Influence of inertia, gravity, and substrate topography on the two-dimensional transient coating flow of a thin Newtonian fluid film
Influence of inertia, gravity, and substrate topography on the two-dimensional transient coating flow of a thin Newtonian fluid film
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DOI：
10.1063/1.1336154
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发表时间：
2001-01
影响因子：
4.6
通讯作者：
R. Khayat;S. Welke
中科院分区：
文献类型：
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作者：
R. Khayat;S. Welke
在这项研究中，研究了惯性、重力和衬底地形之间的相互作用，以研究牛顿薄膜的瞬时二维流动。假定表面张力效应可以忽略不计。流体从通道中涌出，并由保持在通道内的压力梯度驱动。假定衬底是静止的且形状任意。采用Galerkin投影，结合时间步长隐式格式，沿流动方向进行积分，在垂直方向上按正交法展开流场，求解润滑方程。结果表明，超前阶模明显占优势。重力和衬底地形对瞬变行为有很大影响，但这种影响明显不同，这取决于流体惯性的水平。研究了高惯性流体和低惯性流体的波动和流动结构。研究发现，低惯量流体在流道出口附近聚集，表现为驻波现象。
The interplay between inertia, gravity, and substrate topography is examined in this study for the transient two-dimensional flow of a thin Newtonian film. Surface tension effect is assumed to be negligible. The fluid emerges from a channel and is driven by a pressure gradient maintained inside the channel. The substrate is assumed to be stationary and of arbitrary shape. The lubrication equations are solved by expanding the flow field in terms of orthonormal modes in the vertical direction and using the Galerkin projection, combined with a time-stepping implicit scheme, and integration along the flow direction. The leading-order mode is found to be clearly dominant. Gravity and substrate topography can have a significant effect on transient behavior, but this effect varies significantly, depending on the level of fluid inertia. The wave and flow structures are examined for high- and low-inertia fluids. It is found that low-inertia fluids tend to accumulate near the channel exit, exhibiting a standing wav...