Condensed Matter Theory

Abstract:

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.

Abstract:

The dynamics of the deformations of a moving contact line on a disordered substrate are formulated, taking a proper account of the various interfacial forces as well as the dissipation mechanisms. Prompted by the results from dynamical renormalization group calculations, it is suggested that the coating transition in contact lines receding at relatively high velocities can be understood as a roughening transition in the contact line. A phase diagram is proposed for the system in which the phase boundaries corresponding to the coating transition and the pinning transition meet at a junction point, and suggest that for sufficiently strong disorder a receding contact line will leave a Landau-Levich film immediately after de-pinning.

Abstract:

We use a three-dimensional lattice Boltzmann model to investigate the spreading of mesoscopic droplets on homogeneous and heterogeneous surfaces. On a homogeneous substrate the base radius of the droplet grows with time as t(0.28) for a range of viscosities and surface tensions. The time evolutions collapse onto a single curve as a function of a dimensionless time. On a surface comprising of alternate lyophobic and lyophilic stripes the wetting velocity is anisotropic and the equilibrium shape of the droplet reflects the wetting properties of the underlying substrate. (C) 2003 Elsevier B.V. All rights reserved.

Abstract:

We study shear flow in liquid crystal cells with elastic deformations using a lattice Boltzmann scheme that solves the full, three-dimensional Beris-Edwards equations of hydrodynamics. We consider first twisted and hybrid aligned nematic cells, in which the deformation is imposed by conflicting anchoring at the boundaries. We find that backflow renders the velocity profile non Newtonian, and that the director profile divides into two regions characterized by different director orientations. We next consider a cholesteric liquid crystal, in which a twist deformation is naturally present. We confirm the presence of secondary flow for small shear rates, and are able to follow the dynamical pathway of shear-induced unwinding, for higher shear rates. Finally, we analyze how the coupling between shear and elastic deformation can affect shear banding in an initially isotropic phase. We find that for a nematic liquid crystal, elastic distortions may cause an asymmetry in the dynamics of band formation, whereas for a cholesteric, shear can induce twist in an initially isotropic sample.

Abstract:

The buckling of multi-walled carbon nanotubes and rods was discussed. It was shown that electrostatic interactions exert a significant effect on the buckling instability of a rod. The threshold value of the compressional force needed to induce buckling was found to be independent of rod length for long charged rods. The critical buckling force crosses over from the classic inverse-square length dependence to asymptotic length-independent form with increasing rod length, in the case of rods of intermediate length. It was suggested that this effect leads to the possibility of electromechanical stiffening of nanotubes, which would allow relatively long segments of them to be used as atomic force probes.