The velocity of ‘large’ viscous drops falling on a coated vertical fibre
The velocity of ‘large’ viscous drops falling on a coated vertical fibre
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DOI：
10.1017/jfm.2013.540
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发表时间：
2011-11
影响因子：
3.7
通讯作者：
Liyan Yu;J. Hinch
中科院分区：
文献类型：
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作者：
Liyan Yu;J. Hinch
[摘要]Kalliadasis， Chang [j] .流体力学。（vol. 261, 1994, pp. 135-168）在润滑理论中表明，如果液膜厚度超过临界值，液滴将加速生长，而膜较薄时液滴则以恒定速度下降。当膜的厚度增加到临界值时，液滴的移动速度更快，体积更大。我们重新审视他们对这些大下降的渐近分析。虽然我们恢复了他们的领先顺序和第一次修正的结果，但我们不同意进一步的修正。特别是，我们发现有必要评估第三种校正，这是他们没有考虑的，在我们获得速度对无量纲控制参数的依赖的第一个近似之前。为了改进对速度的第一个近似，我们进一步进行两次修正。
Abstract Kalliadasis & Chang (J. Fluid Mech., vol. 261, 1994, pp. 135–168) showed within lubrication theory that if a liquid film is thicker than a critical value then drops will accelerate and grow, whereas with thinner films the drops fall at a constant velocity. As the thickness of the film increases to the critical value, the drops move faster and are larger. We revisit their asymptotic analysis of these large drops. While we recover their results for the leading-order and first correction, we do not agree on further corrections. In particular we find it necessary to evaluate the third correction, which they do not consider, before we obtain a first approximation to the dependence of the speed on the non-dimensional control parameter. We proceed to two further corrections in order to improve this first approximation to the speed.