  We analyze flow of non-Newtonian fluids in a Hele-Shaw cell, subjected to
spatially non-uniform electroosmotic slip. Motivated by their potential use for
increasing the characteristic pressure fields, we specifically focus on
power-law fluids with wall depletion properties. We 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, allowing its use in
the analysis and design of microfluidic systems involving electro-kinetic
transport of such fluids.
