Growth Of Cloud Drops by Condensation: A Criticism of Currently Accepted Theory and a New Approach

R. C. Srivastava Laboratory for Atmospheric Probing, Department of the Geophysical Sciences, The University of Chicago, Chicago, Illinois

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Abstract

The currently accepted theory of the growth of cloud drops by condensation employs an equation for the rate of increase of drop mass and an equation for the supersaturation. The latter equation gives the average supersaturation over a large volume, or the macroscopic supersaturation. Use of this supersaturation in the equation for the growth of cloud drops is criticized. In a first approach at a microscopic theory, the average supersaturation over the volume occupied by a drop, called the microscopic supersaturation, is used to calculate the growth of the drop. The microscopic supersaturation can differ from drop to drop due to randomness in their spatial distribution and is affected differently by fluctuations of vertical air velocity than the macroscopic supersaturation. In a second approach at a microscopic theory, the diffusion equations for water vapor and heat, together with appropriate boundary conditions, are solved for an assemblage of drops. It is shown again that a microscopic supersaturation may be defined for calculating drop growth and that this supersaturation can also differ from drop to drop and responds differently to vertical air velocity fluctuations than the macroscopic supersaturation. In the microscopic approaches both the random distribution of drops and vertical air velocity fluctuations can affect the growth of cloud drops by condensation; this is in contrast to conclusions drawn from the currently accepted theory. Estimates of the variance of the microscopic supersaturation are given. It is shown that diffusive interactions between drops in a population can be neglected if the dimensionless parameter [(l*/r0) (Dτ)] where l* is the volume fraction of the drops, r0 is a typical drop radius, D is the diffusivity, and τ is the age of the diffusion process, is very small compared to unity.

Abstract

The currently accepted theory of the growth of cloud drops by condensation employs an equation for the rate of increase of drop mass and an equation for the supersaturation. The latter equation gives the average supersaturation over a large volume, or the macroscopic supersaturation. Use of this supersaturation in the equation for the growth of cloud drops is criticized. In a first approach at a microscopic theory, the average supersaturation over the volume occupied by a drop, called the microscopic supersaturation, is used to calculate the growth of the drop. The microscopic supersaturation can differ from drop to drop due to randomness in their spatial distribution and is affected differently by fluctuations of vertical air velocity than the macroscopic supersaturation. In a second approach at a microscopic theory, the diffusion equations for water vapor and heat, together with appropriate boundary conditions, are solved for an assemblage of drops. It is shown again that a microscopic supersaturation may be defined for calculating drop growth and that this supersaturation can also differ from drop to drop and responds differently to vertical air velocity fluctuations than the macroscopic supersaturation. In the microscopic approaches both the random distribution of drops and vertical air velocity fluctuations can affect the growth of cloud drops by condensation; this is in contrast to conclusions drawn from the currently accepted theory. Estimates of the variance of the microscopic supersaturation are given. It is shown that diffusive interactions between drops in a population can be neglected if the dimensionless parameter [(l*/r0) (Dτ)] where l* is the volume fraction of the drops, r0 is a typical drop radius, D is the diffusivity, and τ is the age of the diffusion process, is very small compared to unity.

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