Mobility of Power-law and Carreau Fluids through Fibrous Media

TL;DR

This study develops models and scaling laws to evaluate the mobility of power-law and Carreau fluids flowing through fibrous media, revealing how porosity and shear rates influence flow regimes and effective viscosity.

Contribution

It introduces new analytical and scaling models for predicting fluid mobility in fibrous media with non-Newtonian fluids, accounting for porosity and rheological properties.

Findings

Mobility becomes independent of Carreau number at porosities below 0.65.

Derived simple expressions for transverse mobility functions.

Identified criteria for flow regime transitions based on a rescaled Carreau number.

Abstract

The flow of generalized Newtonian fluids with a rate-dependent viscosity through fibrous media is studied with a focus on developing relationships for evaluating the effective fluid mobility. Three different methods have been used here: i) a numerical solution of the Cauchy momentum equation with the Carreau or power-law constitutive equations for pressure-driven flow in a fiber bed consisting of a periodic array of cylindrical fibers, ii) an analytical solution for a unit cell model representing the flow characteristics of a periodic fibrous medium, and iii) a scaling analysis of characteristic bulk parameters such as the effective shear rate, the effective viscosity, geometrical parameters of the system, and the fluid rheology. Our scaling analysis yields simple expressions for evaluating the transverse mobility functions for each model, which can be used for a wide range of medium porosity and fluid rheological parameters. While the dimensionless mobility is, in general, a function of the Carreau number and the medium porosity, our results show that for porosities less than $\varepsilon\simeq0.65$, the dimensionless mobility becomes independent of the Carreau number and the mobility function exhibits power-law characteristics as a result of high shear rates at the pore scale. We derive a suitable criterion for determining the flow regime and the transition from a constant viscosity Newtonian response to a power-law regime in terms of a new Carreau number rescaled with a dimensionless function which incorporates the medium porosity and the arrangement of fibers.