The spitting drop: How a double-emulsion droplet bursts during its cryopreservation

Solidification of a complex liquid is pertinent to numerous natural and industrial processes. Here we examine the solidification of a water-in-oil double-emulsion droplet in water when a freezing front passes over. We show that the solidification of such a complex liquid can trigger the topological transition from the W/O/W state to an O/W single emulsion configuration. Strikingly, during this transition the encapsulated water droplet bursts first, and is then expelled from the oil droplet. This bursting of the encapsulated droplet occurs at extremely short-time-scales ($t \sim 10\mu$s), reflecting the vastly different time-scales involved in this solidification process, spanning over 8 orders of magnitude. We argue that the transition is triggered by the freezing of the encapsulated water droplet from outside in, and discuss the dependence of this phenomenon on the control parameters, i.e., the solidification rate and the water droplet size. Furthermore, we show that upon expulsion of the encapsulated droplet it may migrate within the solidified bulk via a mechanism equivalent to 'brine-diffusion'. Our findings are relevant for exerting better control over cyropreservation procedures of food emulsions and bio-specimen.