Interfacially driven flows: from electrohydrodynamics to active interfaces

Interfacially driven flows are ubiquitous in biological processes and engineering applications. In these systems, the interface separating adjacent fluid phases is subject to mechanical stresses that drive the fluid into motion and cause deformations. The origin of interfacial stresses may vary from one physical system to another. In some cases, such as in electrohydrodynamic flows, an external electric field induces interfacial stresses that drag the fluid into motion. Alternatively, in active matter systems, an internal mechanism converts chemical energy into mechanical work and drives the system out of equilibrium. The main challenge in studying these systems lies in unraveling the complex interplay between the bulk flow, nonlinear transport on the interface, and interface mechanics, which collectively give rise to intricate dynamical behaviors.We develop robust theoretical and computational frameworks to address these challenges. In the first part of this thesis, we employ analytical and numerical analyses to study different canonical electrohydrodynamic problems. The interfacial charge dynamics is modeled by considering different transport mechanisms including Ohmic conduction, advection by the flow, and finite charge relaxation. Using this model, we identify different modes of instability and explore how the non-equilibrium evolution of flow and interfacial charge dynamics lead to nonlinear phenomena observed in experiments, such as tip streaming in liquid films, Quincke rotation in drops, tip formation, and the growth of charge density shocks in stratified systems.Furthermore, our investigation extends to biological surfaces that exhibit in-plane order, such as nematic or polar, and are driven internally by microscopic chemical reactions. We study morphological dynamics in a freely-suspended viscous drop with surface nematic activity, which serves as a simplified model for understanding self-organized behaviors in active living systems such as cells. We demon