Dervaux Julien, Roché Matthieu, Limat Laurent
Laboratoire Matière et Systèmes Complexes, CNRS UMR 7057, Université de Paris, Université Paris Diderot, 10 Rue A. Domon et L. Duquet, F-75013 Paris, France.
Soft Matter. 2020 Jun 10;16(22):5157-5176. doi: 10.1039/d0sm00395f.
The spreading of a liquid over a solid material is a key process in a wide range of applications. While this phenomenon is well understood when the solid is undeformable, its "soft" counterpart is still misunderstood and no consensus has been reached with regard to the physical mechanisms ruling the spreading of liquid drops over soft deformable materials. In this work we provide a theoretical framework, based on the nonlinear theory of discontinuities, to describe the behavior of a triple line on a soft material. We show that the contact line motion is opposed both by nonlinear localized capillary and visco-elastic forces. We give an explicit analytic formula relating the dynamic contact angle of a moving drop to its velocity for arbitrary rheology. We then specialize this formula to the experimentally relevant case of elastomers with the Chasset-Thirion (power-law) type of rheologies. The theoretical prediction is in very good agreement with experimental data, without any adjustable parameters. We then show that the nonlinear force balance presented in this work can also be used to recover classical models of wetting. Finally we provide predictions for the dynamic behavior of the yet largely unexplored case of a viscous drop spreading over a soft visco-elastic material and predict the emergence of a new form of apparent hysteresis.
液体在固体材料上的铺展是众多应用中的关键过程。当固体不可变形时，这种现象已得到充分理解，但其“软”对应情况仍被误解，对于控制液滴在软可变形材料上铺展的物理机制尚未达成共识。在这项工作中，我们基于非线性间断理论提供了一个理论框架，以描述软材料上三相线的行为。我们表明，接触线运动受到非线性局部毛细力和粘弹力的共同阻碍。对于任意流变学，我们给出了一个明确的解析公式，将移动液滴的动态接触角与其速度联系起来。然后，我们将此公式专门应用于具有Chasset - Thirion（幂律）型流变学的弹性体这一实验相关情况。理论预测与实验数据非常吻合，无需任何可调参数。然后我们表明，这项工作中提出的非线性力平衡也可用于推导经典的润湿模型。最后，我们对粘性液滴在软粘弹性材料上扩散这一尚未充分探索的情况的动态行为进行了预测，并预测了一种新形式的表观滞后现象的出现。
