Viscous flow down a slope in the vicinity of a contact line
Viscous flow down a slope in the vicinity of a contact line
复制标题
接触线附近斜坡上的粘性流
DOI：
10.1063/1.858113
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发表时间：
1991
影响因子：
4.6
通讯作者：
G. Homsy
中科院分区：
文献类型：
--
作者：
Ralph T. Goodwin;G. Homsy
通过分析和数值求解相结合的方法研究了最终表现出与接触线相关的不稳定性的二维基态。在全球范围内，这些流动的特征可能是具有一个下坡长度尺度，远远大于垂直于斜坡的长度尺度。这允许通过匹配展开的解，其中外部解由简单的运动学控制并由润滑理论描述。为了完成求解，必须确定靠近接触线的内部区域的流量。结果表明，在同时要求：(1)自由曲面在接触线上与平面相遇，(2)自由曲面曲率变化率在接触线上有界的情况下，不可能用润滑近似来模拟内部区域的流动。然而，完整的二维斯托克斯方程允许确定内解。采用边界积分技术对施加接触角边界条件的问题进行了数值求解。对于三个相关参数：毛细数、接触角和倾角，本文报道了广泛的解决方案。计算结果表明，由于运动学因素引起的应力场，自由表面在接触线附近形成了一个驼峰。数值结果的标度分析证实，除非接触角非常小，否则在接触线附近的润滑近似是不合适的。
The two‐dimensional base state that ultimately exhibits a contact‐line‐related instability is investigated by a combination of analysis and numerical solution. Globally, these flows may be characterized as having a down‐slope length scale that is much greater than the length scale normal to the slope. This allows a solution by matched expansions, where the outer solution is governed by simple kinematics and describable by lubrication theory. In order to complete the solution, the flow in an inner region near the contact line must be determined. It is shown that it is not possible to model the flow in the inner region using the lubrication approximations while also requiring both that (1) the free surface meets the plane at the contact line and (2) the rate of change of the curvature of the free surface be bounded at the contact line. However, the full two‐dimensional Stokes equations allow the inner solution to be determined. A boundary integral technique is used to obtain numerical solutions to the problem in which a contact angle boundary condition is imposed. Solutions are reported for a wide range of the three relevant parameters: the capillary number, the contact angle, and the inclination angle. The computations reveal that the free surface develops a hump near the contact line as a result of a stress field that results from kinematic considerations. A scaling analysis of the numerical results verifies that, except possibly at very small contact angles, the lubrication approximations are inappropriate near the contact line.