Fundamental Singularities in a Two-Fluid Stokes Flow with a Plane Interface

Abstract

ABSTRACTA modified image method is presented for obtaining the solutions of the fundamental singularities in the neighborhood of a plane interface between two semi-infinite, immiscible, and incompressible viscous fluids. The fundamental singularities considered are the stokeslet, rotlet, stresslet, stokes-doublet, source, and source-doublet. The Galerkin vector function representation introduced reduces the complexity of the expressions for the solutions. Moreover, the physical meaning of each solution is clearly identified by these new expressions.