A Model for Flow and Deformation in Unsaturated Swelling Porous Media |
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Authors: | Haolin Zhu Ashish Dhall Subrata Mukherjee Ashim K Datta |
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Institution: | (1) Department of Earth and Atmospheric Sciences and Department of Mathematics, Purdue University, W. Lafayette, IN 47907, USA; |
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Abstract: | A thermomechanical theory for multiphase transport in unsaturated swelling porous media is developed on the basis of Hybrid
Mixture Theory (saturated systems can also be modeled as a special case of this general theory). The aim is to comprehensively
and non-empirically describe the effect of viscoelastic deformation on fluid transport (and vice versa) for swelling porous
materials. Three phases are considered in the system: the swelling solid matrix s, liquid l, and air a. The Coleman–Noll procedure is used to obtain the restrictions on the form of the constitutive equations. The form of Darcy’s
law for the fluid phase, which takes into account both Fickian and non-Fickian transport, is slightly different from the forms
obtained by other researchers though all the terms have been included. When the fluid phases interact with the swelling solid
porous matrix, deformation occurs. Viscoelastic large deformation of the solid matrix is investigated. A simple form of differential-integral
equation is obtained for the fluid transport under isothermal conditions, which can be coupled with the deformation of the
solid matrix to solve for transport in an unsaturated system. The modeling theory thus developed, which involves two-way coupling
of the viscoelastic solid deformation and fluid transport, can be applied to study the processing of biopolymers, for example,
soaking of foodstuffs and stress-crack predictions. Moreover, extension and modification of this modeling theory can be applied
to study a vast variety of problems, such as drying of gels, consolidation of clays, drug delivery, and absorption of liquids
in diapers. |
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