Creeping couette flow over an undulated plate
Creeping couette flow over an undulated plate
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波状板上的蠕动库埃特流
DOI：
10.1007/s00419-004-0334-9
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发表时间：
2004
影响因子：
2.8
通讯作者：
M. Scholle
中科院分区：
文献类型：
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作者：
M. Scholle
在蠕动流动条件下，我们考虑了牛顿流体在两个平板之间的定常Couette流动，其中一个平板是平面，另一个平板是正弦曲线。利用复变函数理论对Stokes方程进行了精确的解析处理，得到了流动的流线。这种非传统的方法，最近已经开发的薄膜流，[16，17]，允许减少的问题，以解决常微分和积分方程的一个变量的功能。基于我们的计算，我们可视化的旋涡的形成和演变的流动。参数研究表明，板的波动和涡结构上的阻力和流量的影响。我们还讨论了经典润滑近似及其局限性。以曳流作为润滑剂摩擦的简单模型，我们还讨论了由此产生的摩擦系数和润滑剂的材料输运。
SummaryUnder creeping flow conditions, we consider the steady Couette flow of a newtonian fluid between two plates, one of them a plane, the other one with a sinusoidal profile. The streamlines of the flow are obtained from an exact analytical treatment of the Stokes equations by making use of complex function theory. This nonconventional approach, which has been recently developed for film flows, [16, 17], allows for a reduction of the problem to the solving of ordinary differential and integral equations for functions of one variable. Based on our calculations, we visualize the formation and evolution of vortices in the flow. The influence of the plate undulations and vortex structure on the drag force and flow rate is shown by parameter studies. We also discuss the classical lubrication approximation and its limitations. Taking the drag flow as a simple model for lubricant friction, we also discuss resulting friction coefficients and material transport of the lubricant.