Detailed finer features in spectra of interfacial waves for characterization of a bubble-laden drop
Detailed finer features in spectra of interfacial waves for characterization of a bubble-laden drop
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用于表征充满气泡的液滴的界面波光谱中的更精细特征
DOI：
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发表时间：
2017
影响因子：
3.7
通讯作者：
S. Bhattacharya
中科院分区：
文献类型：
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作者：
Udugama R. Sumanasekara;S. Bhattacharya
这篇文章描述了气泡液滴表面的小振幅波的有趣光谱表现的未被探索的细节。其界面脉动的固有频率随空穴在液体中的位置而呈现出不平凡的变化。利用一种新的方法，在低毛细管数和低键数限制下，计算了空穴任意位置下光谱的构型依赖关系。分析基于两组基函数的展开，其中它们的相互变换被用来实施界面边界条件。所获得的结果量化了几个具有科学和技术意义的重要特征。对于同心几何，固有的方位简并性使得许多振动模式的频率完全相同。然而，对于气泡的偏心位置，这种简并性消失了，在对应于不同方位角模式的光谱值中产生了微小的偏差。这种行为类似于原子系统中的精细结构分裂，不同的量子数确保了状态能级的微小偏差。制定的数学程序可以确定界面振荡的各个频率值，即使这些频率值紧密地组合在一起。这篇文章展示了如何利用带内精细结构的数目及其特定值来预测不透明水滴中空穴的大小和位置，而不需要直接看到它的内部。
This article describes unexplored details of the intriguing spectral manifestation of the small-amplitude waves at the surfaces of a bubble-laden drop. Its natural frequencies of interfacial pulsation reveal a non-trivial variation with the position of the cavity inside the liquid. This configurational dependence of spectra is calculated for arbitrary location of the void by using a novel approach under low capillary number and low Bond number limits. The analysis is based on expansion in two sets of basis functions where their mutual transformations are utilized to enforce interfacial boundary conditions. The obtained results quantify a few important features which have both scientific and technological significance. For a concentric geometry, the inherent azimuthal degeneracy makes the frequencies for a number of vibrational modes exactly the same. For an eccentric position of the bubble, however, this degeneracy disappears, creating small deviations in the spectral values corresponding to different azimuthal modes. Such behaviour is akin to fine-structure split in an atomic system, where different quantum numbers ensure small deviation in energy levels of the states. The formulated mathematical procedure can determine the individual frequency values for the interfacial oscillation even if these are grouped closely together in bands. The paper shows how the number of fine structures inside a band and their specific values can be exploited to predict the size and position of the cavity in an opaque drop without any direct visualization of its interior.