Mixtures of two or more immiscible viscous and/or complex fluid components are widely used in many science and engineering applications, in particular, in designing advanced materials involving polymers, composites, gels, liquid crystals, etc. It is expected that the proposed models and numerical methods/simulations will contribute to a better understanding of the complex physical and mathematical issues related to multiphase complex fluids, and provide valuable information for the design of advanced materials and on the rheological and hydrodynamic properties of complex fluids. The proposed research will also provide valuable opportunities for undergraduate and graduate students to engage in interdisciplinary research with strong ties to biological and engineering material systems, to learn critical skills of computational and applied mathematics, and to develop state-of-the-art numerical tools for science and engineering applications.
Flows of multiphase complex fluid mixtures usually involve the coupling of microstructures, interfacial morphology and macroscopic hydrodynamics. The complexity of these nonlinear couplings presents many mathematical challenges for modeling and algorithm development, numerical analysis and implementation. The proposed research aims at overcoming these challenges to design efficient and accurate numerical algorithms for nonlinear multiphase complex fluid systems that couple the microstructure, moving material interfaces and hydrodynamics. Very few efforts have been made to address these numerical challenges. This project will result in numerical schemes which satisfy discrete energy dissipation laws, and which allow large time steps and controllable error and capture the interfacial dynamics accurately. In addition, the developed predictive tools and numerical simulations will extend the applicability of mathematical analysis and numerical codes to physical problems of current interest, and contribute to a better understanding of pressing science and engineering applications.
