Finite element modelling of concentration profiles in flow domains within porous walls

To develop a complete numerical model for predicting fluid flow and mass transfer in domains with porous walls such as those found in cross flow filtration is not an easy task to undertake. Many gaps in theory exist that undermine any attempt to build a reliable representation of this process and a sensible effort to solving this problem must be built on sound and logical assumptions. The difficulties with modelling interacting particles, with simulating multiphase flow and with prescribing accurate boundary conditions are very much the essence of the problem. From a comprehensive literature search into areas of combined free and porous flow, mass transfer in porous domains and into the fields of rheology, and mathematical modelling of crossflow filtration it was discovered that present research although great in quantity, is overall limited by the difficulties described above. As well, the present research found in the literature is also limited for use in industrial applications as it generally considers dilute suspensions, it is often found to look at simple flow profiles for Newtonian fluids, the research scarcely looks into the dependency of flow profiles and mass transfer profiles on each other via rheology and many researchers who study crossflow filtration concentrate solely on the porous wall to solve the flux paradox situation and do not generally consider the whole domain. The purpose of the present thesis is to describe the concept, procedure and results behind the integration of a solids transport model into a previously developed flow algorithm and the explanation of ideas for solving the problem of prescribing appropriate concentration boundary conditions at the porous wall. The aim of the research is to develop a fast and cost effective tool for solving the given problem based on rational assumptions.....