Das Siddhartha, Waghmare Prashant R, Mitra Sushanta K
Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G8.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 2):067301. doi: 10.1103/PhysRevE.86.067301. Epub 2012 Dec 14.
In this paper we analyze the inviscid regime (for which viscosity is unimportant and the flow occurs due to the balance between the capillary and the inertial effects) that invariably precedes the classical century-old Washburn regime during capillary filling. We demonstrate that a new nondimensional number, namely, the product of the Ohnesorge number and the ratio between the filling length (ℓ) and the radius of the capillary (R), dictates the occurrence of this regime and the other well-known regimes in a capillary filling problem. We also identify that this inviscid regime occurs for the time that is of the order of the capillary time scale and, as has been quantified before [Quere, Eur. Phys. Lett. 39, 533 (1997); Joly, J. Chem. Phys. 135, 214705 (2011)], is characterized by the filling length being linearly proportional to the filling time. We establish the universality of this regime by pinpointing the existence of this regime (showing appropriate dependencies of the capillary radii and density) from existing experimental and Molecular Dynamics Simulation results that signify disparate ranges of length and time scales.
在本文中，我们分析了无粘滞 regime（在此 regime 中，粘性不重要，流动是由于毛细管效应和惯性效应之间的平衡而发生的），该 regime 在毛细管填充过程中总是先于经典的百年老 Washburn regime 出现。我们证明了一个新的无量纲数，即奥内佐格数与填充长度（ℓ）与毛细管半径（R）之比的乘积，决定了该 regime 以及毛细管填充问题中其他著名 regime 的出现。我们还确定，这种无粘滞 regime 发生的时间量级为毛细管时间尺度，并且如之前所量化的那样[Quere，Eur. Phys. Lett. 39, 533 (1997); Joly, J. Chem. Phys. 135, 214705 (2011)]，其特征是填充长度与填充时间成线性比例。我们通过从现有实验和分子动力学模拟结果中确定该 regime 的存在（显示出毛细管半径和密度的适当依赖性）来确立该 regime 的普遍性，这些结果代表了不同的长度和时间尺度范围。
