Modelling of Multicomponent Diffusion and Swelling in Protein Gels

Abstract

Some protein gels are products of the dairy industry and some are used as pH-sensitive gels for the controlled delivery of biologically active substances. To understand the dynamics of drug delivery it is very important to establish a mathematical model of protein gel swelling. This required the identification and integration of theory and equations from a wide range of topics. The aim of this research was to develop a mathematical model of transport in polyelectrolyte gels (using the example of β-lactoglobulin protein gels).

A complete mathematical model of protein gel swelling was established. The swelling process of protein gels in this thesis involved multicomponent diffusion, chemical ionisation and mechanical deformation. Diffusion of electrolyte solutions through protein gels was modelled using the generalised Maxwell-Stefan (GMS) equation. The swelling pressure as a driving force in the GMS equation was described by rubber elasticity theory. Thermodynamic factors including the charged protein effect were considered in the GMS equation. The model included pH as a variable so it could be applied to both acidic and alkaline cases.

The model yielded a set of partial differential equations with algebraic equations for which COMSOL was selected as the simulation software. Although it was found that COMSOL could not always solve the model equations, numerical solutions were obtained for several cases. The model predicted that the equilibrium swelling degree of the gel decreased with high concentration of salts in the bulk solution. The model also predicted that the non-ideal effects were not always small and they depended on the activity coefficients of the species. Satisfactory solutions could not be obtained for all cases using commercial software such as COMSOL Multiphysics. It was shown that COMSOL did not conserve mass but conservativeness was critical in this application because pH and hence the net protein charge is very sensitive to the mass of hydrogen present.

In the future, research should be carried out to improve the pressure model in the GMS equation. Theoretical research on Manning condensation theory should be done to modify Manning’s model for more robust prediction of activities of water and ions with protein, and experiments should be done to validate the performance of the modified Manning model. Efforts should be made to write the programming code for a finite volume method to solve the system in three dimensions.