Collaborative Research: : Mathematical modeling and computation of morphological instabilities in reactive fluids driven out of equilibrium

合作研究：：失去平衡的反应流体形态不稳定性的数学建模和计算

• 批准号: 2309799
• 负责人: Zahra Niroobakhsh
• 金额: $ 14.63万
• 依托单位: University of Missouri-Kansas City
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2309799&HistoricalAwards=false
• 关键词: Collaborative; Research; Mathematical; modeling; computation

Novel morphological instabilities and phase changes generated by localized reactions in interfacial regions between reacting fluids can be found in physical, biological and engineering systems such as smoldering flame fronts, biomembrane formation, and oil recovery systems. For instance, the formation of solid-like gels at water-oil interfaces during oil recovery processes can be unfavorable because gel build-up can clog wells and pipelines. On the other hand, gel formation can actually be beneficial in flow diversion processes by diverting the flow away from porous rocks and enhancing oil recovery. The interface dynamics and morphologies of this open system cannot be predicted solely by an equilibrium phase diagram, and mathematical models and numerical simulations are needed to fully characterize the nonlinear, out-of-equilibrium dynamics. This project aims to establish a computational framework for models of non-equilibrium phenomena, and design algorithms and experiments to investigate the interface dynamics of complex, reactive fluids. This project will also provide interdisciplinary training for students, and research activities will help develop the next generation of mathematicians, scientists and engineers. The team of PIs consists of the three researchers from three different institutions, where training of graduate students on the topics of the project is expected. Studies of two or more fluids that are reactive, and flow through a porous medium, are fundamental to many fields. At equilibrium, the mixture may behave like a liquid or a gel (viscoelastic solid) depending on the concentrations of the components according to an equilibrium phase diagram. When driven out of equilibrium by, for instance, injection of one fluid into another, the morphology of the expanding interface between them can be very complex and strongly depends on an interplay between thermodynamic phase behavior and hydrodynamic forces. This project builds upon breakthroughs in modeling, computation, and experimental techniques to develop a unified mathematical framework that resolves the interface dynamics of reactive fluids driven out of equilibrium. Thermodynamically consistent equations governing the non-equilibrium dynamics of ternary reacting systems of immiscible fluids will be derived, focusing on the radial Hele-Shaw geometry as a prototype. Both sharp interface and diffuse interface numerical schemes (energy-stable, adaptive finite-difference methods using scalar auxiliary variables) will be developed and validated against asymptotic reductions to sharp interface models and new experimental data generated from this project. The integrated mathematical, computational and experimental approach will provide a framework for understanding the nonequilibrium dynamics, predicting the emergence of complex patterns and developing strategies for controlling the pattern formation process in fundamental multiphysics interface problems.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.

在物理、生物和工程系统中，如阴燃前缘、生物膜形成和石油回收系统中，可以发现由反应流体界面区域局部反应产生的新型形态不稳定性和相变化。例如，在采油过程中，在水-油界面形成固体状凝胶是不利的，因为凝胶积聚会堵塞油井和管道。另一方面，凝胶地层在导流过程中实际上是有益的，它可以将流体从多孔岩石中引开，提高石油采收率。这种开放系统的界面动力学和形态不能仅仅通过平衡相图来预测，需要数学模型和数值模拟来充分表征非线性、非平衡动力学。本项目旨在建立非平衡现象模型的计算框架，并设计算法和实验来研究复杂反应性流体的界面动力学。该项目还将为学生提供跨学科培训，研究活动将有助于培养下一代数学家、科学家和工程师。pi团队由来自三个不同机构的三名研究人员组成，预计将在这些机构就项目主题对研究生进行培训。研究两种或两种以上的反应性流体，并在多孔介质中流动，是许多领域的基础。在平衡状态下，根据平衡相图中各组分的浓度，混合物可能表现为液体或凝胶（粘弹性固体）。例如，当一种流体注入另一种流体时，它们之间膨胀界面的形态可能非常复杂，并且在很大程度上取决于热力学相行为和水动力之间的相互作用。该项目建立在建模、计算和实验技术的突破之上，开发了一个统一的数学框架，解决了脱离平衡的反应性流体的界面动力学问题。将推导出控制非混相流体三元反应系统非平衡动力学的热力学一致方程，以径向Hele-Shaw几何为原型。尖锐界面和扩散界面数值方案（使用标量辅助变量的能量稳定、自适应有限差分方法）将根据尖锐界面模型的渐近约化和本项目产生的新实验数据进行开发和验证。综合数学，计算和实验方法将为理解非平衡动力学，预测复杂模式的出现以及制定控制基本多物理场界面问题的模式形成过程的策略提供框架。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。