Creeping Flow of Non-Newtonian Fluid through Membrane of Porous Cylindrical Particles: A Particle-in-Cell Approach

The present study is an attempt to deal with hydrodynamic and thermal aspects of the incompressible Carreau fluid flow past a membrane consisting of uniformly distributed aggregates of porous cylindrical particles enclosing a solid core which aims to provide a comprehensive study of the impact of non-Newtonian nature of Carreau fluid in the filtration process through membranes. The non-Newtonian characteristic of Carreau fluid is adopted to describe the mechanism of the pseudoplastic flow through membranes. The layout of the fluid flow pattern is separated into two distinct areas in which the area adjacent to the solid core of the cylindrical particle is considered as porous. However, the region surrounding the porous cylindrical particle is taken as non-porous (clear fluid region). The Brinkman equation governs the porous region, whereas the non-porous region is regulated by the Stokes equation. The nonlinear governing equations of the Carreau fluid flow in the different regions are solved using an asymptotic series expansion in terms of the small parameters such as Weissenberg number $(\mathrm{We}\ll 1)$ and a non-dimensional parameter $(S\ll 1)$ for the higher permeability of the porous material. The notable determination of the present study is that the Carreau fluid parameters, such as the Weissenberg number, Power-law index, and viscosity ratio parameter have a significant impact on the velocity, and hence the membrane permeability, Kozeny constant and temperature profile. The findings of the proposed work may be instrumented in analyzing various processes, including wastewater treatment filtration processes, and blood flow through smooth muscle cells.