Recent experiments demonstrated the emergence of regular mesoscopic patterns when liquid droplets form in an elastic gel after cooling. These patterns appeared via a continuous transition and were smaller in stiffer systems. We capture these observations with a phenomenological equilibrium model describing the density field of the elastic component to account for phase separation. We show that local elasticity theories are insufficient, even if they allow large shear deformations. Instead, we can account for key observations using a nonlocal elasticity theory to capture the gel’s structure. Analytical approximations unveil that the pattern period is determined by the geometric mean between the elastocapillary length and a nonlocality scale. Our theory highlights the importance of nonlocal elasticity in soft matter systems, reveals the mechanism of this mesoscopic pattern, and will improve the engineering of such systems.

中文翻译：

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非局部弹性在相分离系统中产生平衡模式

最近的实验证明，当冷却后弹性凝胶中形成液滴时，会出现规则的介观图案。这些图案通过连续过渡出现，并且在较硬的系统中较小。我们用现象学平衡模型来捕获这些观察结果，该模型描述了弹性成分的密度场以解释相分离。我们表明，局部弹性理论是不够的，即使它们允许大的剪切变形。相反，我们可以使用非局部弹性理论来解释关键观察结果，以捕获凝胶的结构。分析近似表明，模式周期由弹性毛细管长度和非定域尺度之间的几何平均值决定。我们的理论强调了软物质系统中非局域弹性的重要性，揭示了这种介观模式的机制，并将改进此类系统的工程。