RUI: Asymptotic and Numerical Techniques in Mathematical Modeling of Membrane Filtration

膜过滤器-多孔介质的薄片-在诸如水处理、生物技术工业中的各种净化过程、在肾透析中从血液中去除杂质、啤酒澄清和面罩生产等应用中得到广泛使用。膜过滤器代表了全球数十亿美元的产业，许多大型跨国公司对改进和优化他们生产的膜过滤器在性能和成本方面保持着浓厚的兴趣。值得注意的是，实验文献远远超过理论和数值;在理论和数值文献中，提供第一原理、预测数学模型和模拟的研究很少。该项目旨在开发新的数学模型，有可能在弥合这一差距方面产生重大影响。长期目标是在性能和成本方面改进和优化膜过滤器。过滤器的性能在很大程度上取决于多孔膜的关键特征，包括膜厚度、内部孔结构和形状、孔连通性以及膜深度孔尺寸的变化。在过滤过程中动态演变的膜形态与载有颗粒的流的细节（包括颗粒的可能随机行为）之间的耦合的复杂性使得过滤和结垢成为具有挑战性的预测建模问题。该项目提出了一个连贯的，第一原理的方法来模拟粒子动力学和内部膜结构的变化的随机效应。该研究旨在制定和分析新的数学模型，通过使用渐近和数值技术来研究具有复杂内部结构的膜过滤器的演变。这些模型将与来自工业合作伙伴的观察、实验和数据进行比较，以更全面地了解多孔介质和膜过滤器背景下膜内部结构和流动的共同进化。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Membrane filters – thin sheets of porous medium – find widespread use in applications such as water treatment, various purification processes in the biotech industry, removing impurities from the blood in kidney dialysis, beer clarification, and mask production, among many others. Membrane filters represent a multi-billion-dollar industry worldwide, and many major multinational companies maintain a keen interest in improving and optimizing the membrane filters they produce, in terms of both performance and cost. It is notable that the experimental literature far outweighs the theoretical and numerical; among the theoretical and numerical literature, there is a paucity of studies that offer first-principles, predictive mathematical models and simulations. This project aims to develop novel mathematical models with potential for significant impact in bridging this gap. The long-term goal is to improve and optimize membrane filters, in terms of both performance and cost. The project will involve students in the research.Filter performance depends strongly on key features of the porous membrane, including membrane thickness, internal pore structure and shape, pore connectivity, and variation of pore dimensions in the depth of the membrane. The complexity of the coupling between the membrane morphology, which evolves dynamically during the filtration process, and the details of the particle-laden flow, including possible stochastic behavior of the particles, make filtration and fouling a challenging predictive modeling problem. This project presents a coherent, first-principles approach to model both stochastic effects of particle dynamics and variations in internal membrane structure. The research aims to formulate and analyze novel mathematical models to investigate the evolution of membrane filters with complex internal structures by using asymptotic and numerical techniques. These models will be compared to observations, experiments, and data from industrial partners to understand more fully the co-evolution of membrane internal structure and flow in the context of porous media and membrane filters.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.