GENERAL DISCUSSION Dr. A. Arrowsmith (University of Birmingham) said In the experimental work on particle deposition Williams has measured particle sizes and concentrations after sampling with a probe of 1 cm diam in the 10 cm diam. duct. At the entrance to the probe the gas/particle flow will be influenced by the flow in the duct which will have component eddies of larger diameter than the probe. Also assuming isokinetic sampling the Reynolds number of the probe flow would be an order of magnitude less than that in the duct. Under such conditions for what lengths of the probe is the flow affected by the duct flow and thereafter it is possible that deposition may take place in the probe through mechanisms which are of a different nature or at least intensity to those which are the object of study.Dr. Ian Williams (Shell Res. Ltd. Chester) (communicated) In reply to Arrow- smith the measurements of interest in this experiment were the radial distribution of polydisperse droplets as a function of several parameters including the axial position in the duct. It has been shown that particle deposition is strongly dependent upon the Reynolds number of the flow and the particle size. For the two values of Re. no. considered the corresponding values in the probe were an order of magnitude less than in the duct ; this factor together with the short residence time of a droplet within the probe is effective in reducing deposition in the probe. Except near the duct wall the ratio of the fluid eddy diameter to the probe diameter is 1 this probably results in near laminar flow within the probe and subsequent low droplet deposition.A correction factor was obtained experimentally to take into account deposition within the probe. Twelve sampling probes each of 1.0cm i.d. and 0.5 crn id. respectively were used to sample an aerosol source of a known constant size distribution and concentration under similar dynamic conditions to those existing in the duct. A deposition factor was obtained as a function of droplet size fluid Re. no. probe diameter and probe length. This factor was applied to all subsequent experimental measurements. Alternatively it was possible to extrapolate the effect of the sampling probe to zero length and thus eliminate the effect of droplet deposition in the probe as a result.Prof. C. S. Kiang (Clark College Atlanta Ga.) said Is it possible to apply the experimental technique of Carabine and Moore to study the initial aerosol formation of aqueous sulphuric acid droplets (via the heteromolecular nucleation and hetero- molecular condensation) ? Dr. M. D. Carabine (Imperial College) said In reply to Kiang the angular varia- tion of scattered light intensity would not be sufficient if clusters of a few tens of molecules are being observed. We have indicated in the paper an approximate lower limit of 0.06 pm using He-Ne radiation. Prof. M. Kerker (Clarkson Coll. Tech. Potsdam N.Y.) said Does Carabine have some experimental results to check the efficacy of his instrument? Our exper- ience with inverting light-scattering data for distributions as broad as oo = 0.50 and a = 0.40 pm has been far less successful than he reported.Indeed for this size we find that the results become multivalued when ao>0.20. In studying the rate of 229 230 GENERAL DISCUSSION growth of sulphuric acid aerosols in a humidified atmosphere,’ we found it necessary to start with nearly 100 % H,SO in order to obtain concentrated sulphuric acid aerosols by the condensation technique. Dr. A. Moore (Imperial College) said In reply to Kerker theoretical light scatter- ing data were generated for 15 angles for the size distributions characterized by I I1 rII IV V VI VII VIII IX dM (pm) 0.1 0.1 0.3 0.4 0.4 0.6 0.8 1.0 1.o 00 0.2 0.6 0.4 0.1 0.6 0.2 0.4 0.05 0.4 The inversion programme was then tested using the following input data (a) theoretical (b) theoretical 23 % random fluctuation (c) theoretical 5 % random fluctuation.Three different starting points were used for each search. The results were as follows (a) correct answers to 3 significant figures in all cases ; (b) answers to within 10 % in all cases except for V and IX at one starting point only. Consider-ably better than 10 % accuracy was achieved in most cases; (c) Answers to within 10 % in all cases except V where there was a 25 % error in dM and VII where all starting points gave answers dM = 0.55 and o0 = 0.52. Details of the procedure will be published soon together with error contour diagrams. These should show that there is one global minimum and possibly other “ shallow areas ” which the present programme interprets as minima.It is hoped to rectify this by further sophistication of the programme. Dr. M. D. Carabine (Imperial College) said In reply to Kerker we have not yet completed our experiments to check the light scattering instrument using polymer latex suspensions of size less than 1 pm. Troublesome back reflections in simple cylindrical vessels have justified the use of the light-trap described in the paper. Moore has commented in this discussion on tests of our strategy in the angular scanning using hypothetical particle size distributions. Mr. J. Maddock (Imperial College) said We have been using a Rapaport-Weinstock Generator to produce sulphuric acid aerosols.2 This relies on mechanical atomization to disperse the aerosol into an air-stream and must therefore produce an aerosol of the same composition as the stock liquid unless the carrier gas contains water vapour.We have been using nitrogen from cylinders containing up to 15 p.p.m. water vapour. This is sufficient to dilute the droplets considerably and there- fore the gas was dried by passing it through phosphorus pentoxide. Our suppliers inform us that helium from cylinders is also likely to contain water vapour. Can Kerker state whether or not and if so how his gas supply was dried? Dr. G. H. Walker (Clark College Atlanta Ga.) said Carabine and Moore have described a potentially useful instrument which can give us valuable information about growth processes in aerosols.However there may be difficulties in this scheme at the low concentration levels which are characteristic of many aerosols (typically 105-106particles ~rn-~) unless suitable restrictions are imposed upon the size of the scattering volume and upon the concentration. These problems arise because the number of particles in a given volume fluctuate and these fluctuations (which decay L. Coutarel E. Matijevic and M. Kerker J. Colloid Interface Sci. 1967 24 338. E.Rapaport and S. Weinstock Experienfia,1955 11 363. GENERAL DISCUSSION 231 very slowly) can influence the measured size distribution. These effects have been studied theoretically first by Smoluchowski and later by Chandrasekhar and experimentally by Schaefer and Berne in optical homodyne experiments using dilute suspensions of polystyrene spheres in water.To gain some estimate of the mean lifetimes of particle number fluctuations in an aerosol we consider spheroids of 1 pm radius suspended in a carrier gas (nitrogen) at 25°C. Using the Einstein-Stokes equation we find the diffusion constant to be roughly 12 x cm2/s. If n(t) is the number of particles in a given volume at time t? then the particle number correlation function (n(O)n(t)) decays in a time z which can be estimated by z-L2/24D where L is a typical dimension of the scattering volume. For L-1 mm (say) Z-3000 s. Even for very small particles (-0.1 pm) z N 300 s. Thus one must observe the scattering volume for relatively long times in order to average out the effects of particle number fluctuations.Since one is interested in making measurements of time-dependent phenomena in an aerosol which is changing much more rapidly than the relaxation of density fluctuations time averaging is not feasible. There are several ways to avoid this problem. For a given concentration one can either increase the scattering volume or else use a flowing carrier gas system (as has been done in recent experiments where optical homodyning has been applied to aerosol measurements. 3 Disregarding the last possibility it is of interest to estimate the size of the volume needed so that the number fluctuations may be safely ignored while keeping in mind that one would like as small a scattering volume as possible to minimize the effects of scattering angle variation.First we consider a monodisperse aerosol with a number density c. The particles are statistically independent and are described by the Poisson distribution. Thus the root-mean-square number density fluctuation is given by = ,/- cY where V is the scattering volume. We can treat the fluctuations in particle number as noise and if a maximum of 4 % noise is tolerable then we must have cY2625. For a typical volume defined by an unexpanded laser beam V'2:0.03cm3 and c>,2 x lo4 particles CM-~in order not to exceed the permissable noise level. For a polydisperse aerosol the situation is similar. Suppose that we try to measure the size distribution by counting the particles in a number of different radial classes and plotting the resultant histogram.In a class with a low frequency of occurrence the effects of fluctuations can be quite significant. For example suppose we have an aerosol with a total concentration of lo5 particles ~m-~ and we use ten radial classes. Then at least one of the classes must contain less than 10 % of the particles in the scattering volume and the concentration of this particular class is less than lo4 particles ~m-~. Applying the method used before we find that V20.0625 cm3 which is substantially greater than one might ordinarily use. Obviously increas- ing the number of radial classes used (or increasing the resolution) necessitates a corresponding increase in the scattering volume. One sees that fluctuations will not present a problem in most cases provided that the scattering volume is made large enough.Only in cases of low concentration and high resolution could the scattering volume become uncomfortably large. Prof. M. Kerker (Clarkson Coll. Tech. Potsdam N.Y.) said Can Brock say anything about the forms of the size distribution of an aerosol formed in a generator which functions by cooling of a mixture of heterogeneous nuclei and vapour. With l Reu. Mod. Phys. 1943 15. Phys. Rev. Letters 1972 28. W. Hinds and P. C.Reist Aerosol Sci. 1972,3. GENERAL DISCUSSION regard to the self-preserving size distribution my understanding is that the semantics originates in the terminology for the spectral distribution of turbulence. What are the physical assumptions relevant to aerosols which are the basis of the mathematical approximations in the self-preserving size theory ? Some astrophysicists estimate that 1000 tons of interplanetary dust enter the earth's atmosphere each day.Would this be a significant factor in the global aerosol economy? Prof. J. R. Brock (Uniu. Texas at Austin U.S.A.)said In reply to Kerker ifthe conditions of growth of the heterogeneous nuclei in the vapour are known precisely it is possible in principle to determine the resultant size distribution by integration of eqn (3.5) or suitable generalizations thereof. As indicated in the paper under unrestricted pure condensational growth an initially polydisperse aerosol will become less polydisperse with time. Such behaviour provided the basis of the original Sinclair-La Mer aerosol generator.In any practical experimental situation one will have imperfect knowledge of the temporal and spatial variations of the physical parameters governing condensation. This would introduce a "randomization " whose effect is generally an increase in measured polydispersity over that predicted from the calculation based on imperfect knowledge. The term "self-preserving " size distribution has been perhaps the source of some confusion. A " self-preserving " size distribution is one found through solution of a coagulation equation using the similarity transformation as proposed originally by Friedlander and colleagues. However an asymptotic limit distribution may exist for a particular coagulation process for which the similarity transformation or " self-preserving " hypothesis may not be valid.The physical assumptions pertinent to " self-preserving " size theory require extensive discussion such as that provided in ref. (1 1). Various estimates tend to show that the contribution of extraterrestrial dust to the global aerosol economy is of negligible order providing less than 0.01 % of the total mass inventory on a world-wide basis. Dr. E. R. Buckle (Shefield University)said With regard to the paper by Brock the coagulation process as usually modelled leads to theoretical distributions in an aged aerosol that are independent of the initial populations of particles. In a spontane- ously condensed aerosol of the kind I described the growth of particles by vapour condensation eventually becomes so slow even when the vapour is still appreciably supersaturated that coagulation becomes the only mechanism of further enlargement.This will not occur while the particles remain small and volatile for under such conditions the particle sizes are governed by much faster processes of growth and decay. While these processes are continuing to dominate the growth kinetics the initial state (i.e. the state of the vapour before the spontaneous process began) is kept in sight in the sense that the aerosol is evolving towards a final state thermo- dynamically related to the initial state. The so-called '' Kelvin effect " in aerosols viz. the tendency for the large particles to grow at the expense of the small arises in the need of the system to attain the final stable distribution by the indefinite enlarge- ment of fewer and fewer growing centres.According to the kinetic theory this effect will slow down in a homogeneous aerosol while the particles are still very small but because of the thermodynamic requirements coagulation processes will not be able to disturb the size distribution while the particles remain sufficiently volatile. Dr. R. G. Picknett (Chem. Defence Est. Porton Down) said The paper by Roach Adams Garland and Goldsmith should prove invaluable in fog studies. One point GENERAL DISCUSSION of note was the sudden increase in depth of fog which occurred between phases IIa and IIb. I have always thought that sudden changes in depth were largely associated with drift fog zones of greater or less depth being presented to the observation point as they are carried by the wind.Thus depth change should be associated with wind. Yet in the transition between phases IIa and IIb there was a sudden increase in depth of 5-10 m associated with a minimum in the wind. Is this attributed to the formation of fog in previously clear air or is there some other explanation? Dr. T. W. Roach (Meteorological Oflice Bracknell) (communicated) When observations are made from one site it is not possible to determine the relative contributions of drift and local development to an observed change in a parameter such as fog depth. It is however reasonable to suppose that changes in a shallow radiation fog which occur within a period of a few minutes are more likely to be due to drift while those changes taking place over 15 min or longer are more likely to be due to local development.The ‘‘ sudden ”change in fog depth referred to by Picknett in fact took about 20min so that we consider this to be more likely to be due to development than due to drift particularly as the wind dropped. Our main thesis was that if the wind dropped turbulent diffusion weakened or even ceased thus allowing radiative cooling to predominate. Dr. M. B. Green (British Gas Corp. London) said An application of chimney dispersal models which is particularly relevant to the symposium is their use in the prediction of the size of visible plumes found by condensing effluents. The essential feature of the analysis is to use the temperature and concentration profiles obtained from the dispersal formulae to compute via vapour pressure considerations the local levels of saturation of the effluent/air mixture.The volume bounded by the surface corresponding to a supersaturation of unity is to a first approximation the region in which condensation of the products is likely to occur. Wessel and Wisse have used this approach in conjunction with the Pasquill dispersal model to develop nomograms for the prediction of the size of cooling tower plumes. In view of the statements made in this paper about the differences between instantaneous and time averaged values of plume dispersal does Moore believe that a true estimate of the saturation region can be obtained with the classical dispersion formulae ? Dr.D. J. Moore (Central Elect. Gen. Board Leatherhead) said In reply to Green the paper by Wessel and Wisse does not take account of the effect of relative motion on plume growth or of plume rise on the plume temperature. These effects will tend to some extent to be self-cancelling with regard to condensation in the plume but Wessel and Wisse’s model should be regarded as a first attempt to solve this problem. It could be seriously in error in the meteorological conditions for some sources but one would need to put numbers in the plume trajectory and rise equations to find out when this would happen. Dr. D. J. Moore (Central Elect. Gen. Board Leatherhead) said I agree with Brock that gas washed plumes can have negative buoyancy especially if they contain liquid water on emission and this subsequently evaporates.It is possible that such plumes could produce higher ground level concentrations of a pollutant which had been partly removed by washing than the corresponding unwashed plume emitted with Atm. Em. 1971,5 751. Atm. Em. 1971,5,743. GENERAL DISCUSSION normal buoyancy (at around 100°C above ambient temperature). Re-heating the washed plume would overcome this problem but might be difficult to achieve on existing plant. Dr. R. G. Picknett (Chem. Defence Est. Porton Down) said Can Moore give more information about the formulae he quotes for a plume with a density at ambient temperature and pressure which differs from that of air? Dr. D. J.Moore (Central Elect. Gen. Board Leatherhead) said :In reply to Picknett the plume rise and dilution are really a function of the buoyancy flux vpb.For plumes which have the same density at ambient temperature and pressure as air where 0; = temperature excess of effluent = 6*-0 and p; = density difference between ambient air and effluent = pe-po = Ap. Since Qh = V6hp,Cp it follows that Tip; may be replaced by Qh/Cp6for plumes of hot air. The general expression for plume rise would therefore be one using the term V’;Cp6 rather than Qh,and this expression would apply to an emission of any density. (The term CpO occurs because of the presence of a similar term in the denominator of the parameter Al).