Electroosmotic Flow Modulation and Enhanced Mixing through a Soft Nanochannel with Patterned Wall Charge and Hydrodynamic Slippage

Abstract

The present study deals with the modulation of electroosmotic flow (EOF) through a soft nanochannel filled with a non-Newtonian fluid. The supporting charged hydrophobic walls of the channel are physicochemically patterned, which in turn leads to possibilities of modulated interfacial slip and surface ζ-potential. In addition, the supporting walls are grafted with an ion-and fluid-penetrable polyelectrolyte layer (PEL), which further entraps ionizable functional groups that give rise to immobile volumetric charges across the PEL. The fluid flow across such engineered devices under an applied electric field gives rise to an intricate electrohydrodynamic coupling over small scales. The mathematical model that describes the modulation of EOF across such a soft nanochannel comprises the Poisson equation for electrostatic potential and Nernst−Planck equations for conservation of the mass of mobile electrolyte ions, the flow field within the PEL is governed by a modified Darcy−Brinkman equation, and the Cauchy momentum equation governs the fluid flow outside the PEL. We adopt a radial basis function (RBF)based meshless computation scheme to simulate the set of governing equations. We further deduced analytical expressions for the electrostatic potential and velocity field for a Newtonian electrolyte through a bare channel with patterned surface potential, valid for a low charge limit. The numerical results are, however, obtained for a wide range of pertinent parameters and are further validated with the deduced theoretical results and available mathematical and experimental results from the literature. We observe an array of counter-rotating vortices that form in the flow field of the background non-Newtonian power-law fluid. Such vortices originate due to spatially periodic variations of hydrodynamic slippage as well as surface ζ-potential. The strength of vortices further intensifies due to the presence of the PEL grafted along the supporting rigid walls. The flow modulation across such a channel is illustrated by considering all of the possible sets of pertinent parameters. We further studied the impact of the rotational flow profile on the mixing of injected uncharged solutes. We observed that the formation of vortices in the flow field across the engineered soft nanochannel significantly affects the mixing efficiency, which can further be enhanced by suitably regulating the physicochemical and hydrodynamic parameters that control the flow modulation across the channel.