Electroosmotic flow of a rheological fluid in non-uniform micro-vessels

Abstract: The paper deals with a theoretical study of electrokinetic flow of a rheological Herschel-Bulkley fluid through a cylindrical tube of variable cross-section. The concern of this study is to analyze combined pressure-driven and electroosmotic flow of Herschel-Bulkley fluid. The wall potential is considered to vary slowly and periodically along the axis of the tube. With reference to flow in the micro-vessels, the problem has been solved using the lubrication theory. The Helmholtz-Smoluchowski (HS) slip boundary condition has been employed in this study. Volumetric flow rate $Q$ is found to be significantly affected by the yield stress parameter $\nu$ only if an applied pressure force is active. The linear superposition of flow components separately due to the hydrodynamic and electric force occurs only for a strictly uniform tube. This linear relationship fails if non-uniformity appears in either tube radius or in distribution of the electrokinetic slip boundary condition. Moreover, converging/diverging nature of the mean tube radius plays a crucial role on the fluid transport. For the benefit of readers, along with the original contribution, some applications of external electrical stimulation (ES) in the human body and HS slip velocity, studied in the past by previous researchers have been discussed in the paper.