Modelling and analysis of diffuse interface models for two-phase micropolar fluid flows

The main aims of this proposal are to develop new mathematical models for mixtures of micropolar fluids, study their mathematical properties, and derive stable and efficient fully discrete numerical schemes for simulations. The key ingredient is the diffuse interface methodology which offers a model that is amenable to further mathematical analysis and allows us to address the existence of weak solutions and the stability of discrete solutions. Also included in the modelling is the dynamics of the contact line that is created when two or more fluids meet at the same solid boundary.