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.....
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.