Introduction to Modeling of Porous Media via Hybrid Mixture Theory and Results On Flow Potentials
Lynn Schreyer-Bennethum
Department of Mathematical and Statistical Sciences,听University of Colorado Denver
Date and time:听
Friday, January 24, 2014 - 3:00pm
尝辞肠补迟颈辞苍:听
ECCR 265
础产蝉迟谤补肠迟:听
Here we introduce a methodical method for deriving governing equations for porous materials called Hybrid Mixture Theory [2-4].听听 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.听 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.听听 In particular we discuss boundary conditions and potentials for macroscopic flow [1].
REFERENCES
[1]听 Bennethum, L.S.: Macroscopic Flow Potentials in Swelling Porous Materials,听Transport in Porous Media听94(1)听(2012), 47-68.
[2]听 Cushman, J.C., L.S. Bennethum, & B.X. Hu,听Primer on Upscaling Tools for Porous Media, Advances in Water Resources,听25(8-10), (2002), 1043-1067.
[2]听 Hassanizadeh, S.M. & W.G. Gray.: General Conservation Equations for Multiphase Systems:听 Averaging Procedure.听Advances in Water Resources听2听(1979), 131-144.
[3]听 Hassanizadeh, S.M. & W.G. Gray.: General Conservation Equations for Multiphase Systems:听 Mass, Momenta, Energy, and Entropy Equations.听Advances in Water Resources听2(1979), 191-208.
[4]听 Hassanizadeh, S.M. & W.G. Gray.: General Conservation Equations for Multiphase Systems:听 Constitutive Theory for Porous Media.听Advances in Water Resources听3听(1980), 25-40.