Electroosmotic flow of a non-Newtonian fluid in a microchannel with heterogeneous surface potential

Abstract

Based on the Nernst–Planck model for ion transport, the electroosmotic flow of a non-Newtonian fluid near a surface potential heterogeneity is studied numerically. The objectives of this study are to highlight the limitations of the linear slip-model and the nonlinear Poisson–Boltzmann model at various flow conditions as well as to develop vortical flow to promote mixing of neutral solutes within the micro-channel. A power-law fluid, both shear-thinning and shear-thickening, for the pseudoplastic behavior of the non-Newtonian fluid or viscoplastic fluid with yield stress is adopted to describe the transport of electrolyte, which is coupled with the ion transport equations governed by the Nernst–Planck equations and the Poisson equation for electric field. The viscoplastic fluid is modeled as either Casson, Bingham or Hershel–Buckley fluid. A pressure-correction based control volume approach has been adopted for the numerical computations of the governing equations. The nonlinear effects are found to be pronounced for a shear thinning liquid, whereas, the electroosmotic flow is dominated by the diffusion mechanisms for the shear thickening liquid. A maximum difference of 39% between the existing analytic solution based on the Debye–Hu¨ckel approximation and the present numerical model is found for a shear thinning power-law fluid. A vortex, which resembles a Lamb vortex, develops over the potential patch when the patch potential is of opposite sign to that of the homogeneous surface potential. Enhanced mixing of a neutral solute is also analyzed in the present analysis. The yield stress reduces the electroosmotic flow however, promotes solute mixing.