Influence of yield stress on electroosmotic flow mixing in a charged modulated microchannel

Abstract

This study numerically investigates vortex-induced electroosmotic mixing of a Casson viscoplastic fluid in a wavy microchannel with sinusoidally heterogeneous surface charge. The coupled electrokinetic transport is described using the Navier–-Stokes–Poisson–Nernst–Planck formulation, while the flow, stress, and species-concentration fields are resolved using a finite volume method. The analysis reveals a coupled mechanism in which wall corrugation and spatially varying surface charge generate transverse recirculation and enlarge the interfacial contact area between the incoming streams, whereas the yield stress modifies the flow through the formation and growth of unyielded regions. Increasing the wave amplitude α and yield-stress parameter τ0 enhances mixing, although the latter simultaneously increases flow resistance and pressure loss. The electrical double-layer (EDL) thickness also plays a decisive role in the mixing process. A thicker EDL strengthens electrokinetic interactions with the bulk fluid and enhances mixing, whereas a thinner EDL weakens these effects. Consequently, for τ0=0.30 and α=0.10, the mixing efficiency decreases by approximately 23% as κH increases from 10 to 40. A maximum mixing efficiency 96.5% is obtained for α=0.25, κH=10, and τ0=0.30. These findings highlight the dual influence of viscoplasticity on mixing performance. Increasing the yield stress enhances fluid homogenization through changes in the yielded–unyielded flow structure but simultaneously increases hydraulic resistance and pressure loss. To capture this trade-off, a mixing performance factor is defined as the ratio of mixing efficiency to the average pressure drop. This metric identifies an operating regime in which enhanced electroosmotic mixing can be achieved without an excessive pressure-loss penalty, providing a physically based criterion for designing efficient micromixers for viscoplastic fluids.