Diffusion Boundary Layer Near the Surface of a Drop Bubble

Diffusion Boundary Layer Near the Surface of a Drop (Bubble) 

Now let us consider the exterior problem about mass exchange between a spherical drop (bubble) of radius a and a translational Stokes flow with limiting diffusion resistance of the continuous phase. 

The process of convective diffusion to the liquid-liquid (liquid-gas) interface substantially differs from the diffusion to the fluid-solid interface. This is due to the difference between the hydrodynamic conditions on the interfaces. The fluid velocity on the surface of a solid is always zero by virtue of the no-slip condition. On the contrary, the interface between two fluids can move, and the tangential velocity on the interface differs from zero. 

Convective transfer of a substance by a moving fluid to the fluid-solid interface takes place under the condition that the flow is somewhat retarded, so that the transfer rate close to the surface is considerably lower than that in the bulk of the solution. On the contrary, diffusion to a liquid-liquid (liquid-gas) interface takes place under the more favorable conditions of nonretarded flow. That is why convective diffusion of a substance to a liquid-liquid interface is much more intensive than that to a fluid-solid interface. 

The mathematical statement of the problem on the concentration distribution outside a drop is described by Eq. (4.4.3) and the boundary conditions (4.4.4) and (4.4.5), in which the dimensionless stream function satisfies the Hadamard-Rybczynski solution (see Section 2.2) 

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