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

尽管水曾经被认为是一种丰富的资源，如果不是无限的话，但人口增长、干旱和污染正在使我们有限的水资源供应紧张，导致对水质和水量的担忧成为当今世界面临的最大环境问题之一。此外，由于地下水被砷污染，从孟加拉国等发展中国家到包括英国和美国在内的发达国家，每天有1亿多人饮用砷含量超过世界卫生组织规定的0.01毫克/L安全浓度阈值的水[M.Argos等人]。2010年，《柳叶刀》，第376,252页]。因此，为生产清洁水寻找新的有效战略的竞赛现在比以往任何时候都更加重要。水净化的核心是膜过滤，在膜过滤中，被污染的水或饲料溶液被推过一个多孔介质，该介质拒绝颗粒，只允许干净的水通过。在膜表面排出的颗粒通常可以很容易地去除，例如通过短时间的倒流，或通过表面的机械清洁。然而，对于深入膜结构并滞留的污染物来说，清除变得明显更具挑战性。有许多特征在膜内捕获颗粒方面起作用。最近的实验观察表明，当流体通过薄膜时，穿过薄膜的压力会引起变形，从而导致毛孔扩张。这使得通常在表面被排斥的颗粒可以深入膜结构，甚至完全穿过整个膜，这两种情况都是不受欢迎的。尽管有这些新的观察结果，但实验目前仅限于启发式方法，以确定对给定任务最合适的膜结构和操作制度。此外，任何动态实验技术都仅限于对宏观观测数据的测量，例如清洁水的处理速度：任何对微观结构的探测都必然是有侵入性的，因此只能在实验运行结束时进行。数学建模能够提供过滤过程中微观结构行为所需的关键洞察力，从而使我们能够将其与宏观可观测性联系起来。微尺度上的行为包括一系列复杂的现象，但均质技术能够平滑这些精细的细节，以提供膜微结构和由此产生的过滤行为之间的基本联系。其结果是提供最佳的膜，最大限度地减少使用的能量和最大限度地提高清洁水的生产速度。这项研究项目将开发一种数学模型，该模型能够捕捉膜在流动时的变形行为。我们的模型将描述颗粒通过膜的传输，这将使我们能够确定在不损害膜结构完整性的情况下处理受污染的水的速度。该模型还将使我们能够预测清洗准备重复使用的膜的最佳策略。我们将与普林斯顿大学和瑞尔森大学的主要实验人员以及世界领先的过滤和分离科学行业Pall公司合作，以确保我们开发的模型能够解决过滤行业面临的紧迫问题。在与实验者和工程师的合作下，新的数学技术的发展将带来新的突破，推动技术边界，以解决我们目前和未来在净水方面的全球挑战。

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.