A Model for Flow and Deformation in Unsaturated Swelling Porous Media

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.

A Finite Element Analysis of Coupling Between Water Absorption and Swelling of Foodstuffs During Soaking

“…This leads us to make modifications to the constitutive relationship Eq. 3.104 presented in Zhu et al (2010).…”

“…The samples were 40 mm long and 6 mm wide with a thickness of 0.5 mm (Cafieri et al 2008). Here we use the mathematical model presented by Zhu et al (2010) to study this moisture transport process into plane sheet pasta across their thickness and the swelling behavior of the material. One dimensional geometry is considered.…”

“…where l denotes the volume fraction of water, D is the coefficient of diffusion, k l is permeability, μ is viscosity of water, p a is the pressure in the air phase, s is the volume fraction of the solid phase, B is a function of time and is related to the viscoelastic parameters of the material as was discussed in Zhu et al (2010), and v s is the velocity of the solid phase. Time derivatives in Eq.…”

“…The constitutive relationship presented in Zhu et al (2010) is general for any two dimensional or three dimensional body. When only one dimension is considered, however, the assumption that the body is elastic in dilation and viscoelastic in shear is not appropriate anymore.…”

“…To apply the mathematical model developed in Zhu et al (2010) and study non-empirically the two way coupled moisture transport in plane sheet pasta and swelling of the pasta sample during soaking. 2.…”