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: 2309798
• 负责人: Shuwang Li
• 金额: $ 24.27万
• 依托单位: Illinois Institute of Technology
• 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=2309798&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，例如阴燃火焰锋、生物膜形成和石油回收系统中，可以发现由反应流体之间的界面区域中的局部反应产生的新型形态不稳定性和相变。例如，在采油过程中，在水-油界面处形成固体凝胶可能是不利的，因为凝胶的堆积会堵塞油井和管道。另一方面，凝胶形成实际上有利于流量转移过程，通过将流量从多孔岩石中转移出来并提高石油采收率。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。 该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，预计将针对该项目的主题对研究生进行培训。对两种或多种反应性流体并流经多孔介质的研究是许多领域的基础。在平衡时，根据平衡相图，混合物可能表现得像液体或凝胶（粘弹性固体），具体取决于组分的浓度。例如，当通过将一种流体注入另一种流体而失去平衡时，它们之间的膨胀界面的形态可能非常复杂，并且很大程度上取决于热力学相行为和流体动力之间的相互作用。该项目建立在建模、计算和实验技术突破的基础上，开发一个统一的数学框架，解决失去平衡的反应流体的界面动力学问题。将导出控制不混溶流体三元反应系统的非平衡动力学的热力学一致方程，重点关注径向 Hele-Shaw 几何形状作为原型。将开发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），并针对尖锐界面模型的渐近约简和该项目生成的新实验数据进行验证。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开发控制基本多物理场界面问题中模式形成过程的策略提供一个框架。该奖项反映了 NSF 的法定使命，并被认为是值得的通过使用基金会的智力优势和更广泛的影响审查标准进行评估来获得支持。