  A recent study has demonstrated that phase separation in binary liquid
mixtures is arrested in the presence of elastic networks and can lead to a
nearly uniformly-sized distribution of the dilute-phase droplets. At longer
timescales, these droplets exhibit a directional preference to migrate along
elastic property gradients to form a front of dissolving droplets [K. A.
Rosowski, T. Sai, E. Vidal-Henriquez, D. Zwicker, R. W. Style, E. R. Dufresne,
Elastic ripening and inhibition of liquid-liquid phase separation, Nature
Physics (2020) 1-4]. In this work, we develop a complete theoretical
understanding of this phenomenon in nonlinear elastic solids by employing an
energy-based approach that captures the process at both short and long
timescales to determine the constitutive sensitivities and the dynamics of the
resulting front propagation. We quantify the thermodynamic driving forces to
identify diffusion-limited and dissolution-limited regimes in front
propagation. We show that changes in elastic properties have a nonlinear effect
on the process. This strong influence can have implications in a variety of
material systems including food, metals, and aquatic sediments, and further
substantiates the hypothesis that biological systems exploit such mechanisms to
regulate important function.
