Orientational dynamics of the compressible nematic liquid crystals induced by a temperature gradient

Recent developments of analysis for hydrodynamic flow of nematic liquid crystals

The study of hydrodynamics of liquid crystals leads to many fascinating mathematical problems, which has prompted various interesting works recently. This article reviews the static Oseen-Frank theory and surveys some recent progress on the existence, regularity, uniqueness and large time asymptotic of the hydrodynamic flow of nematic liquid crystals. We will also propose a few interesting questions for future investigations.

Effect of electric field and temperature gradient on the orientational dynamics of liquid crystals in a microvolume cylindrical cavity

We have considered a homogeneously aligned liquid crystal (HALC) microvolume confined between two infinitely long horizontal coaxial cylinders and investigated dynamic field pumping, i.e., studied the interactions between director, velocity, and electric E fields as well as a radially applied temperature gradient inverted Delta T, where the inner cylinder is kept at a lower temperature than the outer one. In order to elucidate the role of inverted Delta T in producing hydrodynamic flow u, we have carried out a numerical study of a system of hydrodynamic equations including director reorientation, fluid flow, and temperature redistribution across the HALC cavity. Calculations show that only under the influence of inverted Delta T does the initially quiescent HALC sample settle down to a stationary flow regime with horizontal component of velocity u(eq)(r). The effects of inverted Delta T and of the size of the HALC cavity on magnitude and direction of u(eq)(r) have been investigated for a number of hydrodynamic regimes. Calculations also showed that E influences only the director redistribution across the HALC but not the magnitude of the velocity u(eq)(r).

Director reorientation in a hybrid-oriented liquid-crystal film induced by thermomechanical effect

We have carried out a numerical study of a system of hydrodynamic equations including director reorientation, fluid flow, and temperature redistribution across a two-dimensional (2D) hybrid-oriented liquid-crystal (HOLC) cell under the influence of a heat flow directed normal to the upper bounding surface, whereas on the rest boundaries the temperature is kept constant. Calculations based upon the nonlinear extension of the classical Ericksen-Leslie theory shows that the HOLC material under the influence of the heat flow, after some time, more than the time of relaxation, for instance, of the director field in the HOLC cell, settles down to the rest state regime, where the horizontal and vertical components of the velocity vector are equal to zero, and the temperature field across the LC cell finally reaches the value of temperature on the lower and two lateral bounding surfaces. The role of hydrodynamic flow in the relaxation processes of the temperature field to its equilibrium distribution across the 2D HOLC cell, containing 4-n-pentyl-4'-cyanobiphenyl, has been investigated, for a number of dynamic regimes.

Liquid-crystal pumping in a cylindrical capillary with radial temperature gradient

Dynamic field pumping principle has been developed utilizing the interactions of both the director and velocity fields and a temperature gradient inverted deltaT. The orientational dynamics in the hybrid-oriented liquid-crystal (HOLC) microvolume confined between two infinitely long coaxial cylinders under the influence of the radially directed inverted deltaT has been investigated. We have carried out a numerical study of a system of hydrodynamic equations including director reorientation, fluid flow, and temperature redistribution across the HOLC cavity between two cylinders under the influence of inverted deltaT, when the liquid-crystal cavity is heated both from outer (inner) to inner (outer) bounding cylinders. Calculations show that under the influence of inverted deltaT the initially quiescent HOLC drop settles down to a stationary flow regime, with the horizontal u(st)(r) component of velocity. The effects of inverted deltaT , of the character of the preferred anchoring of the average molecular direction to the restricted cylinders, and of the size of the HOLC cavity on magnitude and direction of hydrodynamic flow--for a number of hydrodynamic regimes--has been investigated.