Flow of Power-Law Liquids in a Hele-Shaw Cell Driven by Non-Uniform Electroosmotic Slip in the Case of Strong Depletion

We analyze flow of a non-Newtonian fluid in a Hele-Shaw cell, subjected to spatially non-uniform electroosmotic flow. We specifically focus on power-law fluids with wall depletion properties and derive a p-Poisson equation governing the pressure field, as well as a set of linearized equations representing its asymptotic approximation for weakly non-Newtonian behavior. To investigate the effect of non-Newtonian properties on the resulting fluidic pressure and velocity, we consider several configurations in one and two dimensions, and calculate both exact and approximate solutions. We show that the asymptotic approximation is in good agreement with exact solutions even for fluids with significant non-Newtonian behavior. The asymptotic model thus enables prediction of the flow and pressure fields for non-Newtonian fluids, and may be particularly useful for the analysis and design of microfluidic systems involving electro-kinetic transport of such fluids.