Multiscale fluid transport theory for swelling biopolymers

Abstract

Fluid flow through a (bio) polymeric matrix has multiscale characteristics and is affected by the relaxation of surrounding polymers. Models developed in the past were either single scale (Polymer (1982) 23 (4) 529; Chemical Engineering Science (1992) 47 (12) 3037) or were limited to systems with a short memory (Achanta, 1995; Moisture transport in shrinking gels during drying, Ph.D. thesis, Purdue University, West Lafayette, IN). To address these limitations, we use the generalized Darcy's law equations of Singh (Effect of viscoelastic relaxation on fluid and species transport in biopolymeric materials, Ph.D. thesis) and the mass balance equations of Bennethum and Cushman (International Journal of Engineering Science (1996) 34 (2) 125) to develop a multiscale fluid transport model. The effect of viscoelastic relaxation of solid polymers on the flow of vicinal (adsorbed) fluid is considered at the mesoscale. At the macroscale two bulk fluids are incorporated, one of which is identical to the vicinal fluid. The mass balance equations for the vicinal fluid and its bulk counterpart are coupled via source/sink terms. The resulting fluid transport equation includes a novel integral term related to viscoelastic properties of the biopolymeric matrix. This term incorporates viscoelastic effects with both short and long memory. The model can describe both Darcian (Fickian) and non-Darcian (non-Fickian) modes of fluid transport. The model suggests fluid transport is Darcian in the rubbery and glassy states when the biopolymers are sufficiently far from the glass transition region. In the proximity of glass transition the flow of fluids is anomalous or non-Darcian. These predictions are in agreement with the experimental observations of Kim et al. (Chemical Engineering Science (1996) 51 (21) 4827). In spite of its multiscale characteristics, the resulting transport equation is simple and can be easily solved. The experimental parameters needed to solve the equation are the effective diffusivity, a sorption or drying curve and viscoelastic properties of the material.