Mathematical Simulation of local transfer for non-Newtonian uid in porous fabrics

Abstract

Many processes in the polymer composite, textile, food, and pharmaceutical industries are associated with the flow of non-Newtonian fluids in porous media. This paper considers the mathematical model of a multi-scale process for the filtration of non-Newtonian fluid in periodic porous fabrics. The model should be based on a three-dimensional Navier-Stokes equation with non-Newtonian Carreau-Yasuda viscosity using the asymptotic averaging method. A numerical algorithm was developed for solving local problems of non-Newtonian fluids in periodic cells, and the distribution of velocity, pressure and non-Newtonian viscosity in a single pore was obtained. The algorithm for calculating the permeability tensor is developed, and the effects of fluid rheology are also highlighted.