Mesoscale fluid simulation with the Lattice Boltzmann method

PhDThis thesis describes investigations of several complex fluid effects., including hydrodynamic spinodal decomposition, viscous instability. and self-assembly of a cubic surfactant phase, by simulating them with a lattice Boltzmann computational model. The introduction describes what is meant by the term "complex fluid", and why such fluids are both important and difficult to understand. A key feature of complex fluids is that their behaviour spans length and time scales. The lattice Boltzmann method is presented as a modelling technique which sits at a "mesoscale" level intermediate between coarse-grained and fine-grained detail, and which is therefore ideal for modelling certain classes of complex fluids. The following chapters describe simulations which have been performed using this technique, in two and three dimensions. Chapter 2 presents an investigation into the separation of a mixture of two fluids. This process is found to involve several physical mechanisms at different stages. The simulated behaviour is found to be in good agreement with existing theory, and a curious effect, due to multiple competing mechanisms, is observed, in agreement with experiments and other simulations. Chapter 3 describes an improvement to lattice Boltzmann models of Hele-Shaw flow, along with simulations which quantitatively demonstrate improvements in both accuracy and numerical stability. The Saffman-Taylor hydrodynamic instability is demonstrated using this model. Chapter 4 contains the details and results of the TeraGyroid experiment, which involved extremely large-scale simulations to investigate the dynamical behaviour of a self-assembling structure. The first finite- size-effect- free dynamical simulations of such a system are presented. It is found that several different mechanisms are responsible for the assembly; the existence of chiral domains is demonstrated, along with an examination of domain growth during self-assembly. Appendix A describes some aspects of the implementation of the lattice Boltzmann codes used in this thesis; appendix B describes some of the Grid computing techniques which were necessary for the simulations of chapter 4. Chapter 5 summarises the work, and makes suggestions for further research and improvement.Huntsman Corporation Queen Mary University Schlumberger Cambridge Researc

Phase separation, patterning and orientational ordering on closed surfaces: modelling the dynamics of molecules on biological membranes and vesicles

We investigate the dynamics of scalar and vector fields on closed surfaces through the use of numerical algorithms adapted from the literature or freshly developed. The aim of this study is the creation and numerical integration of models for phase separation, pattern formation and emergence of orientational order on biological membranes, as well as the dynamical evolution of the shape of vesicles. We find mechanisms that explain curvature-induced arrest of phase separation, localisation of patterns within certain regions of the membrane; we explore the parameter space of an elastic model of bicomponent vesicles and finally we set up a numerical model to study the time evolution of a nematic fluid on spherical geometry consistent with the expected behaviour of the field