Fluid droplets can be induced to move over rigid or flexible surfaces under external or body forces. We describe the effect of variations in material properties of a flexible substrate as a mechanism for motion. In this paper, we consider a droplet placed on a substrate with either a stiffness or surface energy gradient and consider its potential for motion via coupling to elastic deformations of the substrate. In order to clarify the role of contact angles and to obtain a tractable model, we consider a 2D droplet. The gradients in substrate material properties give rise to asymmetric solid deformation and to unequal contact angles, thereby producing a force on the droplet. We then use a dynamic viscoelastic model to predict the resulting dynamics of droplets. Numerical results quantifying the effect of the gradients establish that it is more feasible to induce droplet motion with a gradient in surface energy. The results show that the magnitude of elastic modulus gradient needed to induce droplet motion exceeds experimentally feasible limits in the production of soft solids and is therefore unlikely as a passive mechanism for cell motion. In both cases, of surface energy or elastic modulus, the threshold to initiate motion is achieved at lower mean values of the material properties.

中文翻译：

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梯度引起的液滴在软固体上的运动

在外力或体力的作用下，液滴可能会在刚性或柔性表面上移动。我们描述了作为运动机制的柔性基板的材料属性变化的影响。在本文中，我们考虑了以刚度或表面能梯度放置在基材上的液滴，并考虑了通过耦合到基材的弹性变形而产生运动的潜力。为了阐明接触角的作用并获得易于处理的模型，我们考虑使用二维液滴。基材材料属性中的梯度导致不对称的固体变形和不相等的接触角，从而在液滴上产生力。然后，我们使用动态粘弹性模型来预测液滴的动态动力学。量化梯度作用的数值结果表明，用表面能梯度诱导液滴运动更为可行。结果表明，诱导液滴运动所需的弹性模量梯度的大小超出了生产软固体的实验可行极限，因此不可能作为细胞运动的被动机制。在这两种情况下，表面能或弹性模量的起始运动阈值均以较低的材料性能平均值实现。