Spherical Particles, Drops, and Bubbles in Shear Flows

Spherical Particles, Drops, and Bubbles in Shear Flows 

Statement of the problem. Let us consider a linear shear flow at low Reynolds numbers past a solid spherical particle of radius a. In the general case, the Stokes equation (2.1.1) must be completed by the no-slip condition (2.2.1) on the particle boundary and the following boundary conditions remote from the particle (see Section 1.1)  

In the problem of linear shear flow past a spherical drop (bubble), the Stokes equations (2.1.1) and the boundary conditions at infinity (2.5.1) must be completed by the boundary conditions on the interface and the condition that the solution is bounded inside the drop. In particular, in the axisymmetric case, the boundary conditions (2.2.6)-(2.2.10) are used. 

In the sequel we consider some special cases of shear flows described in Section 1.1. 

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

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