Phase-field model for elastocapillary flows of liquid crystals

Abstract

We propose a phase-field model to study interfacial flows of nematic liquid crystals that couple the capillary forces on the interface with the elastic stresses in the nematic phase. The theoretical model has two key ingredients, a tensor order parameter that provides a consistent description of the molecular and distortional elasticity, and a phase-field formalism that accurately represents the interfacial tension and the nematic anchoring stress by approximating a sharp-interface limit. Using this model, we carry out finite-element simulations of drop retraction in a surrounding fluid, with either component being nematic. The results are summarized by eight representative steady-state solutions in planar and axisymmetric geometries, each featuring a distinct configuration for the drop and the defects. The dynamics is dominated by the competition between the interfacial tension and the distortional elasticity in the nematic phase, mediated by the anchoring condition on the drop surface. As consequences of this competition, the steady-state drop deformation and the clearance between the defects and the drop surface both depend linearly on the elastocapillary number.

Particle trapped at the isotropic-nematic liquid crystal interface: Elastocapillary phenomena and drag forces

“…In the following, we only give a brief account of the main ingredients. A notable difference between the present work and that of [33,34] is the presence of a contact line where the three phases isotropic (Iso), nematic (N), and solid (S) meet. PF-based models can naturally handle the contact line dynamics thanks to intrinsic diffusive processes [35,36,37,38,39].…”

“…As aforementioned, we have adapted the recent model developed by Qiu et al [33,34] to describe the behavior of a colloidal particle trapped at the Iso-N fluid interface. The model of Qiu et al [33] uses a phase-field (PF) method to account for elastocapillary flows occurring at the Iso-N interface.…”

“…As aforementioned, we have adapted the recent model developed by Qiu et al [33,34] to describe the behavior of a colloidal particle trapped at the Iso-N fluid interface. The model of Qiu et al [33] uses a phase-field (PF) method to account for elastocapillary flows occurring at the Iso-N interface. It has two key features: (i) A tensor order parameter Q that provides a consistent description of the molecular and distortional elasticity of the N phase, including topological defects, and (ii) a PF formalism that accurately represents the Iso-N interfacial tension and the nematic anchoring stress by approximating a sharpinterface limit.…”

“…Combining this with the equations of motion of the fluids, we obtain a model capable of describing the phenomena resulting from the coupling between capillarity and elasticity. All the details and validation examples of this model can be found in [33,34]. In the following, we only give a brief account of the main ingredients.…”

“…The model, based on a phase-field (PF) method, was originally designed to describe elastocapillary flows of LCs [33]. In the present work, we use this model in numerical simulations to explore both the static and the dynamic behaviors of particles trapped at LC interfaces.…”