Effect of Elasticity on Phase Separation in Heterogeneous Systems

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.