Wall Effects on the Slow Steady Motion of a Particle in a Viscous Incompressible Fluid

摘要

Asymptotic expansions with respect to small Reynolds numbers are proved for the slow steady motion of an arbitrary particle in a viscous, incompressible fluid past a single plane wall. The flow problem is modelled by a boundary value problem for the stationary, nonlinear Navier-Stokes equations. The coefficients of these expansions are the solutions of linear Stokes problems which can be constructed by single layer potentials and corresponding boundary integral equations on the boundary surface of the particle. Asymptotic estimates at small Reynolds numbers for the slow steady motion of an arbitrary particle in a viscous, incompressible fluid between two parallel, plane walls and in a infinitely long, rectilinear cylinder of arbitrary cross section are presented.