Phase-field models, algorithms and simulations for multiphase complex fluids – Phasefield

Phase-field methods have become a major tool to study a variety of interfacial phenomena, such as equilibrium shapes of vesicle membranes, blends of polymeric liquids, multiphase flows including drop deformation in another fluid and liquid films, dendritic growth in solidification, microstructure evolution, grain growth, crack propagation, morphological pattern formation in thin films and on surfaces, self-assembly dynamics of two-phase monolayer on an elastic substrate, and diffusive or diffusion-less solid-state phase transitions, etc.
However, the mathematical studies of multiphase complex materials remain a rich area for research with important applications that can be addressed. Some difficulties include:

(i) the moving interfaces between various components for which, the traditional sharp interfaces model usually leads to an almost intractable theoretical problem;
(ii) the open issues regarding well-posedness of many multiphase models lead to confusion as to whether numerical pathologies are due to the model or the methods; and most importantly
(iii) the nonlinear couplings (hydrodynamics, interface and microstructure) make it difficult to design efficient (energy stable and accurate) numerical schemes that in particular satisfy a discrete energy dissipation laws. It has been shown analytically and numerically that the energy dissipation law is particularly important for the solutions undergoing rapid changes at the interface and the non-compliance of energy dissipation laws may lead to spurious numerical solutions if the grid and time step sizes are not carefully controlled.

The goal of the project is twofold:

1) Make a significant breakthrough concerning some major mathematics and numerical modeling questions such that
(i) Derive suitable energetic variational phase-field models for the multiphase complex material system that couples the hydrodynamics, microstructure and interfacial dynamics;
(ii) Develop efficient, easy-to-implement, energy stable numerical schemes to accurately capture the dynamics of interface singularities as well as the microstructures for the derived multiphase complex material systems.

2) Perform numerical simulations to validate the models and numerical schemes. We aim at designing and analyzing materials used for thermal energy storage at high temperature. The object is to appreciate the efficiency of our phase field algorithms when they are applied to the development and optimization of new materials through modeling and numerical simulation. This general objective can be broken down as follows:
(i) How phase-field approach can help to understand the processes and mechanisms associated with solid-liquid transformations of peritectic systems, especially in porous media.
(ii) How phase-field approach can contribute to develop best structure of the porous support in the hybrid medium comprising, which play a crucial role in the performance and the macroscopic behavior of the final material dedicated to thermal energie storage.