Convective diffusion to a drop under arbitrary conditions of absorption. Diffusion boundary layer approximation

Abstract

The diffusion boundary layer approximation is used to investigate the stationary convective diffusion of substance dissolved in a flow to a spherical drop under arbitrary conditions of absorption on its surface, in particular when a chemical reaction of arbitrary order takes place on the surface. An integral equation is obtained for the local diffusion flux to the surface of the drop. It is shown that 1) the total Sherwood number increases with increasing rate of the reaction and decreases with increasing exponent of the reaction rate; 2) with increasing Péclet number, saturation occurs (i.e., the total diffusion flux to the surface of the drop tends to a limiting value, which depends only on the reaction kinetics). The case of total absorption of diffusing, substance on the surface of reacting solid and liquid particles in a homogeneous Stokes flow at large Péclet numbers was investigated in [1]. The problem of convective diffusion to the surface of a solid spherical particle in the case of mixed kinetics was considered in [2, 3].