Creeping flow of non-Newtonian fluid through membrane of porous cylindrical particles: A particle-in-cell approach

Abstract

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 ( We ≪ 1 ) and a non-dimensional parameter ( S ≪ 1 ), for the higher permeability of the porous material. For large permeability, the expression of velocity is derived, and the same has been used to compute the hydrodynamic permeability, Kozeny constant, and temperature profile. The numerical scheme (NDSolve in Mathematica) is used to solve the singularly perturbed boundary value problems in the case of small permeability of the porous medium [i.e., ( S ≫ 1 )]. The graphical analysis illustrating the outcomes of the effects of varying control parameters such as the power-law index, viscosity ratio parameter, permeability of the porous medium, Weissenberg number, and Nusselt number on the membrane permeability, Kozeny constant and temperature profile are discussed comprehensively and validated with previously published works on the Newtonian fluid in the limiting cases. 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 results showed a significant increase in the flow velocity and hydrodynamic permeability as the dominance of elastic forces over viscous forces increased in the case of high permeability ( S ≪ 1 ). The velocity gets a slight reduction for lower permeability of the porous material ( S ≫ 1 ); however, the hydrodynamic permeability behaves similar to the higher permeability of the porous material. 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. The proposed work, however, requires experimental verification.