Qiu Mingfeng, Feng James J, Loudet Jean-Christophe
Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada.
Department of Mathematics and Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada.
Phys Rev E. 2021 Feb;103(2-1):022706. doi: 10.1103/PhysRevE.103.022706.
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.
