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. The world's natural supply of underground water is being rapidly drained, with water tables falling by about three metres a year across much of the developing world [1]. 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, contributing to more than 20% of all deaths [2]. The connection between arsenic exposure and cancer has now led to recent revisions in the United States Environmental Protection Agency's maximum contaminant levels for arsenic concentration in drinking water [3]. As a result of the significant health issues engendered, developing strategies for the purification of water and the removal of heavy metals such as arsenic, cadmium and nickel is a global issue, demanding the attention of the science and engineering communities.
Mathematical modelling provides a key route to mitigating these environmental issues. The purification and removal of particulates from water exploits many different techniques, including magnetic separation, adsorption, coagulation, ion exchange, and membrane separation, and new techniques are continually being discovered. By taking into account the physical rules that govern these processes, mathematical theories provide a way of determining how such a system will behave. Extracting this information from experimental observations alone can be extremely costly, and often impossible, as technologies advance and become more complex. The strength of a mathematical model is in its ability to elucidate this system behaviour, allowing us to ascertain which features in the process are important and those that are not, to determine the route to system optimization.
A prime example of the need for mathematical modelling is given by the surprising result in the highly cited Science article [4]. Using a nanocrystalline magnetite mesh the authors find that magnetizable particulates much smaller than the mesh size can be filtered from water. Since the principal difficulty in heavy-metal removal is the tiny particle size, this suggests a possible novel way of removing heavy metals from water. However, although the mechanism of removal is thought to involve particle aggregation, as yet, there is no theoretical understanding of the physics that actually underlies the results observed, and thus no way of knowing how to realize and upscale this possible technology. By developing mathematical models for the new frontiers in water purification we can describe the detailed behaviour underlying these strategies. This will allow us to understand how the particles behave in a fluid flow, how they aggregate, and most importantly, how the controllable parameters in the system, such as magnetic field strength, flow rate, and filter type, can be used to remove the contaminants in the most efficient and cost-effective way.
It is clear that technology is advancing faster than ever before, leading to substantial scientific breakthroughs, and the entire scientific community must be equipped to continually adapt and capitalize on these advancements. By working with experimentalists and engineers, the results of this work will help drive forward the boundaries of mathematical methods to find the next innovative solution and solve the current and future global challenges.
[1] D. Pimentel et al. 2004, Bioscience, 54, 909.
[2] M. Argos et al. 2010, The Lancet, 376, 252.
[3] E.O. Kartinen & C.K. Martin. 1995, Desal., 103, 79.
[4] Yavuz et al. 2006, Science, 314, 964.
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