ABSTRACT
We compute the surface-induced morphology and the free-energy pathways as a cylindrical liquid crystalline filament with preferred homeotropic (orthogonal) interface orientation passes through a sequence of growing sinusoidal perturbations and breaks up into droplets. Liquid crystalline morphology is determined using a simulated annealing algorithm [R. K. Goyal and M. M. Denn, Phys. Rev. E, 75, 021704 (2007)] to minimize the Oseen-Frank free energy. A first-order morphological transition with a finite energy barrier is required when the perturbation amplitude exceeds a critical value, and it is possible that progress towards breakup will be kinetically trapped in a varicose cylindrical shape. This result may be related to the apparent kinetic trapping of dispersed nematic 4'-octyl-4-biphenylcarbonitrile in a gel state reported by Inn and Denn [J. Rheol., 49, 887 (2005)].
ABSTRACT
Orientation distributions in droplets of liquid crystals with homeotropic anchoring are computed with a simulated annealing algorithm that minimizes the free energy of the Oseen-Frank continuum theory. The droplets exhibit multiple orientational steady states that are separated by finite energy barriers over the entire range of the dimensionless ratio of surface to elastic forces, with maximum transition energy densities of the order of 2000 J/m3 (Pa) for a typical liquid crystalline droplet with a spherical radius of 1 microm. The transition energy densities decrease with elongation to spheroidal droplets with aspect ratios of four or more, indicating that droplet elongation is favored to drive surface-induced transitions.
ABSTRACT
When a binary mixture of granular materials, differing in shape or size, is poured into a quasi-two-dimensional silo, segregation of the mixture is observed. Depending on the size ratio d2/d1 of the species, the mixture segregates completely or partially into the pure species. To study the partial-segregation effect we propose a theoretical model based on the work of Boutreux and de Gennes [J. Phys. I 6, 1295 (1996)] but we introduce more realistic collision functions. To compare the partial- and complete-segregation effects, we also discuss calculations for the complete-segregation model proposed by Makse [Phys. Rev. E 56, 7008 (1997)]. Our experiments confirm the analytical solutions for both types of segregation. We find that the transition from complete segregation to partial segregation appears as the size ratio of the species is decreased below a critical value, which is found to be d2/d1 approximately 1.4 for our system. Our experimental and analytical studies predict the regime for applicability of both partial- and complete-segregation models in terms of the size ratio of the species and the respective model parameters.
