A visco-poroelastic theory for polymeric gels

Abstract

A polymeric gel can imbibe solvent and swell. Besides the dilatational mode of deformation, which involves long-range solvent migration, a gel may also undergo volume-conserved deformation. For a macroscopic gel with covalent cross-links, the volume-conserved deformation is usually much faster. However, these two modes are coupled for deformation at the microscopic level and for gels containing physical cross-links or large solvent molecules. In this paper, we seek to formulate a unified theoretical framework for the transient behaviour of polymeric gels to account for both solvent migration and viscoelastic deformation. Under this framework, we further develop a simple material model, and implement it into a finite-element code for numerical calculations. By simultaneously tracking the solvent migration and motion of polymer network, we evolve the inhomogeneous fields of stress and chemical potential. Several initial-boundary-value problems are solved as illustrative examples. For macroscopic gels with low viscosity, the time scales for viscoelasticity and poroelasticity are separated, and the long-term behaviour is just as that predicted by a poroelastic model. For structures or processes involving sizes comparable to the intrinsic length of a material, the viscoelasticity and poroelasticity must be considered simultaneously, especially when studying impact responses.

Interplay of Platelet Contractility and Elasticity of Fibrin/Erythrocytes in Blood Clot Retraction

“…The clot contraction dynamics is governed by the viscoelasticity of the clot for smaller volumes, whereas larger clot volumes are better described by the poroelastic limit. The visco-poroelastic model can also describe polymeric gels by accounting for both solvent migration and viscoelastic deformation (31). Macroscopic biological (32) and semi-interpenetrating network (33) gels have a relatively long viscoelastic relaxation time compared with that needed for solvent migration through a relatively long distance, which can be predicted by a poroelastic model.…”

Influence of supramolecular forces on the linear viscoelasticity of gluten

“…The fluid-filled pores experience a change in pressure under stress, which leads to fluid motion. In such systems, relaxation is divided into viscoelastic relaxation that has been described already and into poroelastic relaxation due to solvent migration in the pores of the network (Wang et al 2014;Wang and Hong 2012). This mechanism involves long-range movement of the solvent (aqueous solvent in our Fig.…”

Poromechanics Parameters of Fluid-Saturated Chemically Active Fibrous Media Derived from a Micromechanical Approach

“…Most of the existing models for these materials are generally based on the continuum mixture theory (Truesdell and Toupin 1960). The application of the continuum mixture theory to saturated, chemically active media such as biological tissue and hydrogel polymers has been made by numerous authors, notable among them being the biphasic and triphasic theories (Lai et al 1991; Mow et al 1980; Wang and Hong 2012; Yoon et al 2010). These methods have employed continuum mixture theory to determine the constitutive behavior from the Helmholtz free energy.…”