File Name : si_fig1.eps

Caption : (a) schematic representation of the microfluidic device used to prepare the double-emulsion. the widths of the channels are approximately 0.7 mm. (b) ternary phase diagram showing the binodal line of the ethanol/water/dep (red) and ethanol/water/dbp (blue) systems.  
yellow symbols indicate the approximate initial composition of the ternary ethanol/water/dep mixture to obtain a double-, triple or quintuple-compound droplet (c), respectively.
for our current study we use an initial composition of (0.21/0.05/0.74 vol.) for the ethanol/water/dep system and (0.218/0.032/0.75 vol.) for the ethanol/water/dbp system. 

File Name : si_fig2.eps

Caption : liquid pocket migration of the expelled interior through the ice. the applied thermal gradient induces a concentration gradient. while diffusion restores this concentration gradient, the local phase equilibrium at the colder and warmer sides are altered leading to the migration. eventually, the pocket catches up with the ice front, which propagates with velocity v.

File Name : si_fig3.eps

Caption : mean of the light intensity captured during the topological transition. the inset shows the corresponding experimental snapshots. 

File Name : si_fig4.eps

Caption : experimental snapshots of before and after the freezing of a more densely packed double-emulsion. the compound droplets incorporated in the ice for which r<sub>in</sub> > r<sub>in,crit</sub> will eventually expel their inner core (see red rectangles).