The creeping motion of a non-Newtonian fluid past a sphere

Abstract

The equations of motion and continuity are solved together with the slow-flow stress equations for an incompressible Rivlin-Ericksen fluid. The boundary conditions for slow flow past a sphere are satisfied by matching inner (Stokes) and outer (Oseen) Reynolds-number expansions of the stream function. The terms in the inner expansion are the solutions of non-linear partial differential equations which are solved approximately by expanding in terms of a non-Newtonian parameter λ. The drag force on the sphere is obtained from the solution.