Introduction to Modeling of Porous Media via Hybrid Mixture Theory and Results On Flow Potentials
Lynn Schreyer-Bennethum
Department of Mathematical and Statistical Sciences, University of Colorado Denver
Date and time:
Friday, January 24, 2014 - 3:00pm
Location:
ECCR 265
Abstract:
Here we introduce a methodical method for deriving governing equations for porous materials called Hybrid Mixture Theory [2-4]. Hybrid Mixture Theory is a combination of volume averaging the field equations (conservation of mass, momentum, energy) and using the second law of thermodynamics, constitutive equations (additional, material-dependent equations needed to close the system) are obtained by exploiting the entropy generation inequality. Here we will demonstrate the Coleman and Noll method of exploiting the entropy generation inequality to derive the Navier-Stokes equation, discuss the averaging procedure, and provide results regarding macroscopic flow for swelling porous materials such as drug-delivery polymers, expansive soils, soybeans, and biotissues. In particular we discuss boundary conditions and potentials for macroscopic flow [1].
REFERENCES
[1] Bennethum, L.S.: Macroscopic Flow Potentials in Swelling Porous Materials, Transport in Porous Media 94(1) (2012), 47-68.
[2] Cushman, J.C., L.S. Bennethum, & B.X. Hu, Primer on Upscaling Tools for Porous Media, Advances in Water Resources, 25(8-10), (2002), 1043-1067.
[2] Hassanizadeh, S.M. & W.G. Gray.: General Conservation Equations for Multiphase Systems: Averaging Procedure. Advances in Water Resources 2 (1979), 131-144.
[3] Hassanizadeh, S.M. & W.G. Gray.: General Conservation Equations for Multiphase Systems: Mass, Momenta, Energy, and Entropy Equations. Advances in Water Resources 2(1979), 191-208.
[4] Hassanizadeh, S.M. & W.G. Gray.: General Conservation Equations for Multiphase Systems: Constitutive Theory for Porous Media. Advances in Water Resources 3 (1980), 25-40.