Oscillating phase separation in microemulsions. II. Description by a bending free energy

We propose a mechanism to describe the phase separation of a single phase of water-in-oil microemulsion droplets towards a phase of smaller water droplets coexisting with a water-rich excess phase. The phase separation shows oscillatory behavior when induced by a continuous temperature increase. A periodic clouding and clearing is observed in the extinction of transmitted light which is also reflected in the specific heat. To model this behavior the bending free energy describing the equilibrium phase transition is applied to identify the energy barriers in the dynamics of this transition. They are due to conservation laws preventing the relaxation to a close to equilibrium size distribution of droplets unless volume and surface is redistributed simultaneously for a large number of droplets. By numerical integration of an expression for the time evolution of the size distribution of droplets it is verified that constant heating gives rise to oscillations. Besides clarifying the origin of the oscillations this approach also gives good estimates for heat absorbed during a single oscillation.