Mobility of power-law and Carreau fluids through fibrous media
Name
PhysRevE.92.063012.pdf
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1.32 MB
Format
Adobe PDF
Checksum (MD5)
d4ca3ef270e84bd4ba5978876a4b402a
Author(s)
Shahsavari, Setareh
McKinley, Gareth H
Date Issued
December 2015
Journal
Physical Review E
Publisher
American Physical Society
Citation
Shahsavari, Setareh, and Gareth H. McKinley. "Mobility of power-law and Carreau fluids through fibrous media." Phys. Rev. E 92, 063012 (December 2015). © 2015 American Physical Society
Version
Final published version
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 methods are 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 ɛ≃0.65, the dimensionless mobility becomes independent of the Carreau number and the mobility function exhibits power-law characteristics as a result of the 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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Hatsopoulos Microfluids Laboratory
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.92.063012
