Brickell, T.; (2012) General two-dimensional linear flows of particle suspensions. Masters thesis , UCL (University College London).

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Abstract

This thesis investigates the flow of suspensions of solid spheres in a viscous fluid. We look at a monolayer of particles in an unbounded fluid, and carry out numerical simulations of its behaviour under a variety of linear flows. In chapter 1 we review the field and discuss the different approaches to simulating a suspension of solid spheres in a viscous fluid. We outline the case for the method of Stokesian Dynamics, and explain its derivation. In chapter 2 we introduce the concept of a spatially periodic lattice which self-replicates in time under flow. We then go on to derive a suitable periodic box for each possible two dimensional linear flow, from pure strain to pure rotation, through simple shear and flows of intermediate type. Using the numerical method of Stokesian Dynamics, in chapter 3 we proceed to investigate the macroscopic properties of our two-dimensional suspension in the various flows. The viscosity and normal stress difference are probed at both short and long times. We find evidence of crystallisation, and our major discovery is that crystallisation sets in earlier (in terms of increasing concentration) for flows that are closer to shear flow than those with a larger component of rotation or of strain. We also present results on the duration of transients in start up flow. In chapter 4 we consider the effects of surface roughness on viscosity. Two different models for roughness are considered, the usual hard contact and a new soft contact model first proposed by Wilson in [65]. A comparison of the results of the two models is undertaken and we discuss about the effects of lower viscosity occurring at low concentrations due to surface roughness. In Appendix A we consider the method of Ewald summation which can be used to properly account for far-field interactions in a lattice-periodic system, and derive the relevant forms for a system which is periodic in only two dimensions. Unfortunately we discover a problem with the Hankel transform but the real space relations are still valid. This will have application both to monolayer systems such as the one we have studied, and to confined suspensions in a variety of applications where the relevant geometry has a large aspect ratio.

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