Creeping flow boundary-integral methods

In general, the problem just defined is nonlinear, in spite of the fact that the governing, creeping-flow equations are linear. This is because the drop shape is unknown and dependent on the pressure and stresses, which in turn, depend on the flow. Thus n and F are also unknown functions of the flow field, and the boundary conditions (2-112), (2-122), (2-141), and (8-58) are therefore nonlinear. Thus, for arbitrary Ca, for which the deformation may be quite significant, the problem can be solved only numerically. Later in this chapter, we briefly discuss a method, known as the boundary Integral method, that may be used to carry out such numerical calculations. Here, however, we consider the limiting case... 

The formulation (8-198) was used by Youngren and Acrivos16 to calculate the force on solid particles of different shapes translating through an unbounded stationary fluid, u, (xv ) = 0, in what was likely the first application of the boundary-integral method to creeping-flow problems. Many subsequent investigators have used it to calculate forces on bodies of complicated shape, in a variety of undisturbed flows.17... 

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