The purpose of the work presented in this chapter is to test a recently proven variational principle according to which the irreversible energy dissipation rate is minimal in the linear regime of a nonequilibrium steady state. This test is carried out by performing molecular dynamics simulations of liquid crystals subject to velocity gradients and temperature gradients. Since the energy dissipation rate varies with the orientation of the director of the liquid crystal relative to these gradients and is minimal at certain orientations, this is a stringent test of the variational principle. More particularly, a nematic liquid crystal model based on the Gay-Berne potential, which can be regarded as a Lennard-Jones fluid generalized to elliptical molecular cores, is studied under planar Couette flow, planar elongational flow, and under a temperature gradient. It is found that the director of a nematic liquid crystal consisting of rod-like molecules lies in the vorticity plane at an angle of about 20° to the stream lines in the planar Couette flow. In the elongational flow, it is parallel to the elongation direction, and it is perpendicular to the temperature gradient in a heat flow. These orientations are the ones where the irreversible energy dissipation rate is minimal, so that the variational principle is fulfilled in these three cases.
Part of the book: Non-Equilibrium Particle Dynamics