Viscous fingering and liquid crystals in confinement - Zacharoudiou, I (2012)
This thesis focuses on two problems lying within the field of soft condensed matter: the viscous fingering or Saffman-Taylor instability and nematic liquid crystals in confinement. Whenever a low viscosity fluid displaces a high viscosity fluid in a porous medium, for example water pushing oil out of oil reservoirs, the interface between the two fluids is rendered unstable. Viscous fingers develop, grow and compete until a single finger spans all the way from inlet to outlet. Here, using a free energy lattice Boltzmann algorithm, we examine the Saffman-Taylor instability for two different wetting situations: (a) when neither of the two fluids wet the walls of the channel and (b) when the displacing fluids completely wets the walls. We demonstrate that curvature effects in the third dimension, which arise because of the wetting boundary conditions, can lead to a novel suppression of the instability. Recent experiments in microchannels using colloid-polymer mixtures support our findings. In the second part of the thesis we examine nematic liquid crystals confined in wedge-structured geometries. In these systems the final stable configuration of the liquid crystal system is controlled by the complex interplay between confinement, elasticity and surface anchoring. Varying the wedge opening angle this competition leads to a splay to bend transition mediated by a defect in the bulk of the wedge. Using a hybrid lattice Boltzmann algorithm we study the splay-bend transition and compare to recent experiments on {em fd} virus particles in microchannels. Our numerical results, in quantitative agreement with the experiments, enable us to predict the position of the defect as a function of opening angle, and elucidate its role in the change of director structure. This has relevance to novel energy saving, liquid crystal devices which rely on defect motion and pinning to create bistable director configurations.