THE FLOW OF A LIQUID FILM ON THE INSIDE OF A ROTATING CYLINDER, AND SOME RELATED PROBLEMS
THE FLOW OF A LIQUID FILM ON THE INSIDE OF A ROTATING CYLINDER, AND SOME RELATED PROBLEMS
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旋转圆筒内部液膜的流动及一些相关问题
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
J. Williams
中科院分区：
文献类型：
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作者：
S. Wilson;J. Williams
液膜在旋转的水平圆柱体的内表面上流动。最简单的润滑模型假设粘度和重力流向分量之间的力平衡，并且膜厚度的方程仅在平均厚度小于某个临界值时才允许连续解。在这个值以上，一个不连续的解决方案是可能的，但细节是无法通过简单的理论。这种行为可以追溯到重力的流向分量在流向方向上的逐渐周期性变化。我们还考虑了两个相关的问题，其中这种变化或多或少地突然发生：（i）当移动壁包括以不同角度倾斜的两个直段时，以及（ii）当拖曳膜通过第二上覆液体的自由表面出现时。这些问题是通过引入一个平滑参数，即表面张力，并解决一个合适的初始值问题。我们用线的方法...
A liquid film flows on the inner surface of a rotating horizontal cylinder. The simplest lubrication model assumes a force balance between viscosity and the streamwise component of gravity, and the equation for the film thickness admits a continuous solution only when the average thickness is less than a certain critical value. Above this value, a discontinuous solution is possible but the details are not accessible by means of the simple theory. This behavior can be traced to the gradual periodic variation of the streamwise component of gravity in the streamwise direction. We consider also two related problems in which this variation occurs more or less abruptly: (i) when the moving wall comprises two straight segments inclined at different angles, and (ii) when the dragged film emerges through the free surface of a second, overlying liquid. These problems are approached by introducing a smoothing parameter, namely surface tension, and solving a suitable initial value problem. We use the method of lines ...