Colin Denniston

Lattice Boltzmann Simulations of Liquid Crystal Hydrodynamics

We describe a lattice Boltzmann algorithm to simulate liquid crystal hydrodynamics. The equations of motion are written in terms of a tensor order parameter. This allows both the isotropic and the nematic phases to be considered. Backflow effects and the hydrodynamics of topological defects are naturally included in the simulations, as are non-Newtonian flow properties such as shear thinning and shear banding.

Hydrodynamics of Topological Defects in Nematic Liquid Crystals

We show that backflow, the coupling between the order parameter and the velocity fields, has a significant effect on the motion of defects in nematic liquid crystals. In particular, the defect speed can depend strongly on the topological strength in two dimensions and on the sense of rotation of the director about the core in three dimensions.

Lattice Boltzmann algorithm for three-dimensional liquid-crystal hydrodynamics

We describe a lattice Boltzmann algorithm to simulate liquid–crystal hydrodynamics in three dimensions. The equations of motion are written in terms of a tensor order parameter. This allows both the isotropic and the nematic phases to be considered. Backflow effects and the hydrodynamics of topological defects are naturally included in the simulations, as are viscoelastic effects such as shear–thinning and shear–banding. We describe the implementation of velocity boundary conditions and show that the algorithm can be used to describe optical bounce in twisted nematic devices and secondary flow in sheared nematics with an imposed twist.

Hydrodynamics of domain growth in nematic liquid crystals

We study the growth of aligned domains in nematic liquid crystals. Results are obtained solving the Beris-Edwards equations of motion using the lattice Boltzmann approach. Spatial anisotropy in the domain growth is shown to be a consequence of the flow induced by the changing order parameter field (backflow). The generalization of the results to the growth of a cylindrical domain, which involves the dynamics of a defect ring, is discussed.

Fluctuating lattice-Boltzmann model for complex fluids

We develop and test numerically a lattice-Boltzmann (LB) model for nonideal fluids that incorporates thermal fluctuations. The fluid model is a momentum-conserving thermostat, for which we demonstrate how the temperature can be made equal at all length scales present in the system by having noise both locally in the stress tensor and by shaking the whole system in accord with the local temperature. The validity of the model is extended to a broad range of sound velocities. Our model features a consistent coupling scheme between the fluid and solid molecular dynamics objects, allowing us to use the LB fluid as a heat bath for solutes evolving in time without external Langevin noise added to the solute. This property expands the applicability of LB models to dense, strongly correlated systems with thermal fluctuations and potentially nonideal equations of state. Tests on the fluid itself and on static and dynamic properties of a coarse-grained polymer chain under strong hydrodynamic interactions are used to benchmark the model. The model produces results for single-chain diffusion that are in quantitative agreement with theory.

On the orientation of lamellar block copolymer phases under shear

Self-assembled lamellar structures composed of block copolymers are simulated by molecular dynamics. The response of a bulk system to external shear is investigated, in particular, the average energy, the entropy production, and the stability of the lamellaes orientation. We distinguish two orientations, a parallel orientation in which the normal to the lamellae sheets lies in the direction of the shear gradient, and a perpendicular orientation in which the normal lies perpendicular to the shear gradient and shear direction. The perpendicular phase is stable throughout all shear rates. The parallel phase has higher internal energy and larger entropy production than the perpendicular phase and moreover becomes unstable at relatively small shear rates. The perpendicular orientation should therefore be more stable at any finite shear rate. Surface effects are probably responsible for the stability of the parallel phase observed experimentally at small shear rates.

Flexoelectric surface switching of bistable nematic devices

We report on a novel method of dynamically controlling the boundary conditions at the surface of a nematic liquid crystal using a surface flexoelectric effect. By moving the surface directors we show that one is able to manipulate defects which lie near the surface. This can be used to produce switching of a nematic liquid-crystal device between two states with very similar free energies. This results in a bistable device that can retain either state with no applied voltage. Switching between the states occurs when the movement of the surface directors rotates those in the bulk which are then able to create or annihilate defects which lie near the surface of the device.

Elastic response of a nematic liquid crystal to an immersed nanowire

We study the immersion of a ferromagnetic nanowire within a nematic liquid crystal using a lattice Boltzmann algorithm to solve the full three-dimensional equations of hydrodynamics. We present an algorithm for including a moving boundary, to simulate a nanowire, in a lattice Boltzmann simulation. The nematic imposes a torque on a wire that increases linearly with the angle between the wire and the equilibrium direction of the director field. By rotation of these nanowires, one can determine the elastic constants of the nematic.

Molecular and continuum boundary conditions for a miscible binary fluid.

We show that molecular-dynamics simulations can furnish useful boundary conditions at a solid surface bounding a two-component fluid. In contrast to some previous reports, convective-diffusive flow is consistent with continuum equations down to atomic scales. However, concentration gradients can produce flow without viscous dissipation that is inconsistent with the commonly used Navier slip condition. Also, differential wetting of the two components coupled to a concentration gradient can drive convective flows that could be used to make nanopumps or motors.

Modelling defect-bonded chains produced by colloidal particles in a cholesteric liquid crystal

We use a Landau-de Gennes free-energy model to investigate interactions generated by spherical particles with strong planar anchoring immersed in a cholesteric liquid crystal. With a pitch of ~1.5 times the particle diameter, the +1 boojums present for a particle in a nematic split into four +1/2 defects leading to defect lines in the bulk around the particle which look like handles emerging from its surface. When multiple particles are present, handles from adjacent particles join together, forming a defect bond between them. We present results for defect-bonded chains, and investigate the energies associated with this bonding.