The Application of Generalised Maxwell-Stefan Equations to Protein Gels

• Main Author: Lu, Kang
• Language: en
• Published: University of Canterbury. Chemical and Process Engineering 2008
• Subjects: Diffusion; Maxwell-Stefan equation; protein; gel; swelling; multicompound; mathematical model
• Online Access: http://hdl.handle.net/10092/1236

The removal of milk fouling deposits often requires the diffusion of electrolyte solutions such as sodium hydroxide through a gel. Very often more than one single anion and one single cation are involved and thus the modelling of such diffusion requires a multicomponent description. Diffusion of electrolyte solutions through gels can be modelled using the Maxwell-Stefan equation. The driving forces for diffusion are the chemical potential gradients of ionic species and the diffusion potential, i.e., the electrostatic potential induced by diffusion of the ions. A model based on the Maxwell-Stefan equation was applied to electrolyte solutions and electrolyte solutions with a gel. When modelling the diffusion of electrolyte solutions, the resulting equations were found to be a partial differential algebraic equation system with a differentiation index of two. The identification of this characteristic of the system enabled a solution method using the method of lines to be developed. When modelling the diffusion of electrolyte solutions through a gel an explicit expression for diffusion potential was developed and hence the diffusion equations were solved. Numerical solutions were presented for a number of case studies and comparisons were made with solutions from literature and between different electrolyte systems. It was found that the results of diffusion of electrolytes were in good agreement with those of experiments and literature. In the case of diffusion of electrolytes through a gel, swelling of the gel was predicted. The model can be improved by adding thermodynamic factors and can be easily extended to multiple ion systems.