Analytic Studies of Cloud Droplet Coalescence I

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Abstract
The kinetic equation for the pure growth-by-coalescence process is solved exactly for three types of overall collection probability: proportional to the sum of droplet volumes, proportional to the product of droplet volumes, and constant. Series and asymptotic expressions are given for a variety of initial conditions, and methods indicated for use of arbitrary initial functions. Calculations are presented for initial volume distributions equivalent to Gaussian distributions in radius with σ/ṙ = 0.37, O.25, 0.15 and O.123, and several stages of real time from 69 to 1600 sec. We assume 1 gm m−8 water content, a mean volume radius of 10 μ, and normalization of the collection efficiency formulas to fit those of Shafrir and Neiburger for a 30–10 μ collision. Abstract The kinetic equation for the pure growth-by-coalescence process is solved exactly for three types of overall collection probability: proportional to the sum of droplet volumes, proportional to the product of droplet volumes, and constant. Series and asymptotic expressions are given for a variety of initial conditions, and methods indicated for use of arbitrary initial functions. Calculations are presented for initial volume distributions equivalent to Gaussian distributions in radius with σ/ṙ = 0.37, O.25, 0.15 and O.123, and several stages of real time from 69 to 1600 sec. We assume 1 gm m−8 water content, a mean volume radius of 10 μ, and normalization of the collection efficiency formulas to fit those of Shafrir and Neiburger for a 30–10 μ collision.

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