 28 Bradley, Proc. Roy. SOC. A , 1953, 217, 524. 29 See, e.g., Dunning, Chemistry ofthe Solid State, ed. Gamer (Buttenvorths, London, 2nd ed., 1956). 1955, chap. 6).

ISSN:0366-9033    

DOI:10.1039/DF9603000046

出版商:RSC    

年代:1960

数据来源: RSC

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THE MOLECULAR HYDROSTATIC ANALYSIS OP GIBBS’ THEORY QF CAlpIEEmY BY FRANK P. BUFF* Institute for Theoretical Physics of the University, Utrecht, Netherlands Received 27th July, 1960 Gibbs’ theory of surface phenomena is based on the postulate that the intrinsic energy depends on the area and principal curvatures of the dividing surface located in the non- spherical transition zone. This assumption leads to first-order correction terms to the classical formulas which may be shown to provide asymptotic corrections to the free energy and thus to provide criteria for the breakdown of thermodynamic concepts. It is the purpose of this paper to examine the Gibbs postulate from the point of view of molecular hydrostatics. With use of the equation of hydrostatics and a stress tensor with unequal tangential components, the equilibrium conditions and work elements are computed.This general stress tensor implies that the work and the surface analogue of the equation of hy- drostatics contain two tensions rather than the earlier single surface free energy. The normal component of the two-dimensional hydrostatic equation leads to a generalized Laplace equation and the tangential components determine the spatial dependence of the tensions. The Gibbs postulate is found correct only when to first-order terms the two tensions are taken to be equal. This equality is shown valid for representative surfaces. I The classical investigations of the phenomenological description of surface phenomena culminated in Gibbs’ thermodynamic theory of capillarity.1 The basis of his detailed treatment of curved fluid interfaces is as follows. First, the geometric parameters of the interface are made precise by the introduction of a family of parallel dividing surfaces.They are located in the transition zone separating the bulk phases in such a manner as to be “similarly situated with respect to the condition of adjacent matter ”. Secondly, a small region is con- sidered which terminates within the adjacent bulk phases and encloses the inhomo- geneous film. A specific fundamental equation, summarizing the first and second laws of thermodynamics, is then postulated for reversible changes in state of this region. The analytical consequences of these concepts follow with the use of known mathematical techniques. Since some features of Gibbs’ theory have long been controversial, it is proper to ask whether his fundamental equation is valid and what its physical interpretation might be.The most familiar answers are associated with the investigations of Guggenheim 2 and Tolman.3 In Guggenheim’s view, the detailed aspects of Gibbs’ theory of curved interfaces are vague and irrelevant since, intuitively, thermodynamic concepts break down for systems comparable in size with the thickness of the inhomogeneous layer. On the other hand, Tolman, in his sub- sequent recapitulation of Gibbs’ theory of spherical drops, accepted the funda- mental equation and, with Gibbs, interpreted the results to be valid for micro- scopic droplets. The actual state of affairs 4 is nearer Guggenheim’s position.A careful interpretation of Gibbs’ theory leads to a quantitative criterion which confirms the conclusion that macroscopic concepts cannot be extrapolated into microscopic domains. This arises from the observation that, upon accep tiiig the * permanent address : Department of Chemistry, University of Rochester, Rochester, New York. 52F. P . BUFF 53 correctness of the fundamental equation, the retention of the detailed terms leads to first-order corrections which enter into the asymptotic expansion of the free energy with respect to the geometrical parameters of external force. Although the physical interpretation of Gibbs' detailed theory is now quali- tatively clear, the type of surface to which the fundamental equation applies rigorously is not established.On the basis of the statistical-mechanical theory of the grand ensemble, the fundamental equation has been confirmed for spherical interfaces.5 However, for non-spherical surfaces, encountered in the presence of the gravitational field, only that underlying model 4 is available which is sufficient for the derivation of Gibbs' formalism. Furthermore, important consequences of this theory are only obtained via the thermodynamic route. It is the purpose of the present discussion to explore the general case in greater detail with use of molecular hydrostatics. For comparison with the later analysis, it will now be instructive to review briefly the basic equations in the extended thermodynamic formulation. A region is considered, small on the macroscopic scale, but large compared with the range of intermolecular forces, which encloses the transition zone.The region terminates at points within the fluid phases a and p where bulk properties subsist. The transi- tion zone is spanned by an initially arbitrary set of parallel dividing surfaces which separate the total volume into volumes ucc and vp. For the dividing surface of area s and principal curvatures c1 and c2, the intrinsic energy E is assumed to depend on the entropy S, composition (Nil and the geometrical parameters of the systems : E = E(S,(Ni),u~,vp,s,cl,cz). (1) With this set of molar variables, the following hndamental equation is then postulated for reversible changes in state : T is the temperature, pi is the chemical potential of component i, pa and pp are the respective bulk pressures extrapolated up to the dividing surface and y is identified with the surface tension. The thermodynamic curvature terms Cf and C2 are recognized equal to within first-order terms, i.e., C1 = C2 = C.The fundamental relation, eqn. (2), pertaining to the actual system, is next contrasted with its analogue pertaining to a hypothetical system consisting of bulk properties within volumes v, and up. Subtraction from eqn. (2) of the respective extrapolated fundamental equations which hold for the bulk phases a and p and division by the area s leads to the following relations for the excess intensive thermodynamic functions : n E, = TS, + c piri+ 7, (3) i = 1 and n dE, = TdS, + 1 pidFi + (C/s)d(c, + cJ. i = 1 (4) Es(Ss) is the excess, per unit area, of the actual energy (entropy) diminished by the energy (entropy) within phases a and p if bulk properties were to subsist up to the dividing surface.Ti is the corresponding excess, per unit area, of the composition of component i. The free-energy relation (3) arises from the assump- tion that y possesses the excess free-energy property. The criterion for thermo- dynamic equilibrium, in conjunction with eqn. (3) and (4) for the excess intrinsic energy, leads to the familiar conditions of constancy of T and partial potential pi. It is recalled that - pi = pi+Ii'fi$54 GIBBS’ THEORY OF CAPILLARITY where Mi is the moIecuIar weight of component i andq is the external potential. The remaining equilibrium condition is found to be the extended Kelvin (Laplace) equation, r is the superficial density of mass and Ngp is the unit normal to the arbitrary dividing surface, directed from phase a to phase p.Additional implications follow from the differentiation of eqn. (3) and equating the result to eqn. (4). It leads to the generalized Gibbs adsorption equation Pu - Pp = Y(%+ c,) - (4 + c22)(cls) + w$w. (5) n dy + S,dT + C ridji, = (C/s)d(c, + c,) + Td@. (6) i= I Under the equilibrium conditions of constancy for T and @$, eqn. (6) can be immediately integrated to within the desired first-order terms The subscript 00 designates evaluation at a planar interface and the superscript ‘’ designates the selection of the I?” = 0 dividing surface. The explicit representation of the free energy of the system is the final and most important inference that follows from this approach.It is most con- veniently represented by the T, p work function a, which appears in the grand partition function and is equal to the difference between the Helmholtz and Gibbs free energies. For a two-phase system,6 with use of eqn. (3), the asymptotic repre- sentation of GI with respect to the geometrical parameters of external force is given by r-Y,+(Cjs)’;(c~+c,)+ . . (7) The integrations are extended over the whole system and y is given by eqn. (7). Since it can be shown 4 that (CiSK = -&oY, and that 6 is comparable with the range of intermolecular forces, it is clear that the usefulness of eqn. (8) breaks down for systems comparable in dimension with the range of intermolecular forces. Thus, the retention of the correction terms in the formulation provides the criterion which heralds the breakdown of thermo- dynamic concepts.Once this analysis has been carried out, it is, of course, un- important to retain these terms in applications to macroscopic systems. In conclusion, it should be recognized that, although in the detailed treatment the thermodynamic functions depend on the reference surface selected, those combinations which are operationally meaningful must be invariant to this arbitrary choice. For example, since IR is an invariant, it leads to the familiar variational principle of capillarity, With its use, eqn. (5) follows from eqn. (8). I1 The preceding treatment of curved interfaces has been based on the validity of Gibbs’ fundamental equation and on the assumption that y possesses the free- energy property.In order to analyze these assumptions, it is first convenient to examine the spatial variation of the concentration throughout the system. On the basis of statistical-mechanical considerations,4 it is found that, in the interior of bulk phases, the concentration is constant apart from negligible terms con- taining the local mass fluctuations. However, as the transition zone is approached,F. P. BUFF 55 the concentration variation is more complex. It varies rapidly between its limiting bulk values in a direction normal to the dividing surfaces, but is sensibly constant over a small lateral extension on the various dividing surfaces. The detailed variation of the concentration is fortunately not required for the assessment of the phenomenological description.It is sufficient to examine gross properties of that member of the chain of Born and Green equations 7 which summarizes the balance of external and intermolecular forces. Since this equation is equivalent to the equation of hydrostatics, the subsequent discussion will be formulated in molecular hydrostatic terms. In this approach, the properties of the stress tensor a are of primary importance. Although Q is a known 8 function of the molecular variables, this explicit representation may be postponed to the end of the analysis. The required basic relation may thus be exhibited in the familiar form v . a = pV$, wherep is the mass density. Its application to the theory of capillarity requires further specification of p and a.It is first convenient to divide the whole system into small macroscopic cells which are either located in the interior of the bulk phases or which enclose the transition zone. In the first case, apart from very small corrections, p is constant. Also, for those regions located in the interior of bulk phases CI andp, it is sufficient to assume that the stress tensor is isotropic : Q;. = - p j l ; j = a$. 1 is the three-dimensional unit tensor and p is the pressure at the point considered. In the second case, the region is considered to terminate within the two bulk phases and its transition zone is spanned by a family of parallel surfaces. When generalized co-ordinates u, 0 are introduced, the current point r of a given surface s may be represented parametrically by r = r(u, v), while the current point W of the parallel surface S, located at a constant distance R along the normal from surface s, is related to the corresponding point 1: by r x r , R = r(u,u)+AN(u,v); N = --!-- 1 % X T , I' N is the common unit normal to the surfaces s and S.Our assumption concerning the spatial dependence of the density, within a given small region, may be expressed in the form p = p(A). The stress tensor within the transition zone will be taken to be of the general form a = oT,elel + oT2e2e2 + a,NN. N is the unit normal and el and e2 are the unit vectors along the lines of curvature of the dividing surface under consideration. This stress tensor serves to remove simplifications in our earlier 4 model calculations.Although it will lead to more involved final expressions, it provides greater insight into the problem considered. The phenomenological results of chief interest are the analytic form of the thermodynamic work element and the equation summarizing the equilibrium conditions. Their derivation on the basis of eqn. (11) and (12) is carried out with the use of known9 techniques involving the mathematical theory of parallel surfaces. Accordingly, we shall only examine the main concepts that are en- countered. In both cases, eqn. (12) is extended over the complete small macro- scopic region under consideration. For the work element it is required on its boundaries, while for the equilibrium condition it enters through the hydrostatic condition. It is then recognized that, although the pressure in the interior of bulk phase varies slowly, the components of stress undergo drastic change as the two- phase transition zone is traversed.This complication is circumvented by the respective extrapolation of the bulk stresses for phases a and p, eqn. (lQ), up to the dividing surface. The subtractive procedure finally yields relations which56 GIBBS' THEORY OF CAPILLARITY contain convergent integrals whose integrands involve the difference between the true state of affairs and the extrapolated properties. These integrals represent the thermodynamic functions required for the phenomenological description of surface phenomena. Thus the thermodynamic parameters finally make their appearance in the form of averages of the interfacial variation of the stress and of the density. It should again be recognized that, although the individual functions depend on the reference surface selected, those Combinations which are operationally meaningful must be invariant to this choice.The stress averages that appear are as follows : Y i = CJS = where 0 R<O i o o . A(A) = The distances la and ;ls are located in regions where bulk properties subsist. The physical interpretation of yj and Ci follows from the context in which they appear in the final relations. We shall find that Y j is the generalized excess surface free- energy and Ci is the thermodynamic curvature term. These considerations lead to the following phenomenological description. The dividing surface s, bounded by the closed curve C, separates the total volume into the volume va of phase a and the volume up of phase p.The stress tensor, eqn. (12), then implies that the work done by the system corresponding to an actual (not virtual) increase in extent of the region is given by &,x is the boundary displacement, 4 is the unit tangent along C', t x Nap is drawn outward and yi is given by eqn. (13). For the representation of the equilibrium condition, it is convenient to introduce the two-parametric gradient a v "I v2 =- [r,xWz+Nxru- a . I ru r, I With its use, the equilibrium condition is found to be expressible as a two-dimen- sional analogue of the equation of hydrostatics, v2 . a2 3- (Pa - Pp)Norp - r w = 0, (17) (18) where the phenomenological surface stress ~2 is given by 2 i = 1 a2 = C (yi - ciCi/s)eiei.yj is identical with that appearing in the work corresponding to an actual dis- placement and C; is given by eqn. (14). In order to interpret eqn. (17), it is first necessary to decompose it into its normal and tangential components. With use of the relation 10 e i . V2ei = -ciN-ejV2 . e j ; i # j , (19)F . P. BUFF 57 the respective components are found to be 2 and ei V2(yi - ciCi/s) + (yi - y j - C ~ C ~ / S + cjcj/s)v2 , ei = IT+ . ei; i # j . (21) The condition under which these results reduce to those of the extended Gibbs theory is that the two tensions y1 and y 2 are equal, This can be seen in the following manner. For y1 = y2 = Y, the actual work done by the system reduces to Thus y is the contribution to the excess free energy. Furthermore, this substitution reduces eqn.(20) to the earlier Kelvin (Laplace) eqn. (5). Finally, with use of the Mainardi-Codazzi relation,ll ei . V,cj = (ci-cj)V2 . ei, V2(Y - (c, + CZ)(C/S), - L+) = 0. (23) (24) Y "YCo+(Cl +c,>(Cls)l&. (25) the tangential component reduces to Its integral is identical with the curvature dependence of Y found from the extended Gibbs adsorption eqn. (6), The parameters ya, and (Cis),, evaluated at a planar interface, are by eqn. (13) and (14) given by 03 Yco = 1 (%--%W, (26) -03 (C/s), = 1 z(o,-oN)dz. -03 z is directed along the space-fixed axis. We observe that (i) only at this point of the analysis is it fruitful to represent the stresses explicitly in terms of molecular variables and (ii) that, within the framework of classical statistical mechanics, only the intermolecular force contribution to the stress tensor is required in eqn.(26). Since the condition of validity of the detailed Gibbs formalism has been shown to be y1 = y2, we now examine this equality with use of eqn. (21. Upon ap- plication of the Mainardi-Codazzi relation, eqn. (21) may be transformed to We henceforth restrict ourselves to surfaces of revolution which constitute the main example encountered in practice. Here eqn. (27) may be readily integrated to first-order terms with the result, yi N 700 + (c1+ cZ)( CIS): + ac j i Zj. (28) The integration constant a may be determined by this argument. If it is assumed that the first-order principal curvature expansion of yi applies generally, then by comparison with the rigorous result for a sphere 5 Y N Y m +2c(c/s>:, (29) it follows that a = 0.Under this condition y1 is indeed equal to y2.58 GIBBS' THEORY OF CAPILLARITY The conclusion of this paper is as follows. The detailed Gibbs theory of capil- larity is a device for calculating the higher terms in the asymptotic expansion of the free energy with respect to the geometrical parameters characterizing the system. This expansion provides an explicit criterion which shows the breakdown of macro- scopic thermodynamic concepts for systems comparable with the range of inter- molecular forces. An analysis of the phenomenological equations of capillarity on the basis of molecular hydrostatics shows that the Gibbs theory is valid only when the two tensions that appear in the general formalism are equal. For representative surfaces this condition appears to be satisfied. I gratefully acknowledge the award of a National Science Foundation Senior Fellowship for 1959-60 during which period I had a stimulating discussion with Prof. L. Van Move on the subject of this paper. 1 Gibbs, Collected Works (Yale University Press, New Haven, 1948), vol. I, pp. 55-353. 2 Guggenheim, Trans. Faraday Soc., 1940,36, 397. 3 Tolman, J. Chern. Physics, 1949,17, 333. 4 Buff, J. Chein. Physics, 1956, 25, 146. SBufl', J. Chem. Physics, 1955, 23, 419. 6 At the confluence of three phases, D must be supplemented by the inclusion of a thermodynamic length parameter, Buff and Saltsburg, J. Chern. Physics, 1957,26,1526. 7 Born and Green, Proc. Roy. Sac. A, 1946,188, 10. 8 Irving and Kirkwood, J. Chem. Physics, 1950, 18, 817. 9 Buff and Saltsburg, 9; Chern. Physics, 1957, 26, 23. 10 Weatherburn, Diferential Geometry (Cambridge University Press, Cambridge, 1930), 11 ref. (lo), p. 52. vol. lT, p. 19.

ISSN:0366-9033    

DOI:10.1039/DF9603000052

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr. B. 3. Mason (Imperial College, London) said: As indicated in my paper, I do not believe that the expansion chamber experiments purporting to observe homogeneous condensation have provided such good confirmation of the Volmer- Becker-Doring theory as is commonly supposed. It seems likely that, because of the great difficulty of preventing nucleus formation by irradiation of metal and rubber surfaces and of the air itself, many writers may have, in fact, observed heterogeneous nucleation. The fact that fair agreement between the theory and experiment is observed at temperatures near 0°C but that serious discrepancies occur at apprecialy lower temperatures suggests that perhaps the former agreement is fortuitous. Ds. W. J. Dunning (Bristol University) said: In reply to Dr.Mason, in my paper I mentioned that a thorough test of the theory would require the experi- mental evaluation of the dependence of droplet concentration and droplet size on the time, the supersaturation ratio and the temperature. A " one shot " ex- periment, as carried out by the cloud chamber method, falls far short of this ideal. Further, there is no unique value for S,,i, which will depend on the experimental arrangements and the skill of the observer. It is perhaps fairer to check the form of the relationship between and other variables as determined by one ob- server, rather than seek exact agreement between observers. I also point out that nucleation theory has been applied in explaining the phenomena which occur in expansion nozzles and wind tunnels; there is the possibility of inverting this approach and using these phenomena as a method of studying nucleation and growth theory.It may be hoped that such an investigation would correspond to an experimentum crucis ; at least more variables would be accessible to measure- ment and control than in the cloud chamber. The other method, in which a jet of vapour is supercooled by mixing with a coolant atmosphere, has distinct promise but has the disadvantage that the theory of turbulent jets does not describe quanti- tatively the experimental data. Dr. E. R. Buckle (Imperial College, London) (communicated): It has been remarked by Dr. Mason that serious discrepancies are found between nucleation rates predicted by theory and those indicated by experiment.The result has been a general lack of confidence in the kinetic theory of nucleation, which never- theless has not been substantially improved for 25 years. I would like to draw attention to three factors which may have contributed to the apparent disagree- ment between theory arid experiment. My remarks are mainly concerned with homogeneous nucleation in condensed systems, particularly the freezing of super- cooled liquids. The theoretical expression of Turnbull and Fisher 1 for the specific rate of homo- geneous nucleation in pure liquids may be written J = K exp (-AW/kT), where A@* is the free energy of formation of a critical embryo, or nucleus, and K is a kinetic coefficient given by K = (N,kT/h) exp (- &/kT). Here, NO is the number of molecules in unit volume of liquid, and E is the activation energy for the assimilation of single molecules by a growing crystal embryo.In applying this theory to the calculation of nucleation rates, a relatively small error is automatically introduced due to a mistake in the derivation of (2). It may be 1 Turnbull and Fisher, J. Chem. Physics, 1949, 17, 71. 596Q GENERAL DISCUSSION shown 192 that the expression for K is too large by a factor g*# where g* is the number of molecules in a critical embryo. Values of g* for a wide range of compounds show 3 that nucleation rates predicted by (1) and (2) are consequently too high by one or two orders of magnitude. Since the degree of uncertainty involved in other quantities assumed in calculating K may for some liquids intro- duce errors of similar size, the above correction need mot necessarily result in marked improvement in calculated nucleation rates.A more serious source of error may arise in the method of using theory to interpret critical supercoolings. It is commonly assumed 4-8 as an experimental criterion that the threshold of freezing in an isolated droplet depends on the forma- tion of a single nucleus during the time of observation. This criterion may be expressed as Here, Vis the volume of a droplet, to is the observation time, and Ts is the freezing threshold. The value for I given by (3) is used to calculate either K or A@*, depending on existing knowledge concerning the liquid-solid interfacial free energy 0. In using eqn. (1) for this purpose, the further assumption is made that the threshold nucleus forms under steady-state conditions, i.e., that the relaxation time is exceeded by the observation time.It is shown elsewhere 3 that where (3) is assumed the nucleation time-lag E, defined by I = JV = lito; T= T,. (3) Q(t) = (t-L)J; t + ~ , (4) where Q(t) is the flow of embryos in time t, may not fulfil this requirement. For example, an upper limit to the time lag, applicable where the nucleating system relaxes from an initial distribution comprising only single molecules, is given by L, N No/J. ( 5 ) Since for the observation of steady-state nucleation L1 <to, the criterion (3) implies that iVoVG1, which is completely unrealistic. The difficulty is removed if the freezing criterion (3) is abandoned in favour of one which avoids arbitrary specifica- tion of the threshold nucleation frequency I.An obvious alternative is L- t o , (6) IN NOVit,, (7) which, using (5), leads to a stationary nucleation frequency exceeding that postulated in (3) by as many as ten orders of magnitude. Although (5) probably over-estimates actual time lags in most types of experiment, since it is based on the most unfavourablle initial condition of the system, it is evident that grave errors may still be introduced into estimates of Kusing (3) as the threshold criterion. Finally, in studies where nucleation rates have been obtained by counting the number of droplets crystallizing in a given time under isothermal conditions, it has not always been clearly established that freezing was initiated in each droplet by a single nucleus, although this is assumed in the interpretation of results.It seems that in this way also nucleation frequencies may have been grossly under- estimated. 1 Turnbull, private communication, 1959. 2 Buckle, to be published. 3 Buckle, Nature, 1960, 186, 875. 4 Turnbull, J. Chem. Physics, 1950, 18, 198, 768, 769. 5 Turnbull, J. Appl. Physics, 1950, 21, 1022. 6 Turnbull, J. Chem. Physics, 1952, 20,41 I.. 7 Thomas and Staveley, J. Chem. SOC., 1952, 4569. 8 De Nordwall and Staveley, J. Chem. SOC., 1954,224.GENERAL DISCUSSION 61 To summarize briefly : in tests of the theory of nucleation in supercooled liquids based upon the magnitude of the kinetic coefficient K there is a tendency for cal- culated values to be 10-100 times too large, while " observed " values depending on nucleation frequencies assumed in threshold or isothermal experiments may be too small by much larger factors.Dr. N. H. Pletcher (University of New England, N.S. W.) (communicated) : This comment is concerned with nucleation by foreign particles in a supersaturated environment. It may be o€ interest to note that Twomey,l working in Australia. has provided an experimental verification of the Volmer eqn. (12) and (13) relating to the nucleation efficiency of a flat surface with contact angle 8. Twomey was able to produce controlled water-vapour supersaturations ranging from 0.3 % to 100 % using a diffusion chamber containing water and dilute HC1, and, by examining the glass walls of the chamber, to detect the onset of con- densation upon them.The glass was then coated with a variety of materials to produce contact angles ranging from 15" to 80°, these contact angles being measured by ordinary methods. Throughout the whole range of contact angles examined the nucleation threshold was found to agree very well with that predicted by the Volmer theory, Eqn. (12) and (13) have also recently been generalized to give a detailed treat- ment of nucleation by small spherical particles.2 As suggested by the analysis of Reiss, referred to in Dunning's paper, the effect of particle size becomes ap- preciable when the particles are not much bigger than critical embryos. In practice, this occurs for particle diameters of the order of 0 . 1 micron and so is quite important in discussions of the nucleation activity of many aerosol systems.Dr. H. Wilman (Imperial College, London) said: With respect to the last section of Dr. Mason's paper, there is surely no reason to doubt that water molec- ules can and do condense to form solid crystalline ice directly on a substrate at a temperature below the melting point, in just the same sort of way as molecules of other materials, such as NaCl or CdI2, do. This can be seen from some of Dr. Mason's beautiful photographs of ice crystals growing on faces of mica, silver iodide, and other crystals. The hexagonal plate-like shape of the ice crystals is direct evidence that the water molecules (at the substrate temperature con- cerned) migrate considerable distances from their initial point of impact on arrival, until they are preferentially held in the deeper potential troughs at the edges of the growing crystal face, thereby prolonging the main facb further.In the slide showing ice condensing as hexagonal plates at the edges of the spiral step present on a silver iodide face, this preferential location of the ice crystals indeed corresponds well to such an interpretation. It appears that the water molecules have migrated to the edges of the silver iodide face and have been held there preferentially at such sites, just as the AgI molecules had evidently done during the formation of the AgI substrate previously; and their preferential aggregation to form ice crystal nuclei has then occurred correspondingly in these regions which are more densely populated with water molecules, at the edges of the steps on the AgI.It is thus clear that although the individual water molecules had considerable mobility at first, after their arrival on the substrate, there is no evidence of con- densation as a continuous liquid layer. Dr. N. H. Fletcher (University of New England, N.S. W.) (communicated): This comment is concerned with the nucleation of droplets from supersaturated water vapour by small ions. Eqn. (3) of Mason's paper gives the equilibrium supersaturation over a small droplet of radius r and charge q, under the assumption that the dielectric constant of the liquid is infinite, or equivalently that the liquid is sufficiently conducting that the ionic charge may be regarded as uniformly distributed over the droplet surface. This assumption may be questioned, and 1 Twomey, J.Chem. Physics, 1959, 30, 941. 2 Fletcher, J. Chem. Physics, 1958, 29, 572; 1959,31, 1136.62 GENERAL DISCUSSION it seems probable that a better model would treat the ionic charge as localized at the centre of the droplet, the material of the droplet then being regarded as behaving as an ideal dielectric whose permittivity would be very much less than the low field value for water because of saturation effects in the strong field of the ion. A more serious objection may be raised, however, to the use of this equilibrium equation to calculate nucleation thresholds. Such a procedure neglects the statistical fluctuations which are the whole basis of nucleation theory. Such fluctuations are of supreme importance in cases such as this in which the total number of molecules in a critical embryo is only about 30.The agreement of the critical supersaturation calculated in this way with the experimental value is only fortuitous and in fact the critical value of S given by (3) approaches infinity as the charge q approaches zero, instead of tending to a value near 6 as required for homogeneous nucleation. A theory of nucleation upon ions which takes proper account of statistical fluctuations and which makes use of a more realistic model for the charged droplet can be worked out along the same lines as the treatment of homogeneous nucleation leading to eqn. (2). Such a treatment was, in I'act, given as long ago as 1938 by Tohmfor and Volmer.1 The chief uncertainty in their treatment is the appropriate value to be used for the dielectric constant of the drop material.Values in the vicinity of 3 were found to give good agreement with experiment for several liquids, and such values seem reasonable in view of saturation effects. A further comment concerns the difference in nucleation eificiency between positive and negative ions. As suggested in the paper, this result is probably due to the existence of an oriented layer at a normal water surface, and in fact It is easy to show that the effect to be expected is of about the order observed. For a droplet about 10-7 cm in radius, such as those with which we are dealing, the energy of a water dipole oriented against the direction of the ionic field is -10 kT so that essentially all dipoles will be oriented parallel to the local field determined by the sign of the ion.Now there is good evidence that in a normal water surface the outermost molecular layer, and probably several beneath it, are oriented with the hydrogen ions directed inwards to the liquid. The entropy deficit associated with such an orientation restriction is about k log 2 per molecule, so that the enthalpy re- duction per molecule produced by such orientation must be more than RT log 2. A water surface in which the dipoles are pointed in the " wrong " direction should thus have its surface free energy increased by about 2 IcT log 2 per molecule or about 50 erg/cm2 to a value near 130 erglcm2. Now for a negative ion the normal surface orientation is reinforced and the Tohmfor-Volmer theory predicts a nucleation threshold at about S = 4.For a positive ion, however, the surface orientation is reversed so that the surface free energy is increased from about 80 to about 130 erg/cm2. The effect of such an increase would be to raise the value of S for the nucleation threshold by about a factor three. The experimental difference between S for ions of different sign is about a factor 1.5, which is less than the factor estimated above, but in viev of the order-of-magnitude nature of the argument used, this agreement is fairly satisfactory. A really good theory must necessarily, as pointed out in the paper, take proper account of the pseudo-crystalline nature of the growing embryo, Dr. B. J. Mason (Imperial College, London) (communicated) : I agxm, of course, with Dr. Fletcher that my eqn.(3) does not describe the rate of droplet formation on ions and that this may be discussed on a statistical basis similar to that described in the section of my paper dealing with homogeneous nucleation. I have serious misgivings about the Volmer theory of homogeneous nucleation and also its ex- tension by Tohmfor and Volmer to describe condensation on ions because i t s 1 Tohmfor and Volnier, Ann. Physik, 1938,33, 109.GENERAL DISCUSSION 63 most serious limitations are just those of eqn. (3) which €oms an essential part of the theory. My intention was therefore to discuss the limitations of eqn. (3) which is incapable of accounting €or the well-established fact o€ sign preference. I agree entirely that it is fortuitous that the supersaturation required for the formation of nuclei of critical size predicted by eqn.(3) is dose to that observed €or a detectable rate of droplet formation on -ve (but not +ve) ions and 1 am not sure that we are much better off by modifying eqn. (3) to take into account the polarization of the droplet surface by an ion in the manner of Tohmfor and Volmer and writing where 81, 82 are the dielectric constants of the surroundings and the droplet respect ivd y. What values shall we choose for 82 ? If we use the bulk values, 81 = 1 , EZ = 100, the correction is negligible, The alternative is to leave 82 as a further disposable parameter in the equation for the nucleation rate giving four unknowns, 82, ~ L V (or doLV/dr), r, (the effective initial radius o€ the ion) and S.One may assume values for EZ, CTLV and r, and use the experimental data on nucleation rates to calculate a corresponding theoretical value of S to be compared with the measured value ; or, alternatively, follow Volmer and use the bulk value of BLV, the experi- mental value of S, guess at r,, and compute the effective value of 82 = 3 which Fletcher mentions. But here we are really only camouflaging our ignorance and we must not delude ourselves that the experiments provide an independent check of the theory which is manifestly inadequate because it does not account for sign preference. My general feeling is that a disproportionate effort in nucleation physics has been spent titivating the Volmer-type theories and to manipulating the parameters to obtain agreement with selected results from rather doubtful experiments and muchtoolittle attention to designing good experiments which may ascertain the facts. Dr- W.J. Dunning (Bristol Uaiversity) said: Dr. Fletcher suggests that the basal (8001) planes of AgI and PbIz should not nucleate ice efficiently, despite their close structural resemblance to it. I should like to ask Dr. Fletcher if there is any evidence that the (0001) habit faces are 0001 faces on a molecular scale? If a b FIG. 1 .-(a) nominal ( O W ) surface ; (b) scheme of narrow corrugations simulating nominal (001) stdam. they were, consisting of ions all of the same sign, we should expect them to have very high surface energies. It seems possible that such nominal 0001 faces may consist of a number of short or narrow surfaces all of lower surface energy.For example the nominal (0001) surface may really consist of narrow corrugations formed from (1011) faces. Dr. Fletcher mentions the possibility that the barrier €or heterogeneous nucle- ation may be lowered by the effects of the vapour molecules adsorbed on the sub- strate surface. If the adsorbed film on the surface builds up in thickness, its stability will depend upon the sign of dp2ldr2, where p2 and r2 are the chemical potential and surface excess of the adsorbate. Should a fluctuation occur in which64 GENERAL DISCUSSION the film becomes thinner in one part and thicker in another, the fluctuation will be transient if dp2lpr2 is positive. On the other hand if, within a certain range of r2 values, dp2/dlT2 is negative, then the thick part will become thicker and the thin part thinner.When such surface phase separation occurs, it simplifies matters if a condition of equilibrium between the two surface phases can be introduced. A simple case would be when one of the surface phases is a liquid film and the equilibrium can be expressed by Young’s equation. In surface nucleation the question arises whether the process is such that nucle- ation occurs before the surface film is built up or whether the surface film builds up first and then collapses. At low supersaturations it might be expected that the film builds up and then collapses, whilst at high supersaturations it might be expected that nucleation occurs directly from the vapour. Dr. B. J. Mason (Imperial College, London) said: Because we now have abundant evidence that ice nucleation (and the photolytic decomposition of silver iodide) occurs preferentially at special sites on the substrate, e.g., at dislocations, edges of growth steps, re-entrant corners, etc., I doubt whether the nucleating ability of a surface can be discussed realistically in teilns of macroscopic concepts of surface energies and contact angle.We are not concerned so much with the average force field over large, flat areas of a perfect crystal face as with the much more complicated force field in the neighbourhood of imperfections. In these regions the probability of nucleation will be determined by a combination of factors : the degree to which the local geometry (e.g. a step) enables the nucleus to surmount the energy barrier for two-dimensional nucleation; the degree of misfit between the host and guest lattices; and the associated degree of strain which will determine the stability of the deposit.At supersaturations of about 10 %, our experiments show that, on large crystals of Agl, PbI2, CdIz, epitaxial deposits of ice crystals appear only on steps, etch pits, etc., and that supersaturations of about 100 % are required for nucleation on flat, perfect areas of the crystal, Silver iodide particles of radius 0.1-1 p act as ice nuclei if the air is sub-saturated relative to liquid water provided it is supersaturated relative to ice by at least 12 %. On the other hand, much smaller particles, of radius about 0.01 p, form ice crystals only if the relative humidity exceeds about 120 % which is understandable if the particles are involved in condensation followed by freezing.This is contrary to Dr. Fletcher’s deduction that such silver iodide particles must act as sublimation nuclei in natural clouds. I agree that relative humidities of 120 % are not achieved in clouds, and so the inference is that very small silver iodide particles can act only by being captured by super- cooled cloud droplets. can, however, act as sub- limation guclei. Mr. W. R. Lane (War Dept., Porton Down) (communicated) : Dr. Fletcher finds fair agreement between his calculated curve for the activity of a model AgI aerosol and activity curves measured on the smoke produced from practical generators and he quotes this in support of the validity of his approximate theory of the particle size effect.It is as well to keep in mind the fact that the activity of silver iodide smoke appears to depend upon the manner in which the nuclei are produced. For example, in experiments on the nucleation of supercooled water clouds by smoke produced (i) by vaporization of an acetone solution of silver iodide in a paraffin- burning generator of a type which has been employed in large-scale cloud seeding operations and (ii) from a small electrically-heated laboratory vaporizer, we obtained the following comparative results for smokes tested 3 min after generation. Larger particles, with r>@1 temp. of supercooled cloud O C number of ice crystals per g Ag I paraffin burner small vaporizer - 10 1.45 X 1012 2.6 X 1011 - 15 PO x 1013 6.3 x 1013 - 20 1-65 x 1013 20 x 1015GENERAL DISCUSSION 65 (If it is desired to allow for particle losses from coagulation, diffusion and sedimentation during the 3-min storage before test, these numbers should be increased by approximately 25 %.) At temperatures below about - 12°C the AgI aerosol generated from the small vaporizer shows a considerably higher activity than that from the paraffin burner, but this is not maintained at higher temperatures.In attempting to discover the reason for the different nucleation activities of AgI aerosols produced in these two ways, representative samples of each smoke were examined by electron microscopy. The smoke from the paraffin burner showed not only a lower proportion of very small individual particles than that from the laboratory device, but also numerous " stains " whose appearance sug- gested that many AgI particles had been engulfed in droplets formed, presumably, in the burning of the acetone solution in the generator.The lower activity of the smoke from the paraffin burner may be associated with these particle character- istics. Dr. E. R. Buckle (Imperial College, London) said: Since the completion of the work on alkali halides reported in my paper, we have been studying halides of heavier metals in the cloud chamber. Freezing thresholds for AgCl, CdI2, PbC12 and PbI2 have been located by observing the onset of twinkling and by rnicro- scopical examination of cloud fall-out. Crystalline particles in PbI2 clouds show very marked twinkling when first seen, but on continued circulation further growth takes place and the twinkling becomes less distinct.This appears to be due to dendritic growths formed by direct sublimation on the hexagonal prisms which crystallize from the melt. The resulting crystals closely resemble those common in snowflakes. Dr. B. J. Mason (Imperial College, London) said: The appearance of twinkling particles is widely accepted as a reliable indication of the onset of crystallization in clouds of supercooled droplets. But in order to twinkle, the particles must develop flat crystal faces o€ diameter several times the wavelength of the incident light, i.e. of at least a few microns. The time taken for the appearance of such faces will depend upon the temperature and supersaturation of the vapour.When watching micron-size water droplets falling through a temperature gradient in air I have noticed that their freezing at - 40°C is indicated by a sudden brightening of the droplet and after a delay of a second or two they become transformed into twinkling ice crystals. We have also observed that thin circular disc-like ice crystals deposited from the vapour or grown from the melt develop into six-sided plates more readily when they are growing slowly. I imagine a frozen droplet to be surrounded by an almost infinite number of small crystal faces of different orientation. As growth proceeds, the high-index faces grow faster and tend to grow out until, ultimately, the particle is surrounded by a small number of low-index faces and we have a recognizable crystal.If, however, the particle continues to grow rapidly, imperfections are built in and lead to the constant regeneration of high-index faces, and the appearance of fiat faces large enough to cause specular reflection is delayed. This also may be true at low temperatures when the surface migration of molecules is much reduced and the condensation may, in extreme cases, acquire an amorphous structure. I should like to ask Dr. Buckle if he recognizes this as a problem in determining the onset of crystallization in his high-temperature smokes. Also, does he believe that the crystals which he observed always arose from the freezing of supercooled droplets or was there any evidence to suggest that some may have formed by direct sublimation from the vapour phase? Dr.E. R. Buckle (Imperial CoZZege, London) said: In reply to Dr. Mason, one of the most important factors determining the rate of growth of crystals is the dissipation of the heat of crystallization. I think that this can occur very rapidly in our experiments on alkali halides, since it is calculated 1 that the hot particles 1 Buckle and Ubbelohde, to be published. C66 GENERAL DISCUSSION generated near the supersaturator cool through 300-400°C in periods of the order of a millisecond. It is likely that linear crystallization velocities in molten alkali halides are sufficiently high to cause the melt droplets to solidify completely in a very small fraction of the time of observation of clouds. Regarding the stage at which crystal faces suitable for specular reflection appear, I agree that this may occur quite late in the growth process, but in view of the rapidity of freezing as a whole this would not affect the measurement of Ts.As mentioned in my paper, at low temperatures the crystals may be formed by sublimation. There was fairly conclusive evidence for this in some cases, since it was occasionally possible to obtain clouds at low temperatures without melting the supersaturator bead. By examining fall-out at furnace temperatures around T,, however, we have established that cloud particles are invariably molten just above this temperature and crystalline just below it. Moreover, as was also stated in the paper, theoretical calculations, based on the Becker-Doering theory and reasonable estimates of vapour supersaturation, show that at temperatures just above the melting point of the salt nucleation of droplets should occur very rapidly.Since the supersaturated vapour is initially at even higher temperatures, droplets evidently provide the route by which crystals are formed at T,. Dr. €3. Wilmwn (Imperial College, London) said: I would like to emphasize that, as our own results illustrate, a spherical particle shape does not necessarily by itself mean that the particles have condensed as liquid. For example, in our smoke deposits from arcs between metal electrodes in air, the practically spherical shape of the Ta2Q5 particles is surely most unlikely to be due to condensation of either Ta or Ta2O5 as molten particles, since both these materials have very high melting points (even the crystallization temperature of initially amorphous Ta205 is as high as 700°C). From many electron diffraction investigations we know that if a vapour con- denses to form a solid deposit on a substrate (or for aerosols, the initial nuclei) at a low enough temperature, the deposit is amorphous ; but in a higher substrate- temperature range the deposit is formed as small crystals (e.g., -5OA diam.), but corresponding to the still only very low degree of mobility of the atoms or molecules on the deposit surface, there is then practically no facet development on the crystals, so that with the aerosols the particles must develop roughly spherical shape, In a higher temperature range again, the higher mobility of the atoms or molecules after arrival on the deposit leads to formation of much larger crystals and these develop plane faces which are extended by the atoms or molecules migrating after arrival until preferentially held at the edges of surface sheets of close-packed atoms.Above the melting-point, finally, the deposit is condensed directly in the liquid state, again as spheres; and when such spheres subsequently cool, they may retain this shape if the cooling is rapid enough and extensive enough to reduce the atomic motion to a level at which crystallization, or recrystallization, cannot occur to any appreciable extent. However, in the particular case of condensation of PbI2 from the vapour, to which Dr. Buckle has just referred concerning his cinematograph film, it seems clear that the temperature at which the PbI2 was condensed must have been higher than the melting point, so that the spherical particles must have condensed indeed as liquid. This is similar to our own observations in the condensation of Pb and Bi. On the other hand, when crystalline plates are observed to be formed, this is usually evidence that either all or most of the deposition has occurred directly from vapour to crystalline solid, unless initially liquid drops are formed and cool relatively slowly so that facets develop by, in effect, a recrystallization type of rearrangement of the atoms or molecules into a configuration of lower potential energy than that of the spherical initial shape. Dr. E. 33. Buckle (Imperial College, London) (communicated) : Incidentally, it is possible that twinkling may not always be simply it reflection phenomenon.GENERAL DISCUSSION 67 We have observed 1 an effect in dense clouds, both of liquid and of solid particles, due to the temporary eclipsing of one particle by another. The effect is visible in the telescope as a momentary brightening of the nearer particle. In turbulent clouds, or in clouds composed of sub-micron particles undergoing visible Brownian translations, this momentary brightening occurs repeatedly, and closely resembles the twinkling of isolated crystals. Another reason for suspecting that twinkling is not always due to specular reflection is that we have also observed sub-micron particles to twinkle, even when completely isolated. 1 Buckle and Ubbelohde, I. U.P.A. C. Symp. Thermodynamics (Wattens, 1959).

ISSN:0366-9033    

DOI:10.1039/DF9603000059

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

II. GROWTH OF PARTICLES DROPLET XNTEMCTION IN AQUEOUS-DISPERSE AEROSOLS BY D. P. BENTON AND G. A. H. ELTON* Battersea College of Technology, London, S. W. 1 1 Received 17th June, 1960 Experimental evidence is given to show that the collection efficiencies of droplets in an aqueous aerosol are a function of the electrolyte concentration. A semi-quantitative indication is given of the influence of the Dukhin-Derjaguin diffusional electrokinetic effect on collection efficiencies of droplets of diameter approximately 3 p. A fully quanti- tative test of the theory of Dukhh and Derjaguin must await further experimental data. Aqueous aerosols, produced by spray atomization in an isothermal enclosure which has been previously saturated with water vapowi; show a decrease of opacity with time, and it has been demonstrated 1 that the rate of decay may be markedly reduced by the presence of dissolved materials in the aqueous droplets. Provided that the enclosure is fully saturated so that loss of liquid water due to evaporation of droplets is impossible, the rate of decrease of opacity in such aerosols is deter- mined by processes which lead to growth of the droplets. Increase in droplet size at constant liquid water content leads to a decrease in opacity as the attenuation produced by unit weight of droplets varies inversely with the radius.An increase in droplet size leads to an increased rate of sedi- mentation under gravity and hence to an increased rate of loss of liquid water con- tent. Growth of droplets can occur by two types of mechanism : (i) evaporation- condensation, (ii) collision and coalescence.A problem of particular interest, especially with regard to meteorological studies on clouds and fogs, is the assess- ment of the relative importance of the two mechanisms in determining the rate of growth of droplets. The vapour pressure at any instant in a heterodisperse aerosol corresponds to the equilibrium value over a droplet of average size. Hence, droplets smaller than average tend to evaporate whilst those larger than average tend to grow. The effect of this process in the decay of a pure water fog has been examined theoretically 2 for a number of model droplet size distributions, the results demon- strating a marked dependence of the fog stability upon the initial mean droplet radius, and showing that the initial rate of decay is rapid for mean droplet radii less than approximately 5 p.The presence of dissolved materials tends to retard the evaporation-condensation process, since the concentration of solute in drop- lets smaller than average is increased as evaporation proceeds, while that in droplets larger than average is dwreased, due to condensation, thus reducing the vapour pressure differential . The calculation of the rate of growth of droplets by collision and coalesceiice involves greater difficulties of computation since, even on the basis of hydro- dynamic considerations alone, the efficiency of collision and coalescence between two droplets is a function of their sizes.3-5 Attempts have, however, been made to assess the relative importance of the coalescence and evaporation-condensation processes in model fogs.For example, it is suggested 2 that the latter process is * present address : Baking Industries Research Station, ChorIeywood, Herls. 68D . P. BENTON AND 6. A . H . ELTON 69 of predominant importance in the decay of a pure water fog with 1O-Gg water per cm3, if the mean droplet radius is less than approximately 7 p. However, such assessments involve the use of collection efficiencies derived on purely hydro- dynamical grounds, no account being taken of the possible influence of dissolved materials on the coalescence process. It has been suggested1 that the efficiency of collision between two droplets may be affected by electrical phenomena arising from the distribution of ionic material’ dissolved in the droplets.At the surface of water droplets containing ions an electrical double layer is set up due to the fact that ions of different types (size, charge, etc.) are adsorbed to different extents. For 1-1 inorganic electrolytes, anions are preferentially adsorbed at the air/water interface 6 so that the double layer within the droplet comprises an outer shell of adsorbed anions with a com- pensating inner shell of cations. It is likely that the presence of this ion dis- tribution, either after completion or during formation (particularly in the event of any droplet deformation) will lead to an interaction between droplets at close approach, thus modifying any collection efficiency calculated on purely hydro- dynamical grounds. Dukhin and Derjaguin have shown theoretically7 that a large electric field exists outside a moving neutral droplet having an internal double layer, especially when adsorption is considerable. On the basis of a theory of the diffusional electrokinetic effect, arising from the motion of the droplet surface, these workers calculate that field strengths of the order of 100V/cm may exist outside microii- size droplets containing materials of high surface activity.Assuming reasonable I -5 1.0 1.5 2.0 concentration of KCNS solution (normality) f 0 standard deviation from mean 4 FIG. 1 .-Effect of concentration on collisions of droplets of potassium thiocyanate solution with droplets containing 0.5 N Fe alum and 0.5 N sulphuric acid. values for the surface potential,8 this would imply that the forces of interaction between droplets arising from their internal double layers may extend over several microns.Hence, coalescence may occur between very small droplets where hydro- dynamic calculation indicates zero collection efficiency. Although Dukhin and Derjaguin postulate that electrical effects of this kind may affect the magnitude of the collection efficiency of a moving droplet, experi- mental confirmation of this theory is not easy to obtain. The direct experimental investigation of droplet coalescence in a laboratory-prepared aerosol is usually70 DROPLET INTERACTION hindered by the simultaneous occurrence of growth by the ev~~oratisn-sQnden~~~i~fl processes. However, a direct indication of the effect of electrolyte concentration upon collection efficiencies has recently been obtained.9~10 Mixed aerosols, generated by the simultaneous atomization of ferric ammonium sulphate solution and of potassium or ammonium thiocyanate solution, were prepared, and sampled after a suitable time interval by collection of droplets on a slide thinly coated with 0 I 2 3 4 5 6 7 1/c, p.p.m.surface-active agent FIG. 2.-Effect of additions of anionic and cationic surface-active agents to the thio- cyanate solution. 0 anionic agent added 0 cationic agent added 1 28 91 I I I I I I I 0 I 2 3 4 5 6 7 l / c , p.p.m. surface-active agent Q cationic agent added 0 anionic agent added FIG. 3.-Effect of additions of anionic and cationic surface-active agents to the ferric solution. Vaseline. Microscopic examination of the samples for the presence of droplets coloured red gave a measure of the extent of coalescence between droplets of the unlike solutions.The extent of coalescence was studied as a function of the electrolyte con- centration in the fog droplets, it being found that an increase in concentration of either solution resulted in an increased number of coalescences. The number of droplet coalescences was also found to be markedly affected by the presence in the droplets of small quantities of surface-active agents. Addition of an anionic agent (Teepol) to the thiocyanate solution or of a cationic agent (mixed alkyl dimethyl benzyl ammonium chloride) to the ferric solution resulted in increasedD. P. BENTON AND G. A. H. ELTON 71 coalescence while addition of the anionic agent to the ferric solution or of the cationic agent to the thiocyanate solution resulted in decreased coalescence.These results are illustrated in fig. 1 , 2 and 3. In fig. 1, the percentage of coloured drop- lets in a sample is shown plotted as a function of the concentration of potassium thiocyanate solution atomized simultaneously with a solution of 0.5 N ferric alum CQ.5 N sulphuric acid. In fig. 2 and 3, the percentage of coloured droplets in a sample is shown plotted as a function of concentration of surface-active agents added to the solution atomized. These solutions were ammonium thiocyanate (1 N) and ferric alum (0.5 N), sulphuric acid (0-5 N). The mean diameter of all colourless droplets collected was 3.1 fQ.1 ,u, and that of all coloured droplets was 41 rtO.lp, indicating that most of the coloured droplets had been formed as a result of a single coalescence, and that the effect of multiple collisions was negligible.At the concentrations employed in these experiments, multivalent cations are generally preferentially adsorbed at the air/water interface.6 The observed coal- escence is therefore that between a droplet containing a surface outer shell of negative charge (CNS- ions) with one containing a surface outer shell of positive charge (Fe3' ions). The results in fig. 1 demonstrate that this coalescence is pro- moted by increased concentration which doubtless involves an increase in the magnitude of the charge of the double layer. It may also be inferred by extra- polation of these results that the collection efficiency is approximately zero for droplets of about 3 p diam., in the absence of oppositely-oriented surface-ion distributions, in accordance with hydrodynamic calculation for pure water droplets.The collection efficiency is thus dependent on the surface ion distribution. The results obtained with added surface-active agents (fig. 2 and 3) further indicate the importance of the magnitude and orientation of the surface charge layers in the droplets. Addition of an anionic agent reduces the magnitude of the double-layer charge with a positive outer shell while addition of a cationic agent reduces that with a negative outer shell. Experimental support is thus given to the effect postulated by Dukhin and Derjaguin and the results give some indication of the quantitative effect on collec- tion efficiency of electrical double layers within droplets. A precise quantitative evaluation of the theory must await further experimental results covering, in par- ticular, the effect of droplet size on the variation of collection efficiency with electrolyte concentration. 1 Benton and Elton, Proc. 2nd Int. Congr. Surf. Activity, 1957, 3, 587. 2 Elton, Mason and Picknett, Trans. Faraday Soc., 1958,54, 1724. 3 Mason, The Physics of Clouds (Oxford Univ. Press, 1957). 4 Pearcey and Hill, Austral. J. Physics, 1956, 9, 19. 5 Hocking, Quart. J. Roy. Met. Soc., 1959, 85, 44. 6Bach and Gilman, Acta Phys. Chim. U.R.S.S., 1938,9, 1. 7 Drrkhin and Derjaguin, Kolloid Zhur., 1959, 21, 37. 8 Adam, Physics and Chemistry of Surfaces (Oxford Univ. Press, 1941). 9 Benton, Elton, Peace and Picknett, Int. J. Air Pollution, 1958, I, 44. 10 Picknett, P h J . Thesis (London, 1958).

ISSN:0366-9033    

DOI:10.1039/DF9603000068

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

EXPERIMENTAL RESULTS RELATING TQ THE COALESCENCE OF WATER DWQPS WITH WATER SURFACES BY R. M. SCHOTLAND Dept. of Meteorology and Oceanography, New Yorlc University, New York 53, N.Y. Received 11th July, 1960 An experimental study has been made of parameters which control the coalescence of drops in the diameter range 200 to 800 microns with large liquid hemispherical targets. It is shown that the initiation of the coalescence mechanism for electrically neutral drops in equilibrium with their vapour is governed by two dimensionless parameters : where p~ = drop density, PM = medium density, y = surface tension, VN = normal component of impact velocity and D = drop diameter. 711 = PDvI$lY, n2 = PIdPD, 1. REViEW The growth of water drops by the mechanism of coalescence is basic to most theories concerned with the formation of precipitation.Normally the assump- tion is made in such theories that contact between liquids is immediately followed by coalescence. The validity of this concept has been questioned frequently. As early as 1879, Lord Rayleigh 1 noted that drops formed by the collapse of a vertically directed jet of water rebounded upon collision. He believed that this non-coalescence was caused by a layer of air trapped between the impinging surfaces which prevented true contact. His experiments also indicated that the presence of weak electrostatic fields would cause the rebounding drops to coalesce. In 1935, Gorbatschewz and co-workers described a series of experiments in which they determined the mean critical collision velocity required to insure coal- escence between colliding 1 mm drops.Their experiments indicated that the critical velocity did not depend upon surface tension. Studies have shown that the evaporation and condensation of colliding drops can also modify the coalescence mechanism. A series of papers on the subject have been presented by Deriagin and Prokhorov.3 A review of isolated coalescence experiments has been given by Browne 4 and will not be repeated here except to note the contradictory nature of the material presented. 2. INTRODUCTION The growth of a drop falling through a cloud of smaller drops may be written as where dM is the average amount of liquid water captured by a drop of radius r moving a distance dz through a field of drops whose mean liquid water content is q.In this equation the collision efficiency E represents the ratio of the number of smaller drops actually colliding with the larger drops to the number of drops in the volume nr2dz. The quantity C is the coalescence efficiency which for an individual drop collision takes a value of either 0 or 1. However, in considering an ensemble of collision resulting from randomly positioned drops the value of C in the above equation ranges as 0 < C< 1. 72 dM = nr2qECdz, (1.2)R. M. SCHOTLAND 73 UnCortunately, uncertainty exists in the knowledge of E as well as in C. Con- sequently, for the purposes of determining the factors controlling C, it is necessary to design an experiment so that E does not affect the results. The procedure adopted here was to project horizontally a stream of uniformly sized drops, allow- ing them to fall under gravity in a controlled atmosphere upon the desired target.This technique eliminated E as a variable. Provision was made so that both the fall distance of the drop and the location of the target with respect to the drop stream could be electromechanically positioned by the operator. 3. EXPERIMENTAL HYPOTHESIS It is assumed that in the absence of electrical fields the coalescence of drops which are electrically neutral and in equilibrium with their vapour is governed primarily by the following factors : (1) the density of the drop p~ ; (2) the density of the medium p~ ; (3) the surface tension of the fluid y ; (4) the component of collision velocity normal to the impacting surfaces VN; ( 5 ) the diameter of the colliding drops D.Two independent dimensionless products can be formed from the above set of parameters : 711 = PDVgD/?, (3.1) The functional form of the relationship controlling coalescence may be written 711 is proportional to the ratio of the drop kinetic energy to the energy required to deform the target surface. 712 represents the density scale factor. The hypothesis can be tested in this manner : (1) At fixed n2 show that 7c1 is a function of VN and not the total collision (2) At fixed 712 show that 711 is constant over a range y a n d p ~ . (3) For a given liquid show that n1 is a function of n2 over a range of D and velocity. media molecular weights. 4. EXPERIMENTAL APPARATUS The apparatus used in this study was essentially conventional in design.A schematic diagram of the equipment is given in fig. 1. Only the non-standard portion of the apparatus will be described. (i) DROP PRODUCTION Drops of uniform diameter were produced by electromagnetically vibrating a jet of fluid normal to its longitudinal axis as it passed through a hypodermic needle. The theory of the resolution of liquid jets into uniform drops by vibratory methods has been given by Lord Rayleigh.1 The hypodermic needles were cut to resonance length and their tips honed square. Needle sizes 20 through 27 produced uniform drops in the diameter range 300 nicrons to 1000 microns. It should be noted that it is possible to extend the size range to smaller diameters by changing the operating mode to higher harmonics.l[n order to insure electrically neutral drops, all metallic components of the apparatus were grounded and the whole system electrically screened. In addition, a wire ring connected to a variable electrical supply was placed concentric with the needle so that any residual charge could be neutralized by a polarizing field. The drop-producing mechanism was mounted on a motor-driven platform so that the vertical position of the needle with respect to the target could be controlled by the operator. (ii) TARGET The targets used in this experiment consisted of Pyrex glass tubing 6 to 30 mm in diameter filled with liquid to the desired radius of curvature. Fluid was introduced at the base of the tube in such a manner that the fluid surface could be renewed when desired.74 COALESCENCE OF WATER DROPS (iii) OBSERVATIONAL TECHNIQUE Visual observations were made of the coalescence process with the aid of stroboscopic illumination synchronized to the frequency of the oscillating needle.Permanent records were obtained photographically using an electronic flash as an instantaneous light source. I I FIG. 1 .-Schematic diagram of apparatus assembly. (A) water reservoir, (€3) flowrator, (C) water valves, @) filter, (E) psychrometer, (F) target, (G) needle, (H) scale, (I) fan, (J) needle elevator, (K) target control, (L) oscillator, (M) needle control, (N) manometer, (0) thermometer, (P) polarizing ring. 3 c? FIG. 2.-Stages of partial coalescence.R . M. SCHOTLAND 75 I 4 Ib I ,b 2k 10 J5 B 4'5 40 5 , EXPERIMENTAL RESUI~TS Bcforc discussing the results of the experiment it is necessary to define certain stages of the coalescence process.These stages can be understood more clearly from a description of a typical experimental run. At the start of the run the drop needle and target were located nearly at the same level and the drops bounced from the target unchanged in size. As the needle was raised the colliding drops continued to be reflected as before, until at a critical height the coalescence process was initiated. This stage, defined as partial coalescence, was characterized by the formation of a bridge between the drop and the target as the drop was being ejected from the target surfacc. Further height increases resulted in a continued reduction in size of the reflected drops, finally terminating in the complete coalescence of the drops with the target.The details of the stage are shown in fig. 2. TEST I In order to determine the effect of the tangential component of collision velocity upon thc coalescence mechanism, the following experiment was performed. The point of impact between a 300 micron water drop and an 8 mm hemispherical water target was varied in steps from 0 = 0 to 0 = 55" (see fig. 3.) The critical height for partial coalcscence was recorded photographically for each step. During this process the tangential component of velocity varied from 77 cm/sec at 8 = 0 to 19.5 cm/sec at 8 = 55". I€ it is assumed that VN remained constant as 0 varied and that Vz was equal to (2ghc)4 then the following relationship describes the variation of he with 0 : This relationship is plotted as a solid line on fig. 3, together with the measured values of h,, It is apparent from these data that he is independent of the tangential velocity component in the measured range. h, = (VN- V, sin e)2/2g cos2 8 (5.1) TEST 11 For a determination of the effect of a variation of the density of the medium upon the coalescence mechanism, both the drop mechanism and target were placed in a large bell jar.A vacuum pump was connected to the ja so that the density of the enclosed gas could be reduced to any desired value. Degassed distilled water was used for both the drops and target. As before the drops were in equilibrium with their vapour and electrically neutral. The results of this experiment are plotted in fig. 4 with circles, triangles and squares representing air, argon and carbon dioxide media.The lower grouping of data represents4- 3- G .I a, 42 u 2- 8 3 .e( 4- ..-I I- 0 0 O O a0 0 0 0 0 0 0 oao, 0 0 0 0 A n o 0 0 0 0 0 A 0 0 0 0 U 0 cn 0 0 00 0 o 6 ' a -A 0 3 0 Go" A 0 0 QoooA* O A , A a0 0 el Q o A 0 4 0 O8 Ao 0 0 00 o ~ o o * 0 O 6J 0 00 61 O0 C O oo 0 A o 0 o e M n . I I I I 1 I 2 4 6 0 10 12 I4 16 I'B 2'0 drop diameter (microns) FIG~S.K~T~ as a function of D, 7r2 held constant.R . M. SCHOTLAND 77 The results of these measurements are given in fig. 5 as a function of D with circles, triangles and squares representing distilled water, methyl alcohol and benzene respectively. and the standard deviation of the data are presented in table 2. The average value of TABLE 2 a1 0 distilled water 3-3 0.3 methyl alcohol 3.1 0.2 benzene 2 3 0.2 The values of nl are of the same order for the three fluids tested.However, it should be noted that the individual values differ, indicating that other factors must be considered in a complete description of coalescence. It is not suggested that n1 be considered constant even for a particular field. The behaviour of 711 for small drops may be expected to differ from these results due to the increase in relative importance of surface forces. Further, it should be recognized that the ratio of target diameter to drop diameter was always at least a factor of 10 in these experiments. For smaller diameter ratios the target diameter becomes a significant parameter . MEASUREMENT UNCERTAINTY.-The oscillations of the drop and target surfaces which occur due to the periodic nature of the drop formation and collision are the primary cause of the data uncertainty. These oscillations change both the curvature of the contacting surfaces and their relative velocity. These effects were minimized by adjusting the phase of the needle drive system so that the drop was essentially spherical as it struck the target surface. The velocity of the capillary waves produced on the target surface was sufficiently high so that the surface remained nearly undisturbed. The observations reported here were made by D. Canlas, G. Mar and A. Sultan. The research was sponsored by the Air Force Cambridge Research Centre under contract no. AF 19(6M)-6145. 1 Rayleigh, The Theory ofSound, vol. II. (Dover Publications, New York, 2nd ed., 1945). 2 Gorbatschew, Kolloid-Z., 1935, 73, 20. 3 Deriagan and Prokhorov, C.R. Acad. Sci. U.S.S.R., 1946, 54, 307. 4Browne, Quart. J. R. Met. Soc., 1954, 345, 291.

ISSN:0366-9033    

DOI:10.1039/DF9603000072

出版商:RSC    

年代:1960

数据来源: RSC