Mathematical Modelling of Flux Decline due to Concentration Polarisation and Cake Layer Formation in Crossflow Filtration Systems

Crossflow membrane filtration is an effective way of removing both colloidal and dissolved organic matter from contaminated water supplies.
Two phenomena domimate solute flux in crossflow systems; concentration polarization and cake layer formation. Many innovative mathematical models for predicting both flux decline and quasi-steady state flux have been produced in the literature. However, limited regime applicability and conflicting physical predictions have made choosing optimal performance parameters in design a challenging process.
An overview of the current field of models was undertaken, including an assessment of mathematical assumptions, numerical computation workload and number and complexity of system constants.
A new model incorporating viscosity dependence on concentration is developed for the concentration polarization regime. Preliminary results will also be presented from a Monte Carlo based molecular dynamics simulation of volume packing fraction in the cake layer regime.
The novel aspects of these models will be compared with existing models and the experimental results of our collaborators. Laboratory ultrafiltration tests were undertaken using varying concentrations of Dextran.
An outline of future model directions and refinements will be presented.