Department of Mathematics, Southern Methodist University, Dallas, TX 75275, United States.
J Colloid Interface Sci. 2010 Feb 15;342(2):550-8. doi: 10.1016/j.jcis.2009.10.040. Epub 2009 Nov 1.
We studied both static and dynamic values of the apparent contact angle for gravity-driven flow of a volatile liquid down a heated inclined plane. The apparent contact line is modeled as the transition region between the macroscopic film and ultra-thin adsorbed film dominated by disjoining pressure effects. Four commonly used disjoining pressure models are investigated. The static contact angle is shown to increase with heater temperature, in qualitative agreement with experimental observations. The angle is less sensitive to the details of the disjoining pressure curves than in the isothermal regime. A generalization of the classical Frumkin-Derjaguin theory is proposed to explain this observation. The dynamic contact angle follows the Tanner's law remarkably well over a range of evaporation conditions. However, deviations from the predictions based on the Tanner's law are found when interface shape changes rapidly in response to rapid changes of the heater temperature. The Marangoni stresses are shown to result in increase of the values of apparent contact angles.
我们研究了挥发性液体在受热倾斜平面上受重力驱动流动时的静态和动态表观接触角。表观接触线被建模为宏观膜和由不混溶压力效应主导的超薄吸附膜之间的过渡区域。研究了四种常用的不混溶压力模型。静态接触角随加热温度升高而增加，定性上与实验观察结果一致。与等温条件相比，该角度对不混溶压力曲线细节的敏感性较低。提出了经典 Frumkin-Derjaguin 理论的推广，以解释这一观察结果。在一系列蒸发条件下，动态接触角非常符合 Tanner 定律。然而，当界面形状因加热器温度的快速变化而快速变化时，会发现基于 Tanner 定律的预测存在偏差。表明 Marangoni 应力会导致表观接触角增加。
