Transport phenomena of smectic defects through arrays of micropillars

From industrial processes to living systems, simulations and analysis of liquid crystals and their defects reveal fascinating insights into transport processes in these complex liquids. Continuum modelling of liquid-crystal systems is essential to understanding transport in large systems, involving complex geometries. In this study, we use a recently developed complex order parameter tensor to simultaneously describe the local degree of smectic ordering, the orientation of the layers, and local compression. Through minimization of a Landau free energy, we present a range of defect structures in frustrated, confined geometries. By extending our model to simulate the hydrodynamics of smectics, we explore flows through micropillar arrays. We quantify how the competition between material and geometric length scales governs defect dynamics and consequently bulk transport. Our results suggest design principles for engineering microfluidic systems, which can enable or hinder permeation of smectic mesophases, and highlight the strengths of our complex tensorial formalism to enable more comprehensive studies of flowing smectic liquid crystals.