RS Fellow - EPSRC grant (2014):Mathematical modelling of design strategies for membrane filtration.

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Although water was once considered an abundant if not unlimited resource, population growth, drought and contamination are straining our finite water supplies, resulting in water quality and quantity concerns being one of the largest environmental issues facing the world today. Further, as a result of arsenic-contaminated groundwater, every day more than 100 million people, from developing countries such as Bangladesh to developed countries including the U.K. and U.S., drink water that contains arsenic levels above the World Health Organization's 0.01 mg/L safe concentration threshold [M. Argos et al. 2010, The Lancet, 376, 252]. As a result, the race to find new and effective strategies for the production of clean water is now more important than ever. Central to water purification is membrane filtration, in which contaminated water, or feed solution, is pushed through a porous medium that rejects the particulates, allowing only clean water to pass through. Particulates that are rejected at the membrane surface can often easily be removed, for example by reversing the flow for a short time, or by mechanical cleaning of the surface. However, for contaminants that penetrate deeper into the membrane structure and become lodged the removal becomes significantly more challenging. There are many features that play a role in particle trapping within a membrane. Recent experimental observations indicate that the pressures across a membrane as the fluid is pushed through cause deformations that lead to expansion of the pores. This allows particles that would usually be rejected at the surface to be transmitted deep into the membrane structure or even pass through the entire membrane entirely, both of which are undesirable. Despite these new observations, experimentation is currently limited to heuristic approaches to identify the most suitable membrane structure and operating regime for a given task. In addition, any dynamic experimental techniques are limited to measurement of macroscopic observables, such as the rate at which clean water is processed: any probing of the microstructure is necessarily invasive and thus can only be carried out at the end of an experimental run. Mathematical modelling is able to provide the key insight required into the microstructural behaviour during filtration, thus enabling us to connect this to the macroscropic observables. The behaviour on the microscale encompasses a broad range of complex phenomena, but homogenization techniques are able to smooth out these fine details to provide the essential link between the membrane microstructure and the resulting filtration behaviour. The result is to provide optimal membranes that minimize the energy used and maximize the rate of production of clean water. This research project will develop a mathematical model that is able to capture the behaviour of a membrane as it deforms due to the flow. Our model will describe the transport of particles through the membrane, which will allow us to determine how fast we can process the contaminated water without compromising the structural integrity of the membrane. The model will also allow us to predict the best strategy for cleaning the membrane ready for re-use. We will collaborate with key experimentalists at Princeton and Ryerson Universities, and the world-leading filtration and separation science industry Pall Corporation to ensure that the models we develop address the pressing issues faced in the filtration industry. In partnership with experimentalists and engineers, the development of new mathematical techniques will lead to new breakthroughs that will drive forward the technological boundaries to solve our current and future global challenges in water purification.