CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM

                  UNIVERSITY OF COLORADO AT DENVER



TITLE:   Mathematical Modeling of Swelling Porous Media 
         Using a Continuum Approach
 

SPEAKER: Lynn Bennethum, Department of Mathematics, Purdue University 

DATE:    Friday, March 8, 1996

PLACE:   Math Conference Room - Suite 540
         UCD Building, 1250 14th St., Denver

TIME:    noon - 1 pm



ABSTRACT


The modeling of swelling porous media has applications
in material science (polymers), food science (e.g., crackers),
and environmental engineering (low-level radioactive waste is often
deposited in sites lined with clay barriers).  A swelling porous
medium is a medium composed of two phases (e.g., solid and liquid)
which may, for example, swell due to the absorption of additional
fluid or shrink due to evaporation.  Although the two phases may have quite
classical elastic-solid or viscous-liquid behavior when disjoint,
the macroscopic behavior of the medium is often viscoelastic or plastic due
to the interaction between the phases.
In this talk a systematic approach for obtaining
a governing system of partial differential equations is discussed.
The approach generalizes classical mixture theory of continuum
mechanics and produces a system which views the porous medium
as overlaying continua, so that at each spatial point the
thermodynamic properties of each phase are defined.

Specifically, the microscale field equations (conservation
of mass, momentum balance, energy balance, and entropy balance)
are spatially averaged to obtain the correct terms
representing the exchange of thermodynamic properties between
phases at the macroscale.  The entropy inequality is exploited in
the sense of Coleman and Noll and constitutive restrictions
are obtained.  The closure issue, a consequence of losing
information due to the upscaling, is addressed, and some
consequences of the results are mentioned.