GOALI: Network Models for Membrane Filtration

GOALI：膜过滤网络模型

• 批准号: 2206127
• 负责人: Linda Cummings
• 金额: $ 47.76万
• 依托单位: New Jersey Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-08-15 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2206127&HistoricalAwards=false
• 关键词: GOALI; Network; Models; Membrane; Filtration

Membrane filters are used in in an extraordinarily wide range of everyday applications ranging from industrial waste treatment to water purification to air conditioning to food production and, of particular relevance today, medical masks and vaccine manufacture. Since the goal of effective filtration is the removal by the filter of particles or impurities carried by the feed solution, fouling of the membrane is unavoidable, leading ultimately to filter failure. Improved understanding of the fouling mechanisms, critical in improving filter designs, is therefore the target of significant research efforts. In addition to considerations of how particles interact with and adhere to the membrane material, pore structure, size and shape are critical factors in determining filter functionality and efficiency. There is considerable industrial interest in designing and manufacturing efficient filters that allow for fine control of particle removal while maintaining a reasonable lifetime. Such filters typically have pore size that decreases in the membrane depth; and may incorporate varying degrees of connectivity between pores. Our work will use theoretical approaches (combined with experimental calibration) to study general networks of pores within filters and identify optimal pore network structures that maximize filter lifetime while meeting a prescribed impurity removal threshold. This project will also provide training and research and industrial experiences for undergraduate and graduate students.This project addresses issues of flow and fouling in porous membrane filters, where the pore structure may be modeled as a network of connected (sufficiently slender) tubes. Working with industrial collaborators at W.L. Gore & Associates and with a team of students, the PIs will derive new predictive mathematical models to describe situations of practical importance. Our models will be formulated on arbitrary pore networks (where both the length and radius of pores can vary) and will describe fouling both by adsorption of small particulate contaminants at the pore walls, and by sieving of larger particles (with an arbitrary size distribution). We will study networks generated computationally (using a variant of the Random Geometric Graph construction) as well as real pore networks in non-proprietary manufactured membranes. We will also use methods from persistent homology (PH) to study connectivity features of such pore networks and how these evolve in time, to elucidate scaling relationships between geometric/topological features and filtration performance metrics. The work is of significant interest to our industrial collaborators, who will provide us with data and advise on industrial relevance via regular team meetings. This interaction will ensure that the project remains focused and will guarantee that we identify and address questions of real importance to applications. The experimental data provided will also allow us to identify appropriate ranges for unknown parameters in our models, and to test uncertain modeling assumptions. Additionally, we will formulate new modules for our Capstone Course in Applied Mathematics that will involve undergraduate students in the research by means of Monte-Carlo type simulations and persistent homology methods using available software libraries. The research will combine novel mathematical modeling with analytical approaches including graph theory, optimization, homogenization techniques, multiple scales analysis, asymptotic methods, stochastic analysis and probability theory, and efficient numerical techniques.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.

膜过滤器的应用范围非常广泛，从工业废物处理到水净化，从空调到食品生产，以及今天特别相关的医用口罩和疫苗制造。由于有效过滤的目的是通过过滤器去除进料溶液携带的颗粒或杂质，因此膜的污染是不可避免的，最终导致过滤器失效。因此，提高对污垢机制的理解，对改进过滤器设计至关重要，是重要研究工作的目标。除了考虑颗粒如何与膜材料相互作用和粘附外，孔结构、大小和形状是决定过滤器功能和效率的关键因素。有相当大的工业兴趣设计和制造高效的过滤器，允许颗粒去除的精细控制，同时保持合理的使用寿命。这种过滤器的孔径通常随着膜的深度而减小；并且可能包含不同程度的孔隙之间的连通性。我们的工作将使用理论方法（结合实验校准）来研究过滤器内的一般孔隙网络，并确定最佳孔隙网络结构，使过滤器寿命最大化，同时满足规定的杂质去除阈值。该项目还将为本科生和研究生提供培训、研究和工业经验。该项目解决了多孔膜过滤器中的流动和污染问题，其中孔隙结构可以建模为连接（足够细长）的管道网络。与W.L. Gore & & Associates的工业合作者以及一组学生合作，pi将推导出新的预测数学模型来描述具有实际重要性的情况。我们的模型将在任意孔隙网络（其中孔隙的长度和半径都可以变化）上制定，并将通过在孔隙壁上吸附小颗粒污染物和通过筛分大颗粒（具有任意尺寸分布）来描述污染。我们将研究计算生成的网络（使用随机几何图构造的一种变体）以及非专有制造膜中的真实孔隙网络。我们还将使用持续同源性（PH）的方法来研究这种孔隙网络的连通性特征以及这些特征如何随时间演变，以阐明几何/拓扑特征与过滤性能指标之间的比例关系。我们的工业合作者对这项工作非常感兴趣，他们将通过定期的团队会议向我们提供有关工业相关性的数据和建议。这种互动将确保项目保持重点，并将确保我们识别和解决对应用程序真正重要的问题。所提供的实验数据还将使我们能够确定模型中未知参数的适当范围，并测试不确定的建模假设。此外，我们将为我们的应用数学顶点课程制定新的模块，这些模块将通过蒙特卡罗类型模拟和使用可用软件库的持久同源方法让本科生参与研究。该研究将结合新颖的数学建模和分析方法，包括图论、优化、均匀化技术、多尺度分析、渐近方法、随机分析和概率论，以及有效的数值技术。该奖项反映了美国国家科学基金会的法定使命，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。

项目成果

Flow through pore-size graded membrane pore network

流经孔径分级的膜孔网络

• DOI: 10.1103/physrevfluids.8.044502
• 发表时间: 2023
• 期刊: Physical Review Fluids
• 影响因子: 2.7
• 作者: Gu, Binan;Kondic, Lou;Cummings, Linda J.
• 通讯作者: Cummings, Linda J.