Generalized Maxwell−Stefan Approach for Swelling Kinetics of Dextran Gels

Abstract

The swelling kinetics of two types of Sephadex dextran gels in water is described by a model based on the generalized Maxwell−Stefan (GMS) relations. The driving force for the swelling process is the gradient of the chemical potential gradient, which includes terms for mixing of solvent and polymer as well as for the elasticity of the swollen gel network. The friction is related to the relative motion of the components, via an effective diffusion coefficient. This is described as a function of the volume fraction of polymer via the Ogston relation (diffusion based) and a hydrodynamic model (based on the analogy with viscous flow). The resulting swelling model is evaluated via rigorous solution of the equations (homogeneous driving force approach, HDF), in which intraparticle gradients are taken into account, and approximated by a single-step central difference method (linear driving force approach, LDF). The latter allows much faster evaluation of the swelling process. These two numerical solution methods...