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.

在反应流体之间界面区域中局部反应产生的新型形态不稳定性和相变，可以在物理，生物学和工程系统（例如闷烧的火焰阵线，生物膜形成和石油回收系统）中找到。例如，在石油回收过程中，在水油界面上形成固体凝胶可能是不利的，因为凝胶堆积会堵塞井和管道。另一方面，凝胶形成实际上可以通过将流从多孔岩石转移并增强油回收率来对流动转移过程有益。该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，并且需要数学模型和数值模拟来充分表征非线性的，超平衡的动力学。 该项目旨在为非平衡现象模型建立一个计算框架，并设计算法和实验，以研究复杂的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，研究活动将有助于发展下一代数学家，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，在该研究人员中，研究生对项目主题进行了培训。对两个或多个反应性且流过多孔介质的流体的研究对于许多领域都是基础的。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）。当将一种流体注入另一种流体中，将其驱动到平衡中时，它们之间扩展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与流体动力学之间的相互作用。该项目建立在建模，计算和实验技术中的突破性基础上，以开发统一的数学框架，该框架解决了从平衡中驱动的反应流体的界面动力学。将得出不混溶性流体的三元反应系统的非平衡动力学的热力学一致方程，以径向的Hele-shaw几何形状为原型。将开发和验证尖锐的界面和漫画界面数值方案（使用标量辅助变量的能量稳定，适应性有限差异方法）都将得到开发和验证，并验证针对对敏锐的界面模型的渐近降低和该项目产生的新实验数据。综合数学，计算和实验方法将为理解非平衡动态提供一个框架，预测复杂模式的出现，并制定了控制基本多物理界面问题的模式形成过程的策略。这奖反映了NSF的立法任务，并被认为是值得的。通过基金会的智力优点和更广泛的影响评估标准通过评估来支持。