Generalized Maxwell-Stefan approach for swelling kinetics of dextran gels

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 fur 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 vigorous 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 give similar results for the simulation of the expanding outer radius of the gel particles, regardless of which expression is used for the effective diffusivity. When intraparticle dynamics are considered (HDF solution method), some differences between the two effective diffusivity relations arise. The hydrodynamic model predicts steeper composition gradients than the Ogston model and leads to a distinctly later dissolution of the shrinking core. However, there is a lack of reliable dynamic intraparticle profile data to verify either model.