Modeling of bouncing of a single clean bubble on a free surface
Modeling of bouncing of a single clean bubble on a free surface
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DOI：
10.1063/1.3546019
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发表时间：
2011-01-01
影响因子：
4.6
通讯作者：
Watanabe, M.
中科院分区：
文献类型：
--
作者：
Sato, A.;Shirota, M.;Watanabe, M.
本文用一个简单的质量弹簧系统模拟了直线上升气泡在自由表面上的反弹。本模型最显著的特点是它是基于由两个串联弹簧组成的系统的运动方程;因此，我们可以考虑气泡和自由表面的恢复力。该运动方程与能量守恒方程耦合，该能量守恒方程考虑了由于气泡和自由表面的变形而引起的表面能与气泡的动能之间的交换。通过使用这些方程，接触时间，即，气泡接触自由表面的持续时间被确定为振荡器的特征周期的一半。为了验证本模型，我们还进行了超纯水中单个清洁气泡在平坦自由表面上的弹跳实验。我们发现，从模型获得的结果与实验获得的结果吻合得很好，即使在表面变形显着的情况下。当气泡半径小于0.6mm时，气泡和自由表面的变形对气泡的弹跳起着重要的作用。另一方面，在较大气泡的情况下，由于气泡在碰撞之前已经高度变形，因此反弹由自由表面变形主导。我们的结论是，气泡在自由表面上的反弹可以清楚地解释本模型的基础上一个简单的质量弹簧系统。(c)2011年美国物理学会。[doi：10.1063/1.3546019]
Bouncing of a rectilinearly rising bubble on a free surface is modeled with the use of a simple mass-spring system. The most striking characteristic of the present model is that it is based on an equation of motion of the system that consists of two springs connected in series; hence, we can account for the restoring forces of both the bubble and free surfaces. This equation of motion is coupled with a conservation equation of energy that is taking into account an exchange between the surface energy due to deformations of both the bubble and free surfaces and the kinetic energy of the bubble. With the use of these equations, the contact time, i.e., the time duration of a bubble contacting a free surface, is determined to be a half of the characteristic period of the oscillator. We also conducted experiments of a single clean bubble in ultrapure water bouncing on a flat free surface in order to verify the present model. We found that results obtained from the model agree well with the experimentally obtained results, even in cases with significant surface deformations. When bubbles are smaller than 0.6 mm in radius, the deformations of both the bubble and free surfaces play important roles in bouncing. In case of larger bubbles, on the other hand, bouncing is dominated by the free surface deformation since the bubble has already been highly deformed before collision. We conclude that bouncing of a bubble on a free surface can be explained clearly by the present model based on a simple mass-spring system. (c) 2011 American Institute of Physics. [doi:10.1063/1.3546019]