Modelling Spontaneous Motion and Deformation of Active Droplets

This thesis investigates symmetry breaking phenomena and motile steady states in droplets driven by stresses generated by active (out-of-equilibrium) liquid crystals. First, we show that in a fluid droplet with active polar liquid crystal an asymmetric polarisation field is sufficient to drive steady state motility. We are able to approximate the forces and flows generated in such a system analytically, and show how the force distribution on the droplet interface is characteristic of this motion. Second, we consider the case of a passive fluid droplet immersed in an active liquid crystal. Here we see that strong anchoring at the droplet interface can create an asymmetric equilibrium configuration, and thus any active stress can drive propulsion of the drop. Third we analytically perform linear stability analysis calculations on two kinds of active droplet to determine how active stresses can make these systems unstable to symmetry breaking events. Finally, we produce 2D simulations of these systems so that we can find the resulting steady states of these systems. We observe a rich phase space of behaviour, with steady state flows in the droplets that result in motion, symmetric deformations and rotation.