Couette–Poiseuille flow of variable viscosity in a multilayered channel partially filled with a homogeneous anisotropic porous layer: Role of the glycocalyx in attenuating shear stress on endothelial cells

Abstract

We present an analytical solution for the Couette–Poiseuille flow of variable viscosity in a multilayered channel partially filled with a homogeneous anisotropic porous layer. We establish a critical criterion that dictates the dominating factor when the flow is under the influence of shear and pressure gradient combined. This multilayered system resembles blood flow inside an artery where the fluid layer 1, fluid layer 2, and anisotropic porous layer describe the red blood cell layer, plasma layer, and glycocalyx layer, respectively. One of the novel features of this work is to understand the shear stress distribution on the liquid–porous interface (plasma membrane) and the bottom plate (endothelial cell layer) considering the variable viscosity of the fluid layer 1 while accounting for the anisotropic permeability of the porous medium. We use the obtained analytical solution to investigate the effect of the glycocalyx layer on the transmission of the fluid shear stress to the endothelial cell layer. We perceive that the shear stress distribution is more effective at the outer edge of the glycocalyx (plasma membrane) than the endothelial cell layer. On the other hand, the impact of the anisotropy on the shear stress distribution is more significant on the endothelial cell layer. This model is amenable to analytical solutions of the multilayered system considering the variable viscosity property of the blood and providing a framework for designing microfluidic systems that replicate biological glycocalyx, such as glycocalyx scaffolding.