Steady free-surface thin film flows over topography
Steady free-surface thin film flows over topography
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DOI：
10.1063/1.870438
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发表时间：
2000-07
影响因子：
4.6
通讯作者：
S. Kalliadasis;Catherine Bielarz;G. Homsy
中科院分区：
文献类型：
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作者：
S. Kalliadasis;Catherine Bielarz;G. Homsy
我们考虑在外力作用下，在地形特征（沟槽或土丘）上流动的薄粘性薄膜的缓慢运动。利用润滑近似，将运动方程简化为自由曲面在时间和空间上演化的单一非线性偏微分方程。结果表明，该问题由特征深度、特征宽度和特征陡度三个无维参数控制。对于这些参数的广泛范围，自由表面的准稳态解被报道。我们的计算表明，自由表面在海沟入口或土丘出口的正前方形成了一个山脊，对于深度较大的陡峭基材特征，这个山脊可能会变大。在平面基底上的接触线运动中也观察到这样的毛细脊，其中接触线附近的压力积聚是造成这种脊的原因。对于地形上的流动，山脊形成是一个mani…
We consider the slow motion of a thin viscous film flowing over a topographical feature (trench or mound) under the action of an external body force. Using the lubrication approximation, the equations of motion simplify to a single nonlinear partial differential equation for the evolution of the free surface in time and space. It is shown that the problem is governed by three dimensionless parameters corresponding to the feature depth, feature width and feature steepness. Quasi-steady solutions for the free surface are reported for a wide range of these parameters. Our computations reveal that the free surface develops a ridge right before the entrance to the trench or exit from the mound and that this ridge can become large for steep substrate features of significant depth. Such capillary ridges have also been observed in the contact line motion over a planar substrate where the buildup of pressure near the contact line is responsible for the ridge. For flow over topography, the ridge formation is a mani...