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

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.