Pattern Formation and Stress Propagation in Confined Colloidal Flows

Particulate solutions exhibit many interesting and varied behaviours when driven out of equilibrium. Not least of which is their ability to form elaborate and intricate patterns when subject to gravity driven flow in the confined space between a substrate and the fluid-air interface of a thin film.
The present work presents results of investigations into some of the key physical pro- cesses within the fluid, that are thought to lead to the formation of patterns. These were performed using a range of simplified models and numerical simulations. The cen- tral theme of the work is a simplified two fluid model of the particle-laden fluid itself, the results of which reveal a novel pattern formation process, entirely distinct from the conventional instability driven process normally associated with patterning. This process involves the decay of fluctuations in the particle volume fraction in one direction while fluctuations in the other persist. Ultimately, however, it was found, using both simulations and analytical stability analysis, that the physical processes encompassed by this simple model are not sufficient to increase the intensity of the patterns.
As well as considering additions to the model; two more, in depth, studies of physical processes at the microscopic level, thought to be potentially important to the formation of patterns, were also carried out. These consisted of the formulation of a simple, analytical, constitutive relation and a particle scale simulation including full many body hydrody- namic interactions. These highlighted the importance of memory effects and, long range, hydrodynamic interactions as potentially important processes by which band patterns may grow and increase in intensity.
The whole issue of patterning on a surface also leads to the question of how these, two dimensional, patterns should be characterised and, to this end, a number of novel methods for calculating the complexity are also discussed.