REE12: Mathematical modelling of water purification

Researcher: James Herterich
Team Leader(s): Dr Ian Griffiths & Dr Dominic Vella
Collaborators: Dr Nick Hankins
Dr Robert Field


The World Health Organization estimates that more than one billion people lack access to an improved water supply and many more drink water that is grossly contaminated. Water treatment is improving our daily lives and will become even more important in the coming decades. An ideal water purification system would make use of a combination of many different filtration techniques, including microfiltration, ultrafiltration, nanofiltration and reverse osmosis, all of which remove particles of different sizes from contaminated water [1].

Techniques and Challenges

Present techniques in the mathematical modelling of water filtration involve the use of partial differential equations (PDEs). The material properties of the membrane are described in terms of parameters that have to be measured for each membrane and have no clear relation to its geometry. Our goal is to develop mathematical models that give insight into the way these membrane properties are related to the effectiveness of filtration. This will enable the design of novel membrane systems to be optimised in new settings. This requires fundamental understanding of the behaviour of particle suspensions (as particle suspension dynamics play a major role in the migration and removal of particles in a fluid flow) with models for shear-induced migration and the tubular pinch effect. These shed light on problems such as the ‘flux paradox for colloidal suspensions’ [2].


We have developed a model that describes the transport of a suspension (of particles) in a channel with both porous and non-porous walls. Currently, we are investigating how a viscosity dependent on the particle concentration affects the flow characteristics using a combination of asymptotic and numerical techniques, which are valid at low particle concentrations.

The Future

The current model provides a foundation that may be generalised to understand the behaviour of bi-and poly-disperse suspensions in filtration devices. This will lead to governing equations that allow for the optimisation of filtration techniques.


[1] Bowen R.W., Jenner F.: Theoretical descriptions of membrane filtration of colloids and fine particles: an assessment and review, Advances in Colloid and Interface Science, 56:141–200, 1995

[2] Green G., Belfort G.: Fouling of ultrafiltration membranes: lateral migration and the particle trajectory model, Desalination, 35:129–147, 1980