Axisymmetric straining shear flow

Solid particles. In the case of axisymmetric straining shear flow, the boundary conditions (2.5.1) remote from the particle have the form... 

Let us consider mass transfer for a translational flow past a solid spherical particle, where the flow field remote from the particle is the superposition of a translational flow with velocity U and an axisymmetric straining shear flow, the translational flow being directed along the axis of the straining flow. The dimensional fluid velocity components in the Cartesian coordinates relative to the center of the particle have the form... 

The expressions (8-44) and (8 45) represent a complete, exact solution of the creeping-flow equations for a completely arbitrary linear flow. Among the linear flows of special interest are axisymmetric pure strain, which was solved by means of the eigenfunction expansion for axisymmetric flows in the previous chapter, and simple shear flow, for which... 

We have previously obtained solutions by other techniques for the problems of a rigid sphere immersed in axisymmetric straining or simple shear flow of an unbounded fluid. In this subsection, it is shown that those two problems also can be solved very simply by means of a superposition of fundamental singularities at the center of the sphere. 

The closely related problem of a rigid sphere in a linear shear flow is very easy to solve now by analogy to the solution for an axisymmetric straining flow. We consider the problem in the form... 

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