Steady-State Diffusion into a Streaming Sphere at Low Reynolds Number

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Abstract
A solution of the steady-state Smoluchowski equation, describing diffusion into a spherical sink streaming with constant velocity relative to the fluid, is obtained as a power series in a parameter which is directly proportional to the Reynolds number of the flow. For small values of Reynolds number the series converges. The concentration and flux to a freely-falling cloud droplet (aerosol particle) in air is calculated. The effect of the motion of the droplet on the flux is proportional to a first approximation to the square of Reynolds number and consequently except for very large times of observation exerts a negligible influence on the diffusion controlled growth of the droplet. An extension of the method to nonstationary diffusion problems is indicated.

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