Electroosmotic Slip Flow of Powell–Eyring Fluid in a Parallel-Plate Microchannel

The electroosmotic flow (EOF) of non-Newtonian fluids plays a significant role in microfluidic systems. The EOF of Powell–Eyring fluid within a parallel-plate microchannel, under the influence of both electric field and pressure gradient, is investigated. Navier’s boundary condition is adopted. The velocity distribution’s approximate solution is derived via the homotopy perturbation technique (HPM). Optimized initial guesses enable accurate second-order approximations, dramatically lowering computational complexity. The numerical solution is acquired via the modified spectral local linearization method (SLLM), exhibiting both high accuracy and computational efficiency. Visualizations reveal how the pressure gradient/electric field, the electric double layer (EDL) width, and slip length affect velocity. The ratio of pressure gradient to electric field exhibits a nonlinear modulating effect on the velocity. The EDL is a nanoscale charge layer at solid–liquid interfaces. A thinner EDL thickness diminishes the slip flow phenomenon. The shear-thinning characteristics of the Powell–Eyring fluid are particularly pronounced in the central region under high pressure gradients and in the boundary layer region when wall slip is present. These findings establish a theoretical base for the development of microfluidic devices and the improvement of pharmaceutical carrier strategies.