Electroosmotic flow of a power-law fluid through an asymmetrical slit microchannel with gradually varying wall shape and wall potential

Abstract

• Non-parallel electroosmotic flow of power-law fluid in a microchannel. • Lubrication theory for slowly varying channel height and wall potential. • Linear superposition of forces invalidated by asymmetry of channel. • Nonlinear interaction between wall undulation and wall charge modulation. • Flow-rate sensitive to phase shift of wall patterns and power-law index. This study aims to investigate electroosmotic flow of a power-law fluid through a slit channel with walls asymmetrically patterned with periodic variations in shape and zeta potential. On taking into account the near-wall depletion layer, the present problem is simplified on the basis of the lubrication approximation, and through the use of the Helmholtz–Smoluchowski slip boundary condition. Nonlinear equations are to be solved for two unknown functions of axial dependence, one being the induced pressure gradient, and another being an undetermined stress component. An efficient numerical scheme is devised in this work to solve the nonlinear problem. Results are generated to check whether the principle of linear superposition of forces, for electrokinetic flow of a non-Newtonian fluid in the presence of a Newtonian depletion layer, is still applicable to flow in an asymmetric channel. It is also found that phase shifts between the geometrical and electric potential patterns on the two walls may lead to qualitatively disparate effects, depending on the power-law behavior index of the fluid and the applied pressure gradient.