Models of Flow through Porous Media of Polar Fluids with Pressure-Dependent Viscosity

TL;DR

This paper develops mathematical models describing the flow of polar fluids with pressure-dependent viscosity through porous media, incorporating effects of microstructure and fluid-matrix interactions for improved understanding of such complex systems.

Contribution

It introduces new averaged equations and drag functions that account for pressure-dependent viscosity and porous microstructure effects in polar fluid flow models.

Findings

Derived generalized flow equations for polar fluids in porous media.

Included Darcy and Forchheimer terms for granular and consolidated media.

Enhanced modeling of fluid-porous matrix interactions.

Abstract

Equations governing the flow of a polar fluid, with pressure-dependent Newtonian viscosity, through a variable-porosity medium are developed. Averaged equations are obtained using intrinsic volume averaging. A drag function is introduced to account for the interactions of the fluid with the porous matrix. Darcy and Forchheimer generalized terms are included in the model equations for both granular and consolidated media to account for the effects of the porous microstructure.