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.

由流体混合物渗透的弹性基质组成的物理系统无处不在，其实例包括单个生物细胞的形态发生到沉积物中温室气体的迁移。最近的实验研究表明，这些系统中弹性网络的存在，通过对液滴的生长施加高昂的成本，大大改变了它们的相分离响应。但是，缺乏对弹性作用的定量理解。我们的文章通过建立一个全面的理论框架来弥合这一差距，以分析弹性对软，非线性固体中二元混合物相分离的影响。我们采用了一种基于能量的方法，该方法既可以捕获短期的准平衡也可以捕获长期的相分离，在弹性均质材料和非均质材料中确定本构敏感性。我们的理论预测了异质材料中的液滴溶解前沿。至关重要的是，我们还发现了弹性对动力学的非线性影响，这挑战了文献中的当前理解。我们量化热力学驱动力，以确定前传播的扩散限制和溶解限制制度。我们的发现适用于包括食物，金属和水生沉积物在内的各种物质系统，并进一步证实了生物系统利用这种机制来调节其功能的假设。我们还发现了弹性对动力学的非线性影响，这挑战了文献中的当前理解。我们量化热力学驱动力，以确定前传播的扩散限制和溶解限制制度。我们的发现适用于包括食物，金属和水生沉积物在内的各种物质系统，并进一步证实了生物系统利用这种机制来调节其功能的假设。我们还发现了弹性对动力学的非线性影响，这挑战了文献中的当前理解。我们量化热力学驱动力，以确定前传播的扩散限制和溶解限制制度。我们的发现适用于包括食物，金属和水生沉积物在内的各种物质系统，并进一步证实了生物系统利用这种机制来调节其功能的假设。