Core-shell drops coalescing by a diffusion mechanism.  Blue, green and red are incompatible polymers.   

The drops are initially separated by the blue phase.  As they approach, the gradient-dependent chemical potential of the blue phase increases so that the blue polymer diffues out of the gap, being replaced by the green polymer.

As the green phase coalesces, the red phases become close enough that they coalesce as well.  Thus the core-shell morpholopy is preserved.