Linear waves at a surfactant-contaminated interface separating two fluids: Dispersion and dissipation of capillary-gravity waves
Linear waves at a surfactant-contaminated interface separating two fluids: Dispersion and dissipation of capillary-gravity waves
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DOI：
10.1063/1.5027709
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发表时间：
2018-07
影响因子：
4.6
通讯作者：
G. K. Rajan;D. Henderson
中科院分区：
文献类型：
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作者：
G. K. Rajan;D. Henderson
研究了任意密度和粘度的两种无限深流体在污染界面上的二维线性波。污染物被建模为无质量的单层，这可能是由于不溶性表面活性剂，并引入界面弹性。因此，界面支持两种波模式：横向，毛细重力波（CG波）和纵向，马兰戈尼波（M波）。一个全面的色散关系推导出，它可以通过数值求解，以获得作为CG波和M波的无旋波数的函数的复值频率。本文对CG波进行了分析，对M波进行了单独的分析。这里的主要结果是推导出一个操作的近似公式的时间衰减率的CG波。它的预测相比，现有的测量（实验室）重力波，海洋涌浪，（实验室）毛细波。它表明，以前公布的衰减率模型，其中包括由于上层流体或那些由于界面污染（但不是两者）的影响，是本模型的限制情况。衰减率预测的参数研究表明，有系统，包括海洋涌浪的上层流体的动力学和污染的影响是显着的。二维线性波在污染的界面分离两个无限深的任意密度和粘度的流体进行了调查。污染物被建模为无质量的单层，这可能是由于不溶性表面活性剂，并引入界面弹性。因此，界面支持两种波模式：横向，毛细重力波（CG波）和纵向，马兰戈尼波（M波）。一个全面的色散关系推导出，它可以通过数值求解，以获得作为CG波和M波的无旋波数的函数的复值频率。本文对CG波进行了分析，对M波进行了单独的分析。这里的主要结果是推导出一个操作的近似公式的时间衰减率的CG波。它的预测相比，现有的测量（实验室）重力波，海洋涌浪，（实验室）毛细波。它表明，以前公布的衰变r…
Two-dimensional linear waves at a contaminated interface separating two infinitely deep fluids of arbitrary densities and viscosities are investigated. The contamination is modeled as a massless monolayer, which may result from insoluble surfactants, and introduces interfacial elasticity. Thus, the interface supports two wave modes: transverse, capillary-gravity waves (CG-waves) and longitudinal, Marangoni waves (M-waves). A comprehensive dispersion relation is derived; it can be solved numerically to obtain the complex-valued frequency as a function of the irrotational wavenumber for the CG-waves and for the M-waves. The CG-waves are analyzed in this paper; the M-waves are analyzed in a separate work. The main result here is the derivation of an operational approximate formula for the temporal decay rate of the CG-waves. Its predictions are compared to the available measurements of (laboratory) gravity waves, ocean swell, and (laboratory) capillary waves. It is shown that the previously published decay rate models, which include either the effects due to an upper fluid or those due to interfacial contamination (but not both), are limiting cases of the present model. A parametric study of decay rate predictions shows that there are systems including ocean swell for which the influence of both the dynamics of the upper fluid and of the contamination are significant.Two-dimensional linear waves at a contaminated interface separating two infinitely deep fluids of arbitrary densities and viscosities are investigated. The contamination is modeled as a massless monolayer, which may result from insoluble surfactants, and introduces interfacial elasticity. Thus, the interface supports two wave modes: transverse, capillary-gravity waves (CG-waves) and longitudinal, Marangoni waves (M-waves). A comprehensive dispersion relation is derived; it can be solved numerically to obtain the complex-valued frequency as a function of the irrotational wavenumber for the CG-waves and for the M-waves. The CG-waves are analyzed in this paper; the M-waves are analyzed in a separate work. The main result here is the derivation of an operational approximate formula for the temporal decay rate of the CG-waves. Its predictions are compared to the available measurements of (laboratory) gravity waves, ocean swell, and (laboratory) capillary waves. It is shown that the previously published decay r...