Instability of an active droplet in a Hele-Shaw geometry*

Our experiments have uncovered a fingering-like instability for active droplets surrounded by a viscous, passive fluid in a Hele-Shaw geometry. In these experiments, a microtubule-driven active liquid is embedded in a binary, polymeric mixture that phase separates. Light-activated ATP is used to control the onset of the instability. The interface becomes unstable once a critical activity and droplet size are reached.

To study this phenomenon, we use a minimal model of the dynamics of the order parameter tensor coupled to the Stokes equation. We linearize the governing equations about the base state of no flow and random alignment of the microtubules. We then determine the growth rate of a perturbation of the interface as a function of the droplet radius and the gap size. Comparing these predictions with experiment shows good agreement. To test the model further, we also explore the inverse problem, where the droplet is passive but the surrounding fluid is active.