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H. R. Pruppacher

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H. R. Pruppacher

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The classical theory for homogeneous ice nucleation in supercooled water is investigated in the light of recent data published in various physico-chemical journal on the physical properties of supercooled water and in the light of recent evidence that the cooperative nature of the hydrogen bonds between water molecules is responsible for a singularity behavior of pure supercooled water at −45°C.

Recent rates for homogeneous ice nucleation in supercooled water drops field from field experiments at the cirrus cloud level and from cloud chamber studies were shown to be quantitatively in agreement with the laboratory-derived lowest temperatures to which ultrapure water drops of a given size have been supercooled. Using these verified nucleation rates together with the recent physical property data for supercooled water, the activation energy for the transfer of water molecules across the ice-water interface was computed using the classical nucleation rate equation. The thus computed values are significantly different from earlier values that were based on the activation energy for viscous flow but are consistent with present knowledge of structure of supercooled water. The present results eliminate the earlier discrepancies that existed between the results of the classical nucleation equation, the field and laboratory data, and the results from the molecular model of Eadie.

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H. R. Pruppacher and R. Rasmussen

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An experimental study of the effect of ventilation on the rate of evaporation of millimeter sized water drops failing at terminal velocity in air has been carried out in a wind tunnel where drops were suspended freely in the tunnel air stream. It was found that for drops in the size range 1150 µm≤a 0≤2500 µm, the mean ventilation coefficient f̄vh could be expressed as f=(0.78±0.02)+(0.308±0.010)X, where X=N &frac13 Sc,v N½ Re. Previously, we showed that this relation holds for drops in the size range 60 µm≤a 0≤400 µm. Taken together, our present and previous data suggest that with reasonable accuracy f̄=0.78+0.308X, for 1.4≤X≤51.4 (60 µm≤a 0≤2500 µm). For 0≤X≤1.4 (0≤a≤60 µm), one may use our previous result f=1.00+0.108 X 2. To illustrate how the present data may be applied, we computed the distance which is required for a water drop to travel from cloud base through a NACA Standard Atmosphere of various relative humidities, in order to reach the earth's surface with a given size.

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R. Rasmussen and H. R. Pruppacher

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A study has been made on the melting behavior of frozen drops suspended freely at terminal velocity in the UCLA Cloud Tunnel. The relative humidity of the air ranged between 25 and 95%. The warming rates of the tunnel air stream ranged from 2 to 5°C min−1, which for the studied ice particles of radius between 200 and 500 μm, corresponded to warming rates of 0.8 to 5.2°C per 100 m of fall. The rate of melting of the frozen drops and their fall behavior during melting were continually monitored by motion picture. From these observations the dimensions of the ice core inside the melting drop was determined as a function of time, and from the latter the total melting time was found. The present wind tunnel observations were compared with the theoretical predictions of Mason (1956). Considerable disagreement with Mason's theory was found. This disagreement was attributed to the pronounced asymmetric melting and the internal circulation in the melt water, both of which were disregarded in Mason's theory.

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R. L. Pitter and H. R. Pruppacher

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The hydrodynamic interaction between simple ice plates, idealized as oblate spheroids of axis ratio 0.05, and water drops, assumed to be spherical, was numerically investigated for atmospheric conditions of −10C and 700 mb. The ice plates had semi-major axis length between 147 and 404 µm and the water drops had radii up to 53 µm. Since the ratio of the mass of the drop to the mass of the crystal was small, the superposition model was found to be satisfactory. The flow fields around drops were those of LeClair et al., and the flow fields around oblate spheroids were those of Pitter et al. From the trajectories of the water drops relative to the ice crystals, collision efficiencies were determined. The model predicts preferential riming of the drops at the edges of crystals under certain conditions, in agreement with field observations in atmospheric clouds.

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H. R. Pruppacher and R. L. Pitter

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A physical model which predicts the shape of water drops falling at terminal velocity in air is presented. The model is based on a balance of the forces which act on a drop falling under gravity in a viscous medium. The model was evaluated by numerical techniques and the shape of water drops of radii between 170 and 4000 μ (equivalent to Reynolds numbers between 30 and 4900) was determined. The results of our investigation show that the drop shapes predicted by the model agree well with those experimentally observed in our wind tunnel. Both theory and experiment demonstrate that: 1) drops with radii ≲170 μ are very slightly deformed and can be considered spherical, 2) the shape of drops between about 170 and 500 μ can be closely approximated by an oblate spheroid, 3) drops between about 500 and 2000 μ are deformed into an asymmetric oblate spheroid with an increasingly pronounced flat base, and 4) drops ≳2000 μ develop a concave depression in the base which is more pronounced for larger drop sizes. The relevance of these findings to the process of drop breakup is discussed.

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S. N. Grover and H. R. Pruppacher

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A one-dimensional model of the effect of the vertical component of atmospheric turbulent fluctuations on the collection of micron-size aerosol particles by cloud drops is presented. The model includes simultaneous effects of the differential inertial response of the drop and particle to turbulent accelerations and the hydrodynamics of air flowing around the drop. Based on the one-dimensional results, it is inferred that three-dimensional atmospheric turbulence should cause a substantial increase in the collection of particles in the approximate radius range of 0.5 to 2.5 μm, and that this increase should be most prominent for cloud drops in the neighborhood of 30 to 40 μm radius. Also discussed am the expected effects of turbulence on related cloud microphysical processes, including the collection of small droplets by large drops in atmospheric clouds, the collection of submicron particulates and pollutant gases by cloud drops, and the evaporation of cloud drops in subsaturated air.

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K. V. Beard and H. R. Pruppacher

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Measurements of the drag on small water drops falling in water-saturated air at terminal velocity were carried out in a wind tunnel for Reynolds numbers R between 0.2 and 200. The fractional deviation (D/Ds) − 1 of the actual drag D from the Stokes drag Ds was determined as a function of R and empirical formulae for (D/Ds) − 1 were derived for the three ranges 0.2≤R≤2,2≤R≤21 and 21≤R≤200. From these relations drag coefficients were computed and the terminal velocity of water drops of radii between 10 and 475 μ calculated for drops falling in water-saturated air and at pressure levels of 400, 500, 700 and 1013 mb, where the temperature was assumed to be −16, −8, 14 and 20C, respectively.

It is shown, for 0.2≤R≤200, that the values derived for the drag on water drops are in good agreement with those for the drag on solid spheres experimentally determined by Pruppacher and Steinberger, and with those for the drag on solid spheres theoretically computed by Rimon. It is pointed out that there is a strong scatter among the values for the terminal velocity of water drops given in literature. Out data agreed quite closely with those of Gunn and Kinzer.

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K. V. Beard and H. R. Pruppacher

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An experimental study of the effect of ventilation on the rate of evaporation of small water drops falling at terminal velocity in air has been carried out in a wind tunnel where water drops could he suspended freely in the tunnel airstream. For Reynolds numbers NRe≳2 it was found that the Sherwood number NSh was linearly related to NRe 1/2NI, in a manner which could best be expressed by the equation 1/2 Nsh=0.78 + 0.308 Nsc 1/2NRe 1/2, where NSc is the Schmidt number. For NRe≲ the Sherwood number was found to smoothly approach 1/2 NSh=1 at NRe=0, with d(1/2NSh/d(NSc 1/2)=0 according to the relationship 1/2 NSh=1.00 + 0.108 (NSc 1/2NRe 1/2)2. The experimental results are discussed in the light of previous experimental and theoretical work reported in the literature. Excellent agreement was found between our experimental results and the numerical results of Woo and Hamielec presented in an accompanying article. Two tables are given that easily allow computing the evaporation rates for cloud drops and small rain drops of sizes between 20 and 600μ radius for a wide range of atmospheric temperatures from 0–40C and relative humidities from 0–100%. As an example, the evaporation rate of drops failing in a NACA standard atmosphere is calculated and compared to similar computations reported in the literature.

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P. K. Wang and H. R. Pruppacher

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Experiments have been carried out to determine the efficiency with which aerosol particles of 0.25 μm radius are collected due to Brownian diffusion, and due to hydrodynamic, phoretic and electrical effects by water drops of 150 to 2500.μm equivalent radius falling in subsaturated air. In the absence of electrical effects it was found that with increasing drop size the collection efficiency decreases to a minimum and then rises again as the collection due to phoretic forces is overcompensated by the collection due to hydrodynamic forces. With further increase in drop size the collection efficiency was found to rise to a maximum, This rise was attributed to hydrodynamic effects in the rear of the drop which increase as the stagnant eddy at the downstream end of the falling drop increases in size, but progressively decrease as the drop assumes a size, and thus a Reynolds number, large enough for turbulent eddies to be shed from the rear of the drop. The present results are qualitatively consistent with the predictions of experiments reported in the literature and quantitatively agree with the theoretical predictions made by the model of Grover et al. (1977). Electrical charges on drop and aerosol particles were found to significantly raise the collection efficiency, in good agreement with the efficiency theoretically predicted by the model of Grover et al. (1977).

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