Problems in a Bounded Domain

Finally, we briefly consider the case in which the flow domain is bounded. A typical problem is the motion of a particle or drop in the vicinity of a plane wall or within a circular tube. We might also be interested in systems in which there are multiple particles. One approach to this 

A more efficient approach is to base the boundary-integral formulation on a fundamental solution (or more accurately a Green s function) that incorporates the relevant boundary conditions at one or more of the surfaces. In the case of a particle or drop moving near an infinite plane wall, this means finding a solution for a point force that exactly satisfies the no-slip and kinematic boundary conditions at the wall. If we were to consider the motion of a particle or drop in a tube, it would be useful to have the solution for a point force satisfying the same conditions on the tube walls. 

for example, if we wish to consider the motion of a solid particle moving in the vicinity of a plane wall, we can use these solutions in (8-115) to derive a solution that is analogous to (8-117). The result is the same as before, 

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