Ordering kinetics of a conserved binary mixture with a nematic liquid crystal component

Three-dimensional coarsening dynamics of a conserved, nematic liquid crystal-isotropic fluid mixture

“…We use a conserved phase field model (Model B in the nomenclature of of Hohenberg and Halperin [18]) which couples a generalized Cahn-Hilliard equation for the order parameter φ, related to the volume fraction of the species, with a simplified de Gennes-Prost evolution equation [16] for the director field n, which describes the mean orientation of the rigid rod-like, liquid crystal molecules. The same model, which stems from that considered in [35], has been used in the two-dimensional study of Mata et al [26] and the current work is a follow-up report on our findings for the corresponding three-dimensional system. Similar phase field models have been used extensively in phase separation [14,25,19,4,1,2,21,22,5,35,37,36,3,38,13,39,12,30,17,33].…”

“…The model is the same as that used in [26] except that here our domain is three-dimensional. The system can be described with an order parameter φ related to the species concentration ((1 + φ)/2 represents the nematic liquid crystal concentration and (1−φ)/2 the isotropic fluid concentration) and with the director field n, which is a measure of the mean molecular orientation in the nematic liquid crystal phase.…”

“…We evolve the director field using the simplified Leslie-Ericksen theory of de Gennes and Prost [16], first used by Yue et al [35], and in the twodimensional work of Mata et al [26],…”

“…Denoting by K c and τ c characteristic values of the Frank elastic constant and the Leslie twist viscosity, respectively, we define characteristic energy and time scales by E c = aK c L c , t c = bL 3 c /(E c τ c ), respectively, where a and b are dimensionless constants. Following [26,35], we take a = 1/(6.708 × 10 −3 ) and b = 1. We use the same letters to denote the dimensionless variables and parameters, so (9)- (12) can be considered to be in dimensionless form.…”

“…Mixtures in which one of the components is a liquid crystal or a liquid crystalline polymer offer a significant potential for applications and have received increased attention [28,34,20,27,9,8,26].…”