In a new manuscript available on arXiv, Estefania presents a detailed theoretical description of droplet dynamics in elastic media. The work is motivated by our recent publication with our collaborator Eric Dufresne at ETH Zürich, where we showed that an external elastic matrix squeezes droplets so they dissolve in stiff regions and accumulate in soft regions.

In the present manuscript, we present a detailed discussion of the theory of elastic ripening and the respective numerical simulations. In particular, a coarse-grained version of the model reveals that droplets first dissolve in regions of highest stiffness curvature and that the resulting dissolution fronts invade the stiff region in a diffusive motion. This theory allows to predict the droplet arrangements resulting from stiffness profiles in detail and shed light on the driving dynamics of elastic ripening.