Stokes flow through a channel with wavy walls

Abstract

Stokes flow is solved through a channel with three-dimensional wavy walls enclosed by two wavy walls whose amplitude is proportional to the mean clearance of the channel multiplied by the small dimensionless parameter ɛ. The application of an analytical-numerical algorithm yields efficient formulas for the velocities and permeability. These formulas include ɛ in symbolic form. When ɛ increases, the Poiseuille flow (ɛ=0) is disturbed and eddies can arise above a critical value ɛ =ɛe. These results are also successfully compared to the ones derived by a fully numerical solution.