Julia Yeomans OBE FRS

Abstract:

We present lattice Boltzmann simulations of the dynamical equations of motion of a drop of isotropic fluid in a nematic liquid crystal solvent, both in the absence and in the presence of an electric field. The coupled equations we solve are the Beris-Edward equations for the dynamics of the tensor order parameter describing the nematic solvent, the Cahn-Hilliard equation for the concentration evolution, and the Navier-Stokes equations for the determination of the instantaneous velocity field. We implement the lattice Boltzmann algorithm to ensure that spurious velocities are close to zero in equilibrium. We first study the effects of the liquid crystal elastic constant, K, anchoring strength, W, and surface tension, sigma, on the shape of the droplet and on the director field texture in equilibrium. We then consider how the drop behaves as the director field is switched by an applied electric field. We also show that the algorithm allows us to follow the motion of a drop of isotropic fluid placed in a liquid crystal cell with a tilted director field at the boundaries.

Abstract:

We present a free energy lattice Boltzmann approach to modelling the dynamics of liquid drops on chemically patterned substrates. We start by describing a choice of free energy that reproduces the bulk behaviour of a liquid-gas system together with the varying contact angles on surfaces with chemical patterning. After showing how the formulation of the free energy fits in to the framework of lattice Boltzmann simulations, numerical results are presented to highlight the applicability of the approach. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.

Abstract:

I introduce two mesoscale algorithms, lattice Boltzmann and stochastic rotation dynamics, and show how they can be used to investigate the hydrodynamics of complex fluids. For each method I describe the algorithm, show that it solves the Navier-Stokes equations, and then discuss physical problems where it is particularly applicable. For lattice Boltzmann the examples I choose are phase ordering in a binary fluid and drop dynamics on a chemically patterned surface. For stochastic rotation dynamics I consider the hydrodynamics of dilute polymer solutions, concentrating on shear thinning and translocation across a barrier. (c) 2006 Elsevier B.V. All rights reserved.