Self-organized dynamics of viscous drops with surface nematic activity

Biological surfaces are often active, signifying that they are driven internally by chemical reactions at microscopic scales. In addition, they typically exhibit a form of in-plane order, such as nematic or polar alignment, facilitating extensive hydrodynamic interactions and self-organized behavior. It has been evidenced that nematic order emerges in various crucial biological processes such as cytokinesis and tissue morphogenesis. In this work, 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 uncover the intricate interplay between flow, nematic order, and mechanics of deformations, leading to self-organized behaviors and symmetry-breaking phenomena, consistent with experimental observations under small and finite deformations. Diverse dynamical behaviors are observed, from periodic braiding motion of topological defects to chaotic creation and annihilation of defects under high activity levels, and translational motion under finite deformations. Our study offers valuable insights into the emergent dynamics observed in biological and biomimetic systems characterized by active fluid surfaces.