Limiting Diffusion Resistance of the Disperse Phase

Statement of the problem. Preliminary remarks. Let us consider the transient convective mass and heat transfer between a spherical drop of radius a and a translational Stokes flow where the resistance to the transfer exists only in the disperse phase. We assume that at the initial time t = 0 the concentration inside the drop is constant and equal to Co, whereas for t 0 the concentration on the interface is maintained constant and equal to Cs. 

Mass transfer inside a drop is described by Eq. (4.12.1) and the first two conditions (4.12.2). The fluid velocity field v = (vr,vg) at low Reynolds numbers is given by the Hadamard-Rybczynski stream function and, in the dimensionless variables, has the form 

To analyze the asymptotic solution, it is convenient to introduce an auxiliary Peclet number by setting 

Further, we assume that the condition Peg 1 holds. To be more descriptive in the physical interpretation of the process, we shall use a terminology corresponding to complete absorption of the substance at the drop surface for Cs = 0. 

The inner problem of convective mass and heat transfer is essentially different from the similar outer problem, primarily, by the streamline pattern. This leads to a corresponding qualitative distinction between the dynamics of processes of transient mass transfer inside and outside a drop. In the outer problem considered in Section 4.12, all streamlines are open. The lines near the flow axis carry the 

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