Surface Charge Modulation in Electroosmotic Mixing within Sinusoidal Wavy Rotating Micromixers

Electroosmotic mixing in a sinusoidal wavy micromixer subjected to rotational motion about an axis perpendicular to the plane of flow is numerically investigated, with particular emphasis on the combined effects of spatially modulated surface charge and Coriolis-induced secondary flows. A two-dimensional model is developed by solving the coupled Navier–Stokes, Poisson–Boltzmann, and species transport equations, and sinusoidally varying wall zeta potentials are prescribed with a controllable phase lag between the upper and lower walls. The influence of phase lag, electric double-layer thickness, rotation number, and Péclet number on flow structure and mixing performance is systematically examined. The results show that phase-lagged surface charge heterogeneity induces strong transverse perturbations that significantly modify the topology of electroosmotic flow and mixing efficiency. Rotation effects may either enhance or suppress mixing, depending on the surface charge phase difference and the electric double-layer thickness. A phase-dependent critical electroosmotic parameter is identified beyond which rotation consistently improves mixing efficiency. Mixing performance is quantified using the outlet mixing efficiency, mixing length, and mixing time, complemented by a Sobolev norm to characterize the decay of large-scale concentration structures. The Wasserstein-1 distance is also introduced as an optimal-transport-based metric for assessing micromixing quality. The findings provide physical insight and practical guidelines for the design of electroosmotic micromixers operating under rotational motion, with relevance to chemical and biological lab-on-a-chip applications.