This paper presents an overview of the capillary modeling science of nematic liquid crystals and its applications to the stability, structure, and shape of films, membranes, fibers, and drops. Liquid crystals are anisotropic viscoelastic materials possessing long range orientational order, and hence these models are relevant to the capillary science of anisotropic soft matter. A systematic multiscale approach is used to derive the equations that govern the shape of interfaces and contact lines. These shape equations generalize the surface Laplace and the contact line Neuman equations by introducing long range orientational order, gradient elasticity, surfactant adsorbants, magnetic and electric fields. The thermodynamics of capillary systems is used to reveal novel cross-effects such as adsorption-driven shape changes of surfaces and contact lines. The capillary models are used to analyze the structure and stability of films, membranes, fibers, and drops, of direct relevance to the processing and performance of structural and functional liquid crystals. Novel soft materials and mechanisms analyzed in this paper include: (1) stabilization of freely-suspended nematic films by orientation and molecular order heterogeneities, (2) orientational defects in polymer dispersed liquid crystals films, shown to originate from surface anchoring transitions, (3) electric field-induced curvature in membranes for sensor and actuator applications, (4) new helical morphologies of thin nematic filaments driven by strong interfacial anchoring, (5) tunable partial wetting through contact angle modification via gradient and anchoring elasticity, (6) liquid crystal nanoemulsion shape control through anchoring effects, and (7) magnetic shaping in liquid crystal colloids. Readily accessible applications to biological liquid crystal materials and processes indicate that capillary modeling science will be a most active area of research in the very near future.

Carbonaceous mesophases are discotic nematic liquid crystals that are spun into high performance carbon fibers using the melt spinning process. The spinning process produces a wide range of different fiber textures. Planar polar (PP) and planar radial (PR) textures are two ubiquitous ones. This paper presents theory and simulation of the texture formation process using the Landau-de Gennes mesoscopic theory for discotic liquid crystals. The computed PP and PR textures phase diagram, given in terms of temperature and fiber radius, is presented to establish the processing conditions and geometric factors that lead to the selection of these textures. Thin fibers adopt the PR texture, while thicker fibers and higher temperatures adopt the PP texture. The influence of elastic anisotropy to the formation of textures and structure is thoroughly characterized.

Para-nematic phases, induced by unwinding chiral helices, spontaneously relax to a chiral ground state through phase ordering dynamics that are of great interest and crucial for applications such as stimuli-responsive and biomimetic engineering. In this work, we characterize the cholesteric phase relaxation behaviors of β-lactoglobulin amyloid fibrils and cellulose nanocrystals confined into cylindrical capillaries, uncovering two different equilibration pathways. The integration of experimental measurements and theoretical predictions reveals the starkly distinct underlying mechanism behind the relaxation dynamics of β-lactoglobulin amyloid fibrils, characterized by slow equilibration achieved through consecutive sigmoidal-like steps, and of cellulose nanocrystals, characterized by fast equilibration obtained through smooth relaxation dynamics. Particularly, the specific relaxation behaviors are shown to emerge from the order parameter of the unwound cholesteric medium, which depends on chirality and elasticity. The experimental findings are supported by direct numerical simulations, allowing to establish hard-to-measure viscoelastic properties without applying magnetic or electric fields.