Stagnation-point flow against a liquid film on a plane wall
Stagnation-point flow against a liquid film on a plane wall
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平面壁上液膜的驻点流
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
C. Pozrikidis
中科院分区：
文献类型：
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作者：
M. Blyth;C. Pozrikidis
摘要在Stokes流动和任意雷诺数的条件下，研究了半无限粘性流体相对于平板上液膜的错位点流。假定界面始终保持平坦且与壁面平行，扩展横向空间坐标，在垂直于壁面的横向坐标中得到简化的控制方程组，描述了界面的流动和位移的演化。在这种固有的非定常流动中，液膜在时间上保持减薄，而减薄的速度随着界面接近壁面而减小。分别考虑了二维正交流、轴对称流、三维流和斜向流。在每种情况下，构造了相似形式的精确解，并建立了描述薄膜厚度的演化方程，并用数值方法求解。准定常解优于完全计算的非定常流动，表明非定常项对气膜减薄速率的影响很小。在三维流动的情况下，发现了对偶解。
SummaryStagnation-point flow of a semi-infinite viscous fluid against a liquid film resting on a plane wall is considered under conditions of Stokes flow and for arbitrary Reynolds numbers. Assuming that the interface remains flat and parallel to the wall at all times, the lateral spatial coordinate is scaled out to yield a simplified system of governing equations in the transverse coordinate normal to the wall, describing the evolution of the flow and displacement of the interface. In this inherently unsteady flow the film keeps thinning in time, while the rate of thinning decreases as the interface approaches the wall. Orthogonal two-dimensional, axisymmetric, three-dimensional, and oblique two-dimensional flow are individually considered. In each case, exact solutions of a similarity form are constructed, and an evolution equation describing the film thickness is formulated and solved by numerical methods. Quasi-steady solutions compare favourably with full calculations of the unsteady flow, suggesting that the unsteady terms have only a minor effect on the rate of film thinning. Dual solutions are uncovered in the case of three-dimensional flow.