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Research Articles

Tortuosity and the Averaging of Microvelocity Fields in Poroelasticity

[+] Author and Article Information
S. C. Cowin

e-mail: sccowin@gmail.com
Department of Biomedical Engineering,
City College of New York,
City University of New York,
New York, NY 10031;
New York Center for Biomedical Engineering,
City College of New York,
City University of New York,
New York, NY 10031;
Grove School of Engineering,
City College of New York,
City University of New York,
New York, NY 10031

Manuscript received August 23, 2011; final manuscript received March 17, 2012; accepted manuscript posted October 25, 2012; published online February 4, 2013. Assoc. Editor: Younane Abousleiman.

J. Appl. Mech. 80(2), 020906 (Feb 04, 2013) (5 pages) Paper No: JAM-11-1302; doi: 10.1115/1.4007923 History: Received August 23, 2011; Revised March 17, 2012

The relationship between the macro- and microvelocity fields in a poroelastic representative volume element (RVE) has not being fully investigated. This relationship is considered to be a function of the tortuosity: a quantitative measure of the effect of the deviation of the pore fluid streamlines from straight (not tortuous) paths in fluid-saturated porous media. There are different expressions for tortuosity based on the deviation from straight pores, harmonic wave excitation, or from a kinetic energy loss analysis. The objective of the work presented is to determine the best expression for tortuosity of a multiply interconnected open pore architecture in an anisotropic porous media. The procedures for averaging the pore microvelocity over the RVE of poroelastic media by Coussy and by Biot were reviewed as part of this study, and the significant connection between these two procedures was established. Success was achieved in identifying the Coussy kinetic energy loss in the pore fluid approach as the most attractive expression for the tortuosity of porous media based on pore fluid viscosity, porosity, and the pore architecture. The fabric tensor, a 3D measure of the architecture of pore structure, was introduced in the expression of the tortuosity tensor for anisotropic porous media. Practical considerations for the measurement of the key parameters in the models of Coussy and Biot are discussed. In this study, we used cancellous bone as an example of interconnected pores and as a motivator for this study, but the results achieved are much more general and have a far broader application than just to cancellous bone.

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Figures

Grahic Jump Location
Fig. 1

An image of a cancellous bone section; the gray color areas represent the solid matrix portion and the black regions the pores

Grahic Jump Location
Fig. 2

A cartoon of an enlarged RVE for a continuum model of a porous medium

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