Hydrodynamics and Electrohydrodynamics of Liquid Crystals

Incompressibility conditions in liquid crystals

“…Their equations are compatible with (10) and (23), if one interprets their pressure as the redefined pressure (26). In that case the 5 'viscosities' α 1−5 (a sixth one is dependent due to an Onsager relation α 6 = α 5 + α 3 + α 2 ) introduced in their theory can be related to the transport coefficients used here by [12,17] …”

“…ref. [12] for a detailed exposition) is applicable to systems with spontaneously broken continuous symmetries of any kind (e.g. biaxial nematics [13,14]) including strong external fields [15] and can be generalized to systems with slow nonhydrodynamic variables (like nematic polymers [16]).…”

“…Uniaxial nematic liquid crystals differ from simple liquids not only by their lower symmetry due to the preferred direction (denoted by the directorn), but also by additional hydrodynamic degrees of freedom, rotations of n. Their full hydrodynamic equations are well known [11] and can be written as (for more details and a derivation of the equations see [12])ṅ…”

“…For the thermal degree of freedom we need a dynamical equation (for other possible macroscopic degrees of freedom, like concentration in lyotropic systems, order parameter fluctuations in polymeric systems and charge density in conducting systems see [12]), e.g. in the form of an entropy balance equatioṅ…”

“…For the conditions on these parameters to guarantee positivity of R we refer to [12]. Using the entropy production R as potential to derive the dissipative parts of the currents (and R = 0 for the reversible ones) automatically guarantees all possible Onsager relations.…”