Popescu M N, Ralston J, Sedev R
Ian Wark Research Institute, University of South Australia, Mawson Lakes, Adelaide, SA, Australia.
Langmuir. 2008 Nov 4;24(21):12710-6. doi: 10.1021/la801753t. Epub 2008 Oct 4.
The classic description of the rate of capillary rise given by the Washburn equation, which assumes that the contact angle preserves the equilibrium value at all times, has been recently questioned in the light of the known experimental dependence of the dynamic contact angle on the velocity of the contact line. For a number of such proposed functions of velocity for the dynamic contact angle, we analyze the resulting dependences of the contact angle and of the time of rise, respectively, on the height of the capillary rise. By applying our results to the particular cases of a high-viscosity silicone oil and water, respectively, in a glass capillary, we show that, in general, strong similarities arise between the various approaches and the classic theory in what concerns the time dependence of the capillary rise, which explains the lack of consistent experimental evidence for deviations in the rate of capillary rise from the Washburn equation. However, for a strong dependency of the contact angle on the velocity in the range of small velocities, as in the case of water on glass, one of the models predicts significant deviations even for the time dependence of the capillary rise. Moreover, our results show that the time or height dependence of the contact angle during the capillary rise can clearly discriminate between the various models.
沃什伯恩方程给出了毛细管上升速率的经典描述，该方程假定接触角在所有时刻都保持平衡值。鉴于已知动态接触角对接触线速度的实验依赖性，这一经典描述最近受到了质疑。对于一些针对动态接触角提出的速度函数，我们分别分析了接触角和上升时间对毛细管上升高度的依赖关系。通过将我们的结果分别应用于玻璃毛细管中高粘度硅油和水的具体情况，我们表明，一般来说，在毛细管上升时间依赖性方面，各种方法与经典理论之间存在强烈的相似性，这解释了为何缺乏关于毛细管上升速率偏离沃什伯恩方程的一致实验证据。然而，对于接触角在小速度范围内对速度有强烈依赖性的情况，如水在玻璃上的情况，其中一个模型预测即使在毛细管上升的时间依赖性方面也会有显著偏差。此外，我们的结果表明，毛细管上升过程中接触角的时间或高度依赖性可以清楚地区分各种模型。
