Weakly compressible smectic-isotropic model: coalescence, flows and focal conic defects

Curvature driven phenomena in soft matter involves both complex geometry at small scales and anisotropies associated with material symmetries. For instance, smectic liquid crystals consist of layers of molecules than can bend and form focal conic defects. We previously proposed a phase field model to study a smectic-isotropic interface, and our numerical results have shown morphological transitions from focal conics to conical pyramids, which are also observed in experiments on smectic films. Interface equations were derived from the model, revealing the role of the Gaussian curvature on local equilibrium and resulting morphologies. We generalize this model to allow for phases of different density ρ, adding a penalty to the energy for deviations from preferred ρ values, with a multiplying constant that controls the strength of the coupling between the smectic order parameter ψ and ρ. We show that if this constant is large enough, ψ becomes approximately conserved, whereas if the constant is too small, ψ moves almost independently of ρ. Numerical results explore the possibility of coalescence between two stacks of smectic layers, and also interactions between focal conics due to flows. We show how these resulting flows are driven by both curvatures and interface compressibility.