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

摘要

We analyze flow of non-Newtonian fluids in a Hele-Shaw cell, subjected tospatially non-uniform electroosmotic slip. Motivated by their potential use forincreasing the characteristic pressure fields, we specifically focus onpower-law fluids with wall depletion properties. We derive a p-Poisson equationgoverning the pressure field, as well as a set of linearized equationsrepresenting its asymptotic approximation for weakly non-Newtonian behavior. Toinvestigate the effect of non-Newtonian properties on the resulting fluidicpressure and velocity, we consider several configurations in one- andtwo-dimensions, and calculate both exact and approximate solutions. We showthat the asymptotic approximation is in good agreement with exact solutionseven for fluids with significant non-Newtonian behavior, allowing its use inthe analysis and design of microfluidic systems involving electro-kinetictransport of such fluids.