THE AGGREGATION OF SMALL ICE CRYSTALS BY C. L. HOSLER AND R. E. HALLGREN Dept. of Meteorology, College of Mineral Industries, The Pennsylvania State University, University Park, Pennsylvania Received 7th June, 1960 The growth of small aggregates of ice crystals has been observed between -6°C and -25°C by mounting an ice sphere in a moving cloud of ice crystals. The density of the aggregate formed increased with increasing temperature, and observations of the aggregate growth showed that the bonds between ice crystals permit folding of crystal towers. The higher the temperature, the more folding was noted. The proportion of the ice crystals in the path of the aggregate that became attached to it was temperature-dependent, show- ing a maximum collection efficiency at -11°C. Plates formed aggregates at a greater rate than did columnar crystals ; hence, when the cloud composition changed from plates to columns as the temperature increased above -11”C, the amount of aggregation diminished.These data and other evidence are interpreted as indicating that the aggrega- tion of the ice crystals depends upon the existence of a liquid film on the ice surfaces. The film thickness is greater at higher temperatures. A large part of the precipitation falling in middle and high latitudes goes through a stage involving the formation of aggregates of a great number of indi- vidual ice crystals to form the “snowflakes” observed at the ground. These aggregates, upon melting, give rise to much larger raindrops than would otherwise be observed if the ice crystals remained detached.In clouds composed entirely of ice formed at low temperatures, the formation of precipitation particles capable of high rates of fall and rapid subsequent growth may, to a large extent, be de- pendent upon aggregates of individual ice crystals. Knowledge of the degree to which ice crystals cohere on contact is important in evaluating some mechanisms suggested for explaining charge generation and separation in clouds. The follow- ing experiments were aimed at determining the factors acting to limit aggregation in clouds. Systematic experimentation on the ability of ice to stick to ice was begun in September, 1 842, by Faraday. His investigations were periodically resumed and described in his diary as late as February, 1860. 1-3 J.Thomson 4-6 and W. Thomson 7 attributed the phenomenon to melting of ice on contact with ice due to pressure and subsequent freezing. Faraday, however, by careful experimental design, succeeded in producing regelation under conditions where the pressures were negligible and, in his mind, insufficient to produce melting. In fact, Faraday 3 noted flexible adhesion so that torsion forces actually tended to separate the pieces of ice involved. This led him to conclude that water exhibited a property that made it possible for a water film to remain liquid in contact with ice, so long as ice was only on one side of the water ; but when surrounded by ice on both sides, it became solid and formed a bond between the two pieces of ice. In the years since the work of Faraday, many experiments have been performed which bear upon the nature of the surface of ice.Some of these have dealt with the cohesion of pieces of ice 8 or the adhesion of ice to other solids,9 others with the slipperiness of ice.10 A considerable amount of evidence has now been ac- cumulated which indicates the untenability of the concept that these phenomena are the result of pressure-induced melting. A number of these observations were summarized by Jordan et aZ.10 in a Report on Friction on Snow and Ice. It seems 200C. L . HOSLER AND R . E. HALLGREN 201 clear that the hypothesis of Faraday can now be supported by some physical- chemical reasoning, such as that proposed by Weyl, and is most likely the correct explanation of the several surface properties of ice.Nakaya and Matsumoto,s in an interesting experiment in which ice spheres were manipulated, noted the ability of two cohering ice spheres to rotate when in contact with one another prior to separating, indicating the presence of a liquid film on ice at temperatures below the melting point. Laboratory measurements of aggregation of ice crystals at -336OC12 lend support to radar observations indicating aggregation in natural clouds at temperatures this low.13 Fig. 1 presents some of the results of an experiment in which the force required to separate temp., "C FIG. 1.-Plot of the force required to separate manipulated ice spheres against temperature at saturation vapour pressure over ice (ref. 12). two ice spheres was measured after the two spheres had been carefully placed in contact with one another with a minimum of force.12 Each point represents the mean of from 10 to 15 measurements.The ice spheres were at the same temper- ature, and the vapour pressure was equal to the saturation vapour pressure over ice at that temperature. Two interesting features in these data were the con- sistency of the observations and the fact that measurable cohesion of the ice spheres was noted at temperatures down to -25°C." Presuming some degree of roughness of the surface of the spheres used to obtain the data in fig. 1, one could expect a great variation in the area of contact of the spheres and, hence, in the force required to separate them. However, the ease with which a smooth curve can be drawn in fig. 1 suggests the presence of a liquid film of sufficient thickness to give a rather uniform area of contact.The thickness of the film is temperature- dependent, increasing exponentially with:temperature. When the same experiment * Faraday apparently did not work below 0°C or, if he did, the cohesive forces were so small that he could not detect them, for he does not mention the phenomenan of regelation below 0°C. a*202 AGGREGATION OF ICE CRYSTALS wasperformed in an environment flushed with dry air, no sticking was observed below - 3°C. Apparently, when rapid evaporation occurs, the quasi-liquid film is absent or greatly reduced in effectiveness. Hori et al.14 have also gathered evidence of the possibility of thin liquid water films coexisting with ice at low temperatures. More recently, Jellinek,g in ex- tensive measurements of the adhesive properties of ice with metals, concluded that the best explanation for the observed variation in tensile strength of the bond between ice and metal was the existence of a liquid film whose thickness diminished with decreasing temperature, leading to a linear increase of the strength of the bond with decreasing temperature down to - 25°C.One reason for the existence of a layer of " distorted " water on the surface of an ice crystal has been explained by Weyl. His hypothesis states that, in order to keep the surface-free energy at a minimum, the surface ions must be polarized and the protons must be slightly recessed to form a dipole layer on the surface. Further- more, some finite distance below the surface is required as a transition between this distorted surface layer and the bulk structure of water or ice.This transition layer may retain the characteristics of a liquid at temperatures below the melting point of ice. We have suggested that such a distorted layer in a water surface is responsible for the radius-dependence of the spontaneous freezing of water droplets and that the degree of inhibition of ice formation may be a manifestation of the depth of penetration of a distorted structure originating in the surface.ls~ 16 Pertinent experiments 15 tended to show that freezing temperatures of water in capillaries was dependent solely on the capillary diameter and not upon volume or surface area. High-speed stereoscopic motion pictures 17 indicated that nucle- ation of the ice phase in capillaries occurred not at the surface, but in the interior.Kachurin 18 also noted that ice formed first in the centre of a droplet and radiated outward toward the surface, In spite of the experimental evidence that points toward peculiarities in the surface of water and ice, lack of quantitative evidence of Weyl's ideas has deferred wide acceptance of this concept to explain such phenomena as the cohesive properties of ice. In order to study the factors governing the amount of aggregation in an ice cloud, a vertical wind tunnel was constructed 19 within a cloud chamber in which both temperature and vapour pressure could be varied. A schematic diagram of the apparatus is shown in fig. 2. In the test section of the vertical wind tunnel, air speeds, temperatures, and vapour pressures were produced to simulate those which are encountered in the atmosphere.A small ice sphere (127p or 360p diam.) was suspended on the end of a fibre pointing into the air stream and observed while cloud particles were drawn past it at speeds approximating the terminal fall velocity encountered by an ice particle of comparable size falling through a cloud. The cloud particles were from 7 to 18 p diam. in concentrations of 3,000 to 20,000 cm-3. The ice sphere, which subsequently became an aggregate of from 200 to 100Op diam., was observed during its growth, and its dimensions were periodically measured. At the end of an experiment the aggregate was melted quickly and its liquid water content determined. The concentration, crystal type mass and dimensions of the cloud particles were measured. Plastic replicas of ice crystals were counted and measured with an optical microscope, and electron photomicrographs of shadowed replicas were used to obtain the thickness of the crystals.Hence, it was possible to observe the growth of an aggregate of ice, knowing those parameters that would presumably have some effect on its rate of growth. It was then possible to calculate the percentage of ice crystals in the path of the ice sphere that collided with, and adhered to, the sphere. This collection efficiency and the density of the aggregate were studied as a function of temper- ature, relative fall velocity, crystal type, mass of the collected crystals, and size of the collector. Because of the velocity of the small crystals, the collision between two crystals could not be actually seen, The growth of the aggregates was quite interesting.C .L. HOSLER AND R . E . HALLGREN 203 but the overall growth of the sphere could be closely observed. Very frequently the growth was in the form of a tower of crystals. Some towers would extend COMMERCIAL I FREEZER (20"X 24'X 72") Blower T FIG. 2.-Schematic diagram of vertical wind tunnel within a freezer. c t l 0 Q-l 0 -066 A 0 5 4 6042 a 0 3 0 7 -6 -8 -10 -12 -14 -16 -10 -20 -22 -24 temp., "C FIG. 3.- Plot of aggregate density as a function of temperature for collectors of 127 and 360 p initial diam. 0 collector of 360 p diam. x collector of 127 p diam. (standard deviation indicated beside points) as much as 1 0 0 ~ before collapsing or folding.In general, extended towers were more common at the lower temperatures than at the higher temperatures. They204 AGGREGATION OF ICE CRYSTALS also seemed to be more rigid at the lower temperatures and had a greater tendency to collapse as a unit, whereas at the higher temperatures they seemed to fold into the aggregate. In other words, the bonds were more mobile at the higher tem- peratures, an observation which parallels that by Nakaya and Matsumoto men- tioned above.8 In our experiment, the aggregate after being rotated ninety degrees showed that the aggregate, although of a very low density, did not actually have holes where a crystal could pass through without being captured. Although there may not have been crystals on the immediate surface of the aggregate, collision would occur somewhere within the aggregate.The aggregates appeared quite fragile in many cases ; but, at least on the scale that could be observed through the microscope, fracturing of the aggregate occurred on only a few occasions. The fact that the aggregated towers folded to consolidate the mass illustrates the flexibility of an ice-to-ice bond as noted by Faraday. Fig. 3, a plot of aggregate density against temperature, shows further evidence of this flexibility and con- solidation. The density increases as the temperature increases. In order to define FIG. -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 temp., "C cloud, as a function of temperature. 4.-Collection efficiency of an ice sphere of 127 p initial diameter in an ice crystal more precisely the reason for the temperature dependence of aggregate density, the effect of changing ice-crystal mass was evaluated.At - 8°C and - 9°C there was a rather large variation in ice-crystal mass from one experiment to the next. When the episodes with large crystal mass were compared to those with small crystal mass, it was found that there was no systematic variation in density due to changing mass. Between - 11°C and - 24°C the change in mass was insignificant, but there was a quite significant change in density. From these facts we are led to conclude that the aggregate density is determined by the temperature at a given collection rate. Fig. 4 shows the collection efficiency obtained from 98 measurements for a sphere of 127 ,u initial diameter with a relative fall velocity of 43 cmlsec.Fig. 5 gives the collection efficiency using 102 measurements for a 360,~ sphere with a relative fall velocity of 107 cmlsec. The deduction can be made from fig. 4 and 5 that some degree of sticking took place at all temperatures investigated in this experiment. When one considers the masses and the speeds of the particles involved, it becomes difficult to conceive that, at -220°C and below, the sticking was occurring at points where contact pressures exceeded the 2000 atm required for melting. In order to achieve the necessary high pressures on contact, in- conceivably small contact areas would have to have been effective in holding the crystals together and preventing them from continuing in the air stream in theC.L . HOSLER AND R . E. HALLGREN 205 face of the drag by the air stream and the buffeting by other crystals. Also, the folding of the crystal towers would be difficult to explain on the basis of pressure- induced melting. In the lower temperature range the collection efficiency or the degree of sticking was proportional to the temperature-the lower the temperature, the less sticking. However, at a temperature of - 11°C the collection efficiency unexpectedly reached a maximum, and as higher temperatures were approached, the collection efficiency fell to the value obtained for the lowest temperatures investigated. Several phen- omena associated with ice occur close to the temperature of - 11 "C. There was the possibility that we were seeing a manifestation of the maximum vapour pressure gradient between water and ice, although there was no evidence of the presence of supercooled water.Examination and re-evaluation of our apparatus and technique eliminated this possibility, because at no time did we observe ice crystal growth in the test section of the wind tunnel ; the vapour pressure was apparently very close to that for ice at the temperature of the test section. The average mass 0 - - - - 1 I I I I l I I I I I I I I I I I G ,206 AGGREGATION OF ICE CRYSTALS The procedure was to use runs at the same temperature but with different per- centages of plates and columns. The data from two runs with a small percentage of plates were averaged and inserted into an equation with two unknowns : the collection efficiency of plates and that of columns. Another equation was then obtained from another two runs having a higher percentage of plates.The two equations were then solved for the individual collection efficiencies. The results from eight such pairs of equations for temperatures of - 6°C to - 11°C showed a higher collection efficiency for the plates than for the columns. The collection efficiencies for the plates alone were higher than those observed at - 11 "C in fig. 4 and 5, whereas the collection efficiencies for the columns were lower than observed at -6°C. These experiments were designed primarily to shed light upon the fate of an ice particle falling through an ice cloud. The complete explanation of the results will have to wait for experiments specifically designed to determine the surface properties of ice under various conditions.The fact that aggregation occurs at the temperatures investigated, together with the observation of folding of crystal towers and of increased aggregate density with increased temperature, provides additional evidence of the existence of a quasi-liquid film on the surface of ice between 0°C and -25"C, and perhaps at lower temperatures. (The thickness of the film is apparently greater at higher temperatures.) According to earlier experiments, the bond between two ice spheres is stronger at higher temperatures up to 0°C; increased area of contact results in increased bond strength, but, in the case of the collision of small ice crystals, once the contact area or bond reaches some critical size, they will stick, and further increase in contact area does not contribute to greater collection efficiency or better sticking.In our experiments the collection efficiencies de- creased from - 11°C toward higher temperatures. The most important factor in determining collection efficiency above - 11°C is the change in crystal type from plates to columns. Perhaps we should expect plates and columns to behave differently, but we are not able to state with any assurance what is responsible for the difference. The possibilities include the aerodynamic characteristics, the mechanical forces acting at the time of the collision and the change in the dominant type of crystal face available to engage in the collision process. In the light of the evidence pointing to the existence of a quasi-liquid film on the ice surface and the possibility of explaining the existence of such a film on the basis of minimizing surface energy, we would be inclined to suggest that the change in the dominant type of crystal face involved in the collisions may cause the change in collection efficiency.This increased sticking may be due merely to the larger area of contact, which would increase the likelihood of bonding between the two surfaces. On the other hand, there are structural and energy differences between the two types of ice crystal faces. Moreover, the faces grow at different rates depending upon temperature, in the range in which the aggregation was measured. This suggests that, if a liquid film exists on the crystal, such a film would have different characteristics on the two crystal faces. These experiments may indicate that the basal plane is stickier than the planes parallel to the c-axis and that the decreased probability of basal planes colliding at the higher temperatures more than compensates for the tendency for increased aggregation with increased temperature that is in evidence at tem- peratures below - 11°C.This hypothesis could be tested by producing clouds consisting of only plates and columns, respectively, and then introducing them into the test section of the wind tunnel at varying temperatures to observe collection efficiency. This would require a rather elaborate apparatus. 1 Faraday (Bell a- d Sons Ltd., London), 1933, 4, 79 ; 7, 382. 2 Faraday, Phil. Mag., 1859, 17, 162.C. L. HOSLER AND R . E. HALLGREN 207 3 Faraday, Proc. Roy. Soc., 1860, 10, 440. 4 Thomson, Proc. Roy. Soc., 1861, 11, 198. 5 Thomson, Proc. Roy. SOC., 1859, 10, 152. 6 Thomson, Trans. Roy. SOC. Edin., 1859, 16, 575, 7 Thomson, Phil. Mag., 1850, 37, 123. 8 Nakaya and Matsumoto, SIPRE Res. Paper, # 4, 1953. 9 Jellinek, J. Colloid Sci., 1959, 14, 268. 10 Jordan, SIPRE Report Friction on Snow and Ice (U. of Minnesota, 1955), p. 286. 11 Weyl, J. Colloid Sci., 1951, 6, 389. 12 Hosler, Jensen and Goldshlak, J. Meteol., 1957, 14, 415. 13 Douglas, Gum and Marshall, Stormy Weather Research, Group Report MW-21 14 Hori, Teion and Busuri, Low Temp. Sci. Lab., ser. A, 1956, 15, 34. 15 Hosler and Hosler, Trans. A. G. U., 1955, 36, 126. 16 Hosler, Proc. Toronto-Met. Conf., 1953, 253. 17 Hosler and Spalding, Penn. State Univ. Final Report AF Contract 19(604-140), 18 Kachurin, Izvest. Akud. Nauk U.S.S.R., ser. Geofiz, 1951, 2, 43. 19 Hosler and Hallgren, Penn. State Univ. Final Report NSF G-3477, 1960, p. 39. (McGill U., July 1956), p. 45. 1955, p. 7.