期刊
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
卷 154, 期 -, 页码 -出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijengsci.2020.103340
关键词
Dissipation and Damping; Decay rate; Dispersion; Resonance; Minimum decay rate; Maximum decay rate; Marangoni waves; Longitudinal waves; Capillary-gravity waves; Temporally-damped waves; Spatially-damped waves; Interfacial elasticity; Capillarity and gravity; Interfacial contamination; Two-fluid interface; Gradients in interfacial tension
We investigate theoretically the effects of capillarity and gravity on interfacial Marangoni waves (M-waves). Previous studies which neglected these effects have shown the decay rate of M-waves to vary monotonically. In this work, we disprove it by deriving a new dispersion relation (accounting for these effects) for the M-waves, and show that their decay rate passes through a minimum, rather than varying monotonically. This result, obtained numerically elsewhere, was explained using a hypothetical directional packaging process. Our explanation here is consistent with the bigger picture, which includes both capillary-gravity waves (CG-waves) and M-waves, which coexist at the contaminated interface of two fluids. It is known that the CG-waves undergo maximum dissipation at a critical value of interfacial elasticity, which provides the restoring force for the M-waves. Here, we complete the story; we show that the M-waves undergo minimum dissipation at a critical value of capillarity/gravity, which provide the restoring forces for the CG-waves. Previously, it has been hypothesized that the maximum decay rate for CG-waves is caused due to their resonance with M-waves. Here, we show this hypothesis to be true for a temporally-damped wave system, and that the resonance (in addition to causing the maximum decay rate for CG-waves) also causes the minimum decay rate for M-waves. (C) 2020 Elsevier Ltd. All rights reserved.
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