In several experiments, enzymes have shown an in increase in diffusivity in the presence of their substrate. The enhancement in diffusivity ranged from as low as 28% for urease to 80% in the case of alkaline phosphatase. There are two main competing theories. One asserts that catalytically driven boosts propel the enzyme forward in ‘leaps’, while the other argues that phoretic activity due to attractive or repulsive surface interactions on the enzyme are responsible for the enhanced diffusivity. At the moment of writing, no consensus has been reached on the mode of enhancement. A novel agent-based lattice model for the diffusion of enzymes was derived in this Bachelor’s Thesis in accordance to the phoretic theory of enhanced diffusion. The model that was developed is a stochastic model which describes the interactions at the particle level. The model showed that phoresis produces enhanced diffusion in the order that was expected for the enzyme urease. Furthermore, the model showed pattern formation in the case of repulsive interactions between enzyme and substrate. The instability of this phase transition was investigated using linear stability analysis on the continuum limit of the lattice model. This yielded a restriction on the strength of the interactions for which pattern formation could occur.

In this study, a pressure filtration model for a slurry of milk fat crystal aggregates is developed, validated and used to investigate the effect of pressure-time profiles. The model focuses on the expression step and describes oil flow locally. The filter cake is modelled as a double porous non-linear elastic medium with permeabilities described by the relation of Meyer & Smith. Conservation equations lead to a coupled system of differential equations, which are numerically solved exploiting a finite-difference scheme. Simulations with the model give insight through graphs of volume fractions versus filter chamber location at any given time step. Diagrams of oil outflow velocities and solid fat content of produced filter cakes show qualitatively good behaviour when compared to experiments. Studying the effect of pressure-time profiles, the model predicts that a low rate of pressure increase gives the driest filter cakes. Simulations also indicate that putting steps in pressure-time profiles is hardly effective.