THE DYNAMICS OF A THERMOTROPIC LIQUID-CRYSTAL

In this paper, we present a thermodynamically consistent theory describing the dynamics of thermotropic liquid-crystalline systems. This theory is based upon recent developments concerning bracket formulations in continuum mechanics, as described below. The Landau-de Gennes free energy and the Frank distortion energy, in terms of a second-rank structural tensor field, represent the effects of the fluid anisotropy on the total system energy (or Hamiltonian). This energy is then used in the above-mentioned bracket formulation to arrive at the governing equations of thermotropic liquid crystals. This is done in general circumstance for a compressible fluid, so that the overall entropy inequality can also be obtained. Sample calculations are then presented for limiting cases of the resulting equations. These include the phase diagram for the system in steady shear flow and a linear stability analysis of the spinodal decomposition from the isotropic to the liquid-crystalline state under no-flow conditions.