Fluid–structure interactions in nematic liquid crystals: A complex variable approach

Fluid anisotropy, or direction-dependent response to deformation, can be observed in biofluids like mucus or, at a larger scale, self-aligning swarms of active bacteria. A model fluid used to investigate such environments is a liquid crystal. Large colloidal bodies undergo shape-dependent interactions when placed in such an environment, whilst deformable bodies like red blood cells tend to be stretched, offering a passive means of measuring cell material properties. While numerous methods exist for studying the liquid crystalline configurations and fluid–structure interaction for a single body, there are exceedingly few analytical results for the interaction of two or more bodies. In this talk, we will bring the power of complex variables to bear on this problem, presenting a simple methodology to analytically solve for the interactions inside a liquid crystalline environment. This approach allows for the solution of a wide range of problems, opening the door to studying the role of body shape and orientation, liquid crystal anchoring conditions, and body deformability. Shape-dependent forces between bodies, local tractions, surface relaxation, and dynamics will all be discussed.