Orientational Balances ffor Nematic Liquid Crystals

Abstract

Starting from the global balance equations of mass, momentum, angular momentum and energy for discrete systems, new balances are derived by regarding the nematic liquid crystal as a formal mixture of fluids, whose components are defined by the orientation of the particles. The resulting balance equations for the components are called orientational balances. The connections between the dynamical quantities for the components and the mixture itself, such as the stress tensors are discussed.

Macroscopic Internal Variables and Mesoscopic Theory: A Comparison Considering Liquid Crystals

“…Here, the "component index" m is a continuous variable. Because mixture theory is well developed [24,25] mesoscopic balance equations can be written down very easily [26]. The special case of liquid crystals is considered in [27].…”

Systematic remarks on objectivity and frame-indifference, liquid crystal theory as an example

“…In this section, two different descriptions of liquid crystals are shortly juxtaposed: The Ericksen-Leslie theory [22,23] and the mesoscopic theory of liquid crystals [24][25][26][27]. In this section, we consider one material in its fixed state of motion, and only the observers of this material are changed.…”

“…In the mesoscopic theory of liquid crystals [24], a microscopic director n is introduced as an objective vector variable instead of the macroscopic director field d(x, t) n * = Q · n, n · n = 1.…”

“…The result is different from Müller [6]: The heat flux density is objective under changing the observer, but it depends on the material's motion with respect to the standard frame of reference. Finally two different descriptions of liquid crystals are juxtaposed with respect to changing the observer: The macroscopic Ericksen-Leslie theory [22,23] and the mesoscopic theory of liquid crystals [24][25][26][27].…”

Why so many “schools” of thermodynamics?

“…For describing complex materials one needs additional fields m beyond the usual ones of a five-field or a eight-field theory whose basic fields are mentioned in (7). In principle, there are two possibilities for introducing these additional fields: One can add them together with their balance equations to the basic fields, or one can add them as variables completing the space-time [58]. In the first case which is the conventional concept, we have to generate the balances of the additional fields m(x, t), an enterprise which is often difficult.…”