Model of the dynamics of an interface between a smectic phase and an isotropic phase of different density

Abstract

Soft modulated phases have been shown to undergo complex morphological transitions, in which layer remodeling induced by mean and Gaussian curvatures plays a major role. This is the case in smectic films under thermal treatment, where focal conics can be reshaped into conical pyramids and concentric ring structures. We build on earlier research on a smectic-isotropic, two phase configuration in which diffusive evolution of the interface was driven by curvature, while mass transport was neglected. Here, we explicitly consider evaporation-condensation processes in a smectic phase with mass transport through a coexisting isotropic fluid phase, as well as the hydrodynamic stresses at the interface and the resulting flows. By employing the Coleman-Noll procedure, we derive a phase-field model that accounts for a varying density field coupled to smectic layering of the order parameter. The resulting equations govern the evolution of an interface between a modulated phase and an isotropic fluid phase with distinct densities, and they capture compressibility effects in the interfacial region and topological transitions. We first verify a numerical implementation of the governing equations by examining the dispersion relation for interfacial transverse modes. The inverse decay rate is shown to scale as $Q^2$ ($Q$ is the wavenumber of the perturbation) due to hydrodynamic effects, instead of the $Q^4$ expected for diffusive decay. Then, by integrating the equations forward in time, we investigate fluid flow on distorted layers and focal conics, and show how interfacial stresses and density contrast significantly determine the structure of the flow and the evolution of the configuration.

References in corpus (10)

• Two-phase binary fluids and immiscible fluids described by an order parameter
• Coarse-grained description of thermo-capillary flow
• Mass Conservative and Energy Stable Finite Difference Methods for the Quasi-incompressible Navier-Stokes-Cahn-Hilliard system: Primitive Variable and Projection-Type Schemes
• Controlling Gaussian and mean curvatures at microscale by sublimation and condensation of smectic liquid crystals
• Modeling Smectic Layers in Confined Geometries: Order Parameter and Defects
• Hydrodynamic theory for nematic shells: the interplay among curvature, flow and alignment
• Curvature as a guiding field for patterns in thin block copolymer films
• Long-time anomalous swimmer diffusion in smectic liquid crystals
• Focal Conic Flower Textures at Curved Interfaces
• Role of Gaussian curvature on local equilibrium and dynamics of smectic-isotropic interfaces

Cited by in corpus (1)

• Phase-field model for a weakly compressible soft layered material: morphological transitions on smectic-isotropic interfaces