Some of electrokinetic-based biomicrofluidic devices work at zeta potentials that are sufficiently high for ionic size (steric) effects to show up. In the present effort, consideration is given to the steric effects on the hydrodynamics of electroosmotic flow in a rectangular microchannel. The distinction between this research and the previous ones is that we account for non-linear rheology of the fluids encountered in biomicrofluidic systems by means of the power-law viscosity model. The method of analysis consists of a finite-difference-based numerical procedure for a non-uniform distribution of grid points, which is applied to the dimensionless form of the governing equations including the modified Poisson-Boltzmann equation. Our findings show that, unlike the electroosmotic flow of Newtonian fluids, the inclusion of the ionic size may enhance the velocity of the power-law fluids. We demonstrate that this phenomenon is due to the reduction of the fluid effective viscosity which is another consequence of the steric effects, besides the already explored feature of lowering the electroosmotic body force. Consequently, the ultimate influence of the ionic finite volumes on the electroosmotic flow of the power-law fluids is determined by the relative importance of the above-mentioned phenomena. Generally, the reduction of the body force is dominant; nevertheless, the opposite is true for shear-thickening fluids of very high flow behavior index, resulting in higher fluid velocities in the presence of the steric effects.
