Self-organized dynamics in viscous drops with interfacial nematic activity

Biological surfaces are often driven by chemical reactions at microscopic scales. In addition, they often possess an in-plane order, such as nematic or polar, enabling large-scale hydrodynamic interactions and self-organized behavior. Nematic order has been observed to play a key role in the development of important biological processes such as cytokinesis and tissue morphogenesis. Here, we study morphological dynamics in a freely-suspended viscous drop with surface nematic activity that drives the system out of equilibrium. This system serves as a simplified model for understanding complex active living systems, such as cells. Using a spectral boundary integral solver for Stokes flow coupled with a hydrodynamic evolution equation for the nematic tensor, we reveal the intricate interplay between flow, nematic order, and interface mechanics, leading to self-organized behaviors and symmetry-breaking phenomena, consistent with experimental observations. Diverse dynamical behaviors are observed, from periodic braiding motion of topological defects to chaotic creation and annihilation of defects under high activity levels. Our study provides valuable insights into emergent dynamics in biological and biomimetic systems with active fluid surfaces.