Charitatos Vasileios, Kumar Satish
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA.
Soft Matter. 2020 Sep 16;16(35):8284-8298. doi: 10.1039/d0sm00643b.
The spreading of droplets on soft solid substrates is relevant to applications such as tumor biophysics and controlled droplet condensation and evaporation. In this paper, we apply lubrication theory to advance fundamental understanding of the important limiting case of spreading of a planar droplet on a linear viscoelastic solid. The contact-line region is described by a disjoining-pressure/precursor-film approach, and nonlinear evolution equations describing how the liquid-air and liquid-solid interfaces evolve in space and time are derived and solved numerically. Parametric studies are conducted to investigate the effects of solid thickness, viscosity, shear modulus, and wettability on droplet spreading. Softer substrates are found to speed up spreading for perfectly wetting droplets but slow down spreading for partially wetting droplets. For perfectly wetting droplets, faster spreading is a result of more liquid being pumped toward the contact line due to a larger liquid-film thickness there arising from the repulsive component of the disjoining pressure. In contrast, slower spreading of partially wetting droplets is a result of less liquid being pumped toward the contact line due to a smaller liquid-film thickness there arising from the attractive component of the disjoining pressure. The model predictions for partially wetting droplets are qualitatively consistent with experimental observations, and allow us to disentangle the effects of substrate deformability and wettability on droplet spreading. Due to its systematic formulation, our model can readily be extended to more complex situations involving multiple droplets, substrate inclination, and droplet phase changes.
液滴在软固体基质上的铺展与肿瘤生物物理学、可控液滴冷凝和蒸发等应用相关。在本文中，我们应用润滑理论来深入理解平面液滴在线性粘弹性固体上铺展这一重要极限情况的基本原理。接触线区域采用分离压力/前驱膜方法进行描述，并推导了描述液 - 气和液 - 固界面如何在空间和时间上演变的非线性演化方程，并进行了数值求解。进行了参数研究，以考察固体厚度、粘度、剪切模量和润湿性对液滴铺展的影响。发现较软的基质会加速完全润湿液滴的铺展，但会减缓部分润湿液滴的铺展。对于完全润湿液滴，更快的铺展是由于分离压力的排斥分量导致那里的液膜厚度更大，从而有更多液体被泵向接触线。相比之下，部分润湿液滴铺展较慢是由于分离压力的吸引分量导致那里的液膜厚度较小，从而泵向接触线的液体较少。部分润湿液滴的模型预测与实验观察结果在定性上是一致的，并且使我们能够区分基质可变形性和润湿性对液滴铺展的影响。由于其系统的公式化，我们的模型可以很容易地扩展到涉及多个液滴、基质倾斜和液滴相变的更复杂情况。
