Towards Topological Microfluidics — Harnessing surface, elastic and viscous interactions at micro-scales

Liquid crystals (LCs) are mesogenic phases of matter which combine liquid fluidity with crystalline solid properties. The material anisotropy allows us to explore LCs as complex functional materials for microfluidics. Harnessing the anisotropic coupling between the flow and the molecular ordering renders a novel perspective to the conventional concepts in microfluidics. For instance, the topological defects emerging in the system, which are otherwise considered nuisance in applications, can be used as a self-assembled system of rails, along which micro-cargo (droplets and colloids containing the materials of interest) could be transported. Despite significant advances in our understanding of topological defects, and the mutual interactions therein, little is known if defects can emerge, and interact across different material fields within the same system. To address this fundamental question, we have used topological microfluidics as a test bed to characterize how topological defects in the flow and orientational fields co-emerge, and interact with each other. I will discuss how, under appropriate flow and boundary conditions, we have been able to tailor topological motifs through hydrodynamic singularities, and apply them to hierarchically tune the strength of emergent topological defects. This cross-interaction between topological defects originating from different material fields, though demonstrated in a nematofluidic setting, is expected to have more general implications as it sets a stage for potential exploration of multi-field topology systems – from designing novel materials to exploring open questions in the physics of living matter.