Elastocapillarity describes the deformations of soft materials by surface tensions and is involved in a broad range of applications, from microelectromechanical devices to cell patterning on soft surfaces. Although the vast majority of elastocapillarity experiments are performed on soft gels, because of their tunable mechanical properties, the theoretical interpretation of these data has been so far undertaken solely within the framework of linear elasticity, neglecting the porous nature of gels. We investigate in this work the deformation of a thick poroelastic layer with surface tension subjected to an arbitrary distribution of time-dependent axisymmetric surface forces. Following the derivation of a general analytical solution, we then focus on the specific problem of a liquid drop sitting on a soft poroelastic substrate. We investigate how the deformation and the solvent concentration field evolve in time for various droplet sizes. In particular, we show that the ridge height beneath the triple line grows logarithmically in time as the liquid migrates toward the ridge. We then study the relaxation of the ridge following the removal of the drop and show that the drop leaves long-lived footprints after removal which may affect surface and wetting properties of gel layers and also the motion of living cells on soft materials. Preliminary experiments performed with water droplets on soft PDMS gel layers are in excellent agreement with the theoretical predictions.

中文翻译：

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在柔软的多孔弹性基底上脊的生长和松弛

弹性系数描述了软材料由于表面张力而产生的变形，并且涉及从微机电装置到软表面上的单元图案化的广泛应用。尽管绝大部分的弹性毛细管实验都是在软凝胶上进行的，但由于它们具有可调节的机械性能，到目前为止，这些数据的理论解释仅在线性弹性的框架内进行，而忽略了凝胶的多孔性。我们在这项工作中研究了厚的多孔弹性层在表面张力作用下随时间变化的轴对称表面力的任意分布的变形。在推导了一般的分析解决方案之后，我们将重点放在液滴落在软质多孔弹性基质上的特定问题上。我们研究了各种液滴尺寸下，变形和溶剂浓度场如何随时间变化。特别是，我们显示出，随着液体向脊线迁移，三线下方的脊线高度会随时间呈对数增长。然后，我们研究了去除液滴后脊的松弛情况，结果表明，去除后，液滴留下了长寿命的足迹，这可能影响凝胶层的表面和润湿特性，以及软材料上活细胞的运动。用水滴在柔软的PDMS凝胶层上进行的初步实验与理论预测非常吻合。我们显示，随着液体向脊线迁移，三线下方的脊线高度随时间呈对数增长。然后，我们研究了去除液滴后脊的松弛情况，结果表明，去除后，液滴留下了长寿命的足迹，这可能影响凝胶层的表面和润湿特性，以及软材料上活细胞的运动。用水滴在柔软的PDMS凝胶层上进行的初步实验与理论预测非常吻合。我们显示，随着液体向脊线迁移，三线下方的脊线高度随时间呈对数增长。然后，我们研究了去除液滴后脊的松弛情况，结果表明，去除后，液滴留下了长寿命的足迹，这可能影响凝胶层的表面和润湿特性，以及软材料上活细胞的运动。用水滴在柔软的PDMS凝胶层上进行的初步实验与理论预测非常吻合。