Statistical foundation of macroscopic balances for liquid crystals in alignment tensor formulation

Abstract

Starting out with the global balance equations of mass, momentum, angular momentum, and energy formulated on the so-called ten-dimensional doubled phase of position, velocity, orientation, and orientation change velocity, the appropriate local balances are derived, which are defined on the five-dimensional half of the doubled phase space including time, position, and the microscopic director. These so-called orientation balance nematic liquid crystals whose alignment need not be uniform as it is presupposed in theories using macroscopic director fields. In R 3 we get the usual phenomenological balance equations of micropolar media having the advantage that the balanced quantities are defined statistically. By expanding the orientation distribution function into a series of multipoles we get alignment tensor fields and an additional alignment tensor balance equation on R 3.