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Phase-field model for elastocapillary flows of liquid crystals.

Mingfeng Qiu1, James J Feng2, Jean-Christophe Loudet3

  • 1Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada.

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We developed a phase-field model for liquid crystal flows, coupling capillary and elastic forces. This model reveals that drop shape and defect spacing linearly depend on the elastocapillary number.

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Area of Science:

  • Soft Matter Physics
  • Fluid Dynamics
  • Materials Science

Background:

  • Interfacial flows of liquid crystals are complex, involving coupled capillary and elastic forces.
  • Accurate modeling requires capturing both molecular and distortional elasticity, alongside interfacial phenomena.

Purpose of the Study:

  • To introduce a novel phase-field model for interfacial flows of nematic liquid crystals.
  • To investigate the interplay between capillary forces and elastic stresses in nematic systems.

Main Methods:

  • Developed a theoretical model using a tensor order parameter for elasticity description.
  • Employed a phase-field formalism to represent interfacial tension and anchoring stress.
  • Conducted finite-element simulations of drop retraction dynamics.

Main Results:

  • Identified eight representative steady-state solutions in planar and axisymmetric geometries.
  • Demonstrated that dynamics are governed by competition between interfacial tension and distortional elasticity.
  • Observed linear dependence of steady-state drop deformation and defect clearance on the elastocapillary number.

Conclusions:

  • The proposed phase-field model effectively simulates interfacial nematic liquid crystal flows.
  • The elastocapillary number is a key parameter controlling drop morphology and defect behavior.
  • The study provides insights into the fundamental physics of liquid crystal interfacial phenomena.