Interactions in nematic liquid crystals: from activity to deformability

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 nematic liquid crystal. Large colloidal particles undergo shape-dependent interactions when immersed in these complex environments, whilst deformable bodies (like red blood cells) tend to be stretched, offering a passive means of measuring cell material properties. Adding to the complexity are microorganisms that propel themselves through these environments, giving rise to active stresses. In this talk, we will use complex variables to analytically solve for the interaction between bodies immersed in liquid crystalline environments. This approach allows for the solution of a wide range of problems, opening the door to studying the role of body geometry, liquid crystal anchoring conditions, and deformability. Shape-dependent forces between bodies, local tractions, and active stresses will also be discussed.