Analysis of Williamson fluid flow incorporating Darcy’s resistance and electro kinetics: analytical and numerical results

Abstract

Abstract This article discusses a mathematical model for the electrokinetic and Darcy’s resistance of Williamson fluid in an electroosmotic pumping environment. The zeta potential at walls aids in peristaltic movement, and porous dissipation is incorporated into this modulation by the Williamson fluid’s material parameters. Through the use of Debye-Huckel approximations, long wavelengths, and low Reynolds numbers, the model equations are simplified. Mathematica software is used to produce analytical and numerical results, and plots and analyses are done using the included parameters on physical quantities of interest. This study has various practical applications, such as modifying belt resistance in laboratory drainage testing and improving pipeline design. It could also potentially aid in the development of blood filtration and purification techniques and optimize drug delivery systems that utilize fluids. It is observed that the modified Darcy’s law is more accurate for porosity effects in electroosmotic peristaltic channels and results in higher shear stress at the channel wall compared to Darcy’s law.