The investigators and their colleagues study novel instabilities in fluids driven by material complexity occurring only at interfaces. For instance, when two reacting micellar liquids are brought into contact, the reaction may produce a growing gel-like phase at the interface, which significantly stiffens the boundary between the fluids. Another example arises from the presence of nanoscale colloidal particles which accumulate at interfaces. Intercolloid forces also endow the interface with stiffness, and may even jam the interface at sufficiently high volume fraction. The goal of this proposal is to develop comprehensive, physically appropriate models and simulations for these very difficult problems. The highly nonlinear nature of these problems makes fast, accurate and robust numerical methods essential to their study. The research team plans to investigate the nonlinear dynamics of interfaces endowed with complex physical properties and to develop strategies to control their pattern forming abilities by (1) developing and applying state-of-the-art adaptive numerical methods to large-scale computation; (2) performing analytical, numerical and modeling studies of important constituent processes; and (3) performing experiments to calibrate and validate the mathematical models, to test the model predictions, and to help elucidate the underlying physical processes.
Interfacial instabilities occur when driving forces compete with resistive forces with a consequence being the formation of complex patterns. Examples occur in diverse systems such as including filamentary microorganisms, growing biofilms, smoldering flame fronts, and lava flows. The goal of this project is to develop comprehensive, physically appropriate models and efficient numerical methods for solving such problems. Experiments will be performed to validate the models and test the model predictions, and to help elucidate the underlying physical processes. The research will focus on flows with complex interfacial physics such as reactions and nanoscale particles at interfaces. The research activities will provide new integrated theoretical, numerical and experimental results that can be used to (1) further explore these pattern forming systems that are driven out of equilibrium; (2)develop guidelines for controlling the evolving morphologies. While specific and novel applications are investigated here, the new mathematical and adaptive numerical techniques are expected have application beyond the present context. In addition, this project will provide valuable interdisciplinary training opportunities for young researchers, and outreach programs are planned for middle school and undergraduate students (Penn State), high school students (UC Irvine) and undergraduate students (Ill. Inst. Techn.).
