Computational studies on interfacial dynamics in complex fluids

This thesis aims to develop and apply modern computational techniques to study the interfacial dynamics involving complex fluids, where the underlying microstructure strongly affects the behaviour of the fluid. In particular, we have chosen two case studies that are significant to the current state of knowledge in specific fluids. In the first problem, we investigate the interaction between a pair of ferrofluid drops subject to rotating magnetic fields. Through direct numerical simulation using a volume-of-fluid method, we classify four different regimes of the ferrofluid drop interaction. We closely examine the planetary motion regime and identify hydrodynamic interaction to be dominant over magnetic dipole interactions. We also discover a new interaction regime called drop locking, which is confirmed in experiments inspired by our study. In the second problem, we first develop a phase-field method to compute elasto-capillary flows of nematic liquid crystals. The new formulation is able to simultaneously achieve a consistent description of structures of topological defects in the material, as well as an accurate recovery of macroscopic interfacial forces including surface tension and liquid crystal anchoring stress. This is made possible by incorporating a hydrodynamic theory of liquid crystals based on a tensor order parameter in a phase-field formalism approximating the sharp-interface limit. Then the method is applied to the drop retraction problem. We characterize a variety of different cases and examine their dynamics. Our numerical results reveal quantitatively that the drop deformation is a hallmark of competition between bulk distortional elasticity of the liquid crystal and surface tension. The new computational framework opens doors to a large class of fundamental problems concerning colloidal interaction in coupled elasto-capillary fields.Science, Faculty ofMathematics, Department ofGraduat