NSF Award
2309798
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. <br/><br/>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.<br/><br/>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.
