Department of Mechanical Engineering, University of Thessaly, Volos 38334, Greece.
Langmuir. 2013 Jul 16;29(28):8892-906. doi: 10.1021/la4014027. Epub 2013 Jul 3.
We study the two-dimensional dynamics of a droplet on an inclined, nonisothermal solid substrate. We use lubrication theory to obtain a single evolution equation for the interface, which accounts for gravity, capillarity, and thermo-capillarity, brought about by the dependence of the surface tension on temperature. The contact line motion is modeled using a relation that couples the contact line speed to the difference between the dynamic and equilibrium contact angles. The latter are allowed to vary dynamically during the droplet motion through the dependence of the liquid-gas, liquid-solid, and solid-gas surface tensions on the local contact line temperature, thereby altering the local substrate wettability at the two edges of the drop. This is an important feature of our model, which distinguishes it from previous work wherein the contact angle was kept constant. We use finite-elements for the discretization of all spatial derivatives and the implicit Euler method to advance the solution in time. A full parametric study is carried out in order to investigate the interplay between Marangoni stresses, induced by thermo-capillarity, gravity, and contact line dynamics in the presence of local wettability variations. Our results, which are generated for constant substrate temperature gradients, demonstrate that temperature-induced variations of the equilibrium contact angle give rise to complex dynamics. This includes enhanced spreading rates, nonmonotonic dependence of the contact line speed on the applied substrate temperature gradient, as well as "stick-slip" behavior. The mechanisms underlying this dynamics are elucidated herein.
我们研究了在倾斜、非等温固体基底上液滴的二维动力学。我们使用润滑理论获得了一个界面的单一演化方程，该方程考虑了重力、毛细作用和热毛细作用，这些作用是由表面张力对温度的依赖引起的。通过将接触线速度与动态和平衡接触角之差相关联的关系来模拟接触线运动。在液滴运动过程中，允许平衡接触角动态变化，通过液体-气体、液体-固体和固体-气体表面张力对局部接触线温度的依赖关系，从而改变液滴两侧局部基底的润湿性。这是我们模型的一个重要特征，使其有别于之前的工作，其中接触角保持不变。我们使用有限元方法对所有空间导数进行离散化，并使用隐式 Euler 方法推进解的时间演化。进行了全面的参数研究，以研究在局部润湿性变化存在的情况下，热毛细作用、重力和接触线动力学之间的相互作用。我们的结果是针对恒定基底温度梯度生成的，表明平衡接触角的温度诱导变化会导致复杂的动力学。这包括增强的扩展率、接触线速度对施加的基底温度梯度的非单调依赖性，以及“粘滑”行为。本文阐述了这种动力学的机制。
