Interfacial instability of confined three-dimensional active droplets

Instabilities of fluid-fluid interfaces occur in many forms within passive soft matter. Adding activity to one of the fluids can dramatically change the stability of the interface. Triggering active flows externally offers a unique opportunity to study the linear growth of the instability and quantitatively compare experiment and theory. We investigate the interfacial instability of a deformable three-dimensional active nematic liquid crystal droplet confined between two parallel plates. Spontaneous active flows drive the growth of undulations along the active/passive interface, with the mode number of the fastest-growing mode increasing with droplet radius and decreasing with gap height. Applying the lubrication approximation to a minimal nematohydrodynamic model reveals that the growth rates of the interfacial modes are determined by the active timescale and the relaxation timescales associated with liquid crystalline order as well as capillary and viscous stresses. We find multiple points of agreement between experiment and theory, including the shape evolution of individual droplets, the growth rates of unstable modes averaged across many droplets, and the extensional shear flows observed within droplets.