Analytical study of electroosmotically driven shear-thinning flow in a non-uniform wavy microchannel

An efficient mathematical model of electroosmotic blood flow in a non-uniform wavy microvessel is investigated. In the present study, the microvessel is considered as an impermeable microchannel in which the Herschel-Bulkley (H-B) model of shear-thinning character is chosen to represent the complex flow of blood. An external electric field is applied along the channel length. Due to the negative charge of the glycocalyx layer located at the inner surface of the microchannel, an electric double layer is formed. As a result, an electric potential developed, which is described by the Poisson-Boltzmann equation. Eventually, the study analytically solves a boundary value problem to determine the axial velocity of H-B fluid flow by employing a long wavelength and low Reynolds number. Additionally, the analysis derives the volumetric flow rate in the microchannel across a single wavelength and stream function for the flow field. Using Mathematica symbolic software, graphs are plotted to visualize the impact of rheological features on the axial velocity, streamlines, and volumetric flow rate concerning various physical parameters such as H-B shear-thinning flow index, plug radius, Debye length, and Helmholtz-Smoluchowski velocity. It is found that the flow of blood becomes smoother as blood behaves more shear-thinning in nature, which is the key innovation of this work. Also, an increment in Debye length helps in increasing the size of fluid bolus remarkably, which adds the novelty of physics to this study. Such a model can have applications in canalicular flow, transport in human skin, fluid dialysis, and separation methods.