Advancing Mechanistic Understanding of Two-Fluid-Phase Flow in Porous Medium Systems

两相多孔介质系统是包含固体相和两种不同的不混相流体相的系统，它们填满固体颗粒之间的孔隙空间。这类系统出现在许多社会感兴趣的应用中，包括地球表面的水渗透、碳封存、水力压裂井的产气、石油开采、陆地-大气相互作用、工程处理过程和广泛的生物医学应用（例如肿瘤生长、皮肤运输等）。我们对多孔介质系统的科学理解体现在机械数学模型中，这些模型用于评估此类多孔介质系统，进行预测，指导工程设计，并为政策决策提供信息。由于许多多孔介质系统的长度远远大于固相的自然长度尺度，用于表示此类系统的数学模型通常以忽略已知影响此类系统中流动的物理过程的许多方面的尺度提出。虽然物理学在小尺度上得到了较好的理解，但在小尺度和大尺度之间并不存在严格的联系，而大尺度必须解决问题。最近，一种理论已经发展起来，将这两种长度尺度联系起来，产生的模型有望比实际使用的标准模型在物理上更真实、更准确。本研究将把这些新的理论模型简化为完全可解的形式，评估这些模型的具体方面，并在一系列系统中验证这些模型。小尺度实验和高分辨率建模将被用来实现这些目标。由于这类问题的广泛适用性，其结果将对社会产生广泛的益处，而且这项工作将涉及从从事科学研究的人口中大量代表性不足的部分中招募的研究生。水文学中的许多关键问题都涉及到多孔介质系统中的两相流动。所提出的工作将使用热力学约束平均理论（TCAT）将充分理解的微尺度过程与宏观尺度模型联系起来，这将产生封闭的、已解决的模型，并对其进行评估和验证。微流体实验和高分辨率晶格玻尔兹曼模拟将用于提供构建特定形式闭合关系所需的精细尺度细节，并支持对这类新模型的全面评估和验证。计算和实验方法和结果也将产生，这将是价值独立的理论方式，其中宏观系统建模。这项工作将产生一系列更广泛的重大影响。所建立的模型是基于水文的，但其适用性远远超出了水文学。我们将培养和发展我们的合作者，将基于tcat的模型应用于肿瘤生长、糖尿病对极端组织的影响以及超滤膜等工程系统。所开发的晶格玻尔兹曼方法将适用于广泛的系统，超出了本工作的重点水文系统。一本描述理论进展的书的第二版将被制作出来，以传播这项工作的发现。其他影响包括：(1)通过课程内容、学生研究和科学推广对教育的贡献；(2)代表不足的研究人员的参与以及与少数族裔招聘计划的联系；(3)在水文、物理、工程和应用数学期刊上广泛传播研究成果；(4)实验和高分辨率模拟的独特数据集和视频图像的数字化存档和传播。

Two-fluid-phase porous medium systems are systems that contain a solid phase and two distinct immiscible fluid phases that fill the pore space between solid particles. This general class of system arises in many applications of interest to society, including water infiltration from the Earth's surface, carbon sequestration, gas production from hydraulically fractured wells, petroleum recovery, land-atmosphere interaction, engineered treatment processes, and a wide range of biomedical applications (e.g. tumor growth, dermal transport, etc.). Our scientific understanding of porous medium systems is embodied in mechanistic mathematical models, which are used to evaluate such porous medium systems, make predictions, guide engineering design, and to inform policy decisions. Because the length of many porous medium systems is much greater than the natural length scale of the solid phase, the mathematical models intended to represent such systems are typically posed at a scale that neglects many aspects of the physical processes known to influence flow in such systems. While the physics are relatively well understood at the small scale, there has not existed a rigorous connection between the small, well-understood scale and the larger scale where problems must be solved. Recently, a theory has been developed that connects these two length scales and yields models that have the promise to be more physically realistic and accurate than the standard models used in practice. This research will reduce these new theoretical models to completely solvable forms, evaluate specific aspects of these models, and validate the models for a range of systems. Both small scale experiments and high-resolution modeling will be a used to accomplish these objectives. The results will be of widespread benefit to society because of the broad applicability of this class of problem, and the work will involve graduate students recruited from a pool that is rich in under-represented fractions of the population working in scientific research. Many critical problems in hydrology involve two-fluid-phase flow in porous medium systems. The proposed work will connect well-understood microscale processes with macroscale models using the thermodynamically constrained averaging theory (TCAT) that will yield closed, solved models that are evaluated and validated. Microfluidic experiments, and high resolution lattice Boltzmann simulations will be used to provide the fine scale detail needed to construct specific forms of closure relationships and support a thorough evaluation and validation of this new class of model. Computational and experimental methods and results will also be produced that will be of value independent of the theoretical manner in which macroscale systems are modeled. This work will have a significant set of broader impacts. The models developed are hydrologically motivated but have applicability far beyond hydrology. We will nurture and grow our set of collaborators that apply TCAT-based models for applications such as tumor growth, the effects of diabetes on extremal tissue, and engineered systems such as ultrafiltration membranes. The lattice-Boltzmann methods developed will be applicable to a wide range of systems beyond the hydrologic systems of focus in this work. A second edition of a book describing the theoretical advances will be produced to disseminate the findings of this work. Additional impacts include: (1) contributions to education through course content, student research, and science outreach; (2) participation of underrepresented researchers and linkages to minority recruitment programs; (3) broad dissemination of findings in hydrology, physics, engineering, and applied mathematics journals; and (4) digital archiving and dissemination of unique data sets and video images of experiments and high-resolution simulations.