Stokes flow in a rough curved channel

Abstract

A two-dimensional viscous flow in a rough curved channel is investigated. The roughness are considered to be sinusoidal corrugations. The asymptotic solution is obtained using boundary perturbation technique for small amplitude of the corrugations. It is found that, for any radius of curvature, the flow rate is invariably decreased by the corrugations. The effect of corrugations on the flow rate increases with the corrugation wavenumber, as well as the phase difference between the corrugated curved walls. For sufficiently large corrugation wavenumbers, the phase difference between the corrugated walls becomes insignificant. The findings of this study indicate that a smooth curved channel with no corrugations, will give more flow rate than a corrugated curved channel, comparatively, for the same radius of curvature, as the flow resistance is relatively higher for the latter, due to the effects of the wall-surface roughness.