Effects of dynamic contact angle on liquid infiltration into horizontal capillary tubes: (Semi)-analytical solutions
Effects of dynamic contact angle on liquid infiltration into horizontal capillary tubes: (Semi)-analytical solutions
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DOI：
10.1016/j.jcis.2009.04.013
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发表时间：
2009-09-01
影响因子：
9.9
通讯作者：
Hilpert, Markus
中科院分区：
文献类型：
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作者：
Hilpert, Markus
我们通过考虑动态接触角来概括 Washburn 的水平定向管中毛细管流动的分析解决方案。我们考虑动态接触角的两个通用模型：接触线上的未补偿杨氏力取决于毛细管数，其形式为（1）指数为 beta 的幂律或（2）幂级数。通过考虑气液界面速度的常微分方程 (ODE) 而不是界面位置的 ODE，我们能够导出新的解析解。对于这两个动态接触角模型，我们得出了气液界面的传播时间作为界面速度的函数的解析解。通过数值积分可以获得作为时间函数的界面位置。对于幂律和 beta = 1（动态接触角 Cox 模型的近似值），我们获得了界面位置和速度随时间变化的解析解。对于幂律和 beta = 3，我们可以将界面速度表示为时间的函数。 (C) 2009 Elsevier Inc. 保留所有权利。
We generalize Washburn's analytical solution for capillary flow in a horizontally oriented tube by accounting for a dynamic contact angle. We consider two general models for dynamic contact angle: the uncompensated Young force on the contact line depends on the capillary number in the form of either (1) a power law with exponent beta or (2) a power series. By considering the ordinary differential equation (ODE) for the velocity of the gas-liquid interface instead of the ODE for the interface position, we are able to derive new analytical solutions. For both dynamic contact angle models, we derive analytical solutions for the travel time of the gas-liquid interface as a function of interface velocity. The interface position as a function of time can be obtained through numerical integration. For the power law and beta = 1 (an approximation of Cox's model for dynamic contact angle), we obtain an analytical Solution for both interface position and velocity as a function of time. For the power law and beta = 3, we can express the interface velocity as a function of time. (C) 2009 Elsevier Inc. All rights reserved.