The effect of solute concentration on hindered diffusion of sphere-like colloidal solutes
in stiff polymer hydrogels is examined theoretically and experimentally. In the
theoretical development, it is shown that the presence of the gel fibres enhances the
effect of concentration on the thermodynamic driving force for gradient diffusion,
while simultaneously reducing the effect of concentration on the hydrodynamic drag.
The result is that gradient diffusion depends more strongly on solute concentration
in gels than it does in pure solution, by an amount that depends on the partition
coefficient and hydraulic permeability of the gel–solute system. Quantitative calculations
are made to determine the concentration-dependent diffusivity correct to first
order in solute concentration. In order to compare the theoretical predictions with
experimental data, rates of diffusion have been measured for nonionic micelles and
globular proteins in solution and agarose hydrogels at two gel concentrations. The
measurements were performed by using holographic interferometry, through which
one monitors changes in refractive index as gradient diffusion takes place within a
transparent gel. If the solutes are modelled as spheres with short-range repulsive
interactions, then the experimentally measured concentration dependence of the diffusivities
of both the protein and micelles is in good agreement with the theoretical
predictions.