Theoretical Collision Efficiencies of Cloud Droplets at Small Reynolds Numbers

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  • 1 Dept. of Physics, New Mexico Institute of Mining and technology, Socorro 87801
  • | 2 National Center for Atmospheric Research, Boulder, Colo. 80302
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Abstract

An outline is presented of a new solution of the hydrodynamic equations for the motion of two spherical drops falling in a viscous fluid at small but non-zero Reynolds numbers. In this solution the flow of the medium is assumed to be governed by a modified form of the Oseen equations, and the boundary conditions at the two drops are simultaneously satisfied approximately. Although the equations allow partially for the effects of fluid inertia, a factor omitted in previous analyses based upon Stokesian hydrodynamics, the method of solution requires use of approximations to a larger extent than Stokesian solutions used by Davis and Sartor and by Hocking and Jonas.

Collision efficiencies are presented for larger drops in the range 10–70μ radius. The new results tend to be larger than most previous theoretical computations, especially for drops of comparable size. For small size ratios, for which the coalescence efficiency should he close to unity, the present results appear to be consistent with collection efficiencies determined by experiment and by computations based on the method of superposition.

Abstract

An outline is presented of a new solution of the hydrodynamic equations for the motion of two spherical drops falling in a viscous fluid at small but non-zero Reynolds numbers. In this solution the flow of the medium is assumed to be governed by a modified form of the Oseen equations, and the boundary conditions at the two drops are simultaneously satisfied approximately. Although the equations allow partially for the effects of fluid inertia, a factor omitted in previous analyses based upon Stokesian hydrodynamics, the method of solution requires use of approximations to a larger extent than Stokesian solutions used by Davis and Sartor and by Hocking and Jonas.

Collision efficiencies are presented for larger drops in the range 10–70μ radius. The new results tend to be larger than most previous theoretical computations, especially for drops of comparable size. For small size ratios, for which the coalescence efficiency should he close to unity, the present results appear to be consistent with collection efficiencies determined by experiment and by computations based on the method of superposition.

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