| Summary: | © 2020 Physical systems consisting of an elastic matrix permeated by fluid mixture are ubiquitous, with examples ranging from morphogenesis of a single biological cell to the migration of greenhouse gases in sediments. Recent experimental studies show that the presence of the elastic networks in these systems significantly alters their phase-separation response by imposing an energetic cost to the growth of droplets. However, a quantitative understanding of the role played by elasticity is lacking. Our paper bridges this gap by building a comprehensive theoretical framework to analyze the effect of elasticity on the phase separation of a binary mixture in soft, nonlinear solids. We employ an energy-based approach that captures both the short-time quasi-equilibrium and the long-time evolution of the phase separation, in elastically homogeneous as well as heterogeneous materials, to determine the constitutive sensitivities. Our theory predicts a droplet dissolution front in heterogeneous materials. Crucially, we also find a nonlinear effect of elasticity on the dynamics, which challenges the current understanding in the literature. We quantify the thermodynamic driving forces to identify diffusion-limited and dissolution-limited regimes of front propagation. Our findings are applicable to a variety of material systems including food, metals, and aquatic sediments, and further substantiate the hypothesis that biological systems exploit such mechanisms to regulate their function.
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