Das Siddhartha, Mitra Sushanta K
Micro & Nano-scale Transport Laboratory, Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G8.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jun;87(6):063005. doi: 10.1103/PhysRevE.87.063005. Epub 2013 Jun 12.
In this paper, we identify that the different regimes encountered in a vertical capillary filling or a capillary-rise problem are determined entirely by two dimensionless parameters: Ohnesorge number (Oh) and Bond number (Bo). The initial universal inertial regime, which has been analyzed in our recent paper [Das et al., Phys. Rev. E 86, 067301 (2012)], is followed by any one of three possible regimes, dictated by the ratio Oh/Bo. For Oh/Bo>>1, the viscous effects dominate the gravitational effects, and one encounters the classical Washburn regime. For the other limit, i.e., Oh/Bo<<1, the viscous effects are insignificant and there is no Washburn regime. On the contrary, the inertial regime transits to the oscillatory regime with the filling length ℓ oscillating about the Jurin height (1/Bo), which is the maximum height attained by a liquid column in vertical capillary filling, with the viscous effects (Oh) dictating the nature of the oscillations. For Oh/Bo~1, we get a behavior intermediate of these two extreme regimes. Finally, we identify the correct force picture that drives the oscillatory regime and in the process achieve quantitative match with the experimental results, that was precluded in the previous studies.
在本文中，我们确定了在垂直毛细管填充或毛细管上升问题中遇到的不同状态完全由两个无量纲参数决定：奥内佐格数（Oh）和邦德数（Bo）。在我们最近的论文[Das等人，《物理评论E》86，067301（2012）]中分析过的初始通用惯性状态之后，会出现由Oh/Bo比值决定的三种可能状态中的任何一种。对于Oh/Bo>>1，粘性效应主导重力效应，会出现经典的沃什伯恩状态。对于另一个极限，即Oh/Bo<<1，粘性效应微不足道，不存在沃什伯恩状态。相反，惯性状态转变为振荡状态，填充长度ℓ围绕尤林高度（1/Bo）振荡，尤林高度是垂直毛细管填充中液柱达到的最大高度，粘性效应（Oh）决定振荡的性质。对于Oh/Bo~1，我们得到这两种极端状态之间的一种行为。最后，我们确定了驱动振荡状态的正确力的图景，并在此过程中实现了与实验结果的定量匹配，而这在以前的研究中是无法做到的。
