Mathematical models in water filtration

Thesis

Membrane filtration is a simple concept for water purification: water containing particulate contaminants is forced through a semi-permeable membrane that rejects the particulates leaving clean water to flow out. Nevertheless, there are many complex features of membrane filtration, the most important of which is the accumulation of the particulates at the membrane surface. This leads ultimately to fouling of the membrane and a reduction in the efficiency of the process. Concentration polarization is the precursor of fouling, that is, a high concentration of contaminants develops in front of the membrane without the contaminants attaching to each other or the membrane surface. However, several types of acute membrane fouling develop from the layer formed in concentration polarization, including internal fouling, pore blocking and caking. Addressing these and related problems has been at the forefront of membrane research since the process' inception.

In this thesis we develop mathematical models of aspects of crossflow and directflow filtration operating at constant flux. We begin by addressing questions related to the initial stages of concentration polarization in crossflow systems. In particular, we study the influence of particulates on the viscosity of the filtrate, and show how the filtration efficiency may be improved by tailoring the wall permeability to reduce the effects of osmosis. We then address the development of membrane fouling and caking in directflow systems: the transmembrane pressure difference, the possibility of elastic deformations during filtration, and the influence of these on the development of fouling and caking are all considered. We show that even small elastic effects can worsen fouling and suggest how the process can be operated to avoid this. We then discuss further opportunities for mathematical modelling in this area.

Authors: Herterich, J

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English