Rayleigh–Marangoni oscillatory instability in a 
horizontal liquid layer heated from above: coupling and mode mixing of internal and 
surface dilational waves

Rednikov, Alexei; Colinet, Pierre; Velarde, Manuel G.; Legros, Jean–Claude

doi:10.1017/s0022112099007181

Cited by 35 publications

(26 citation statements)

References 23 publications

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“…13 Mode exchange and mode mixing phenomena as well as resonance have been extensively discussed in the literature in other contexts as well, such as in two-layer Benard-Marangoni instability. 31,32 In light of the exchange in the behavior of the two modes at higher values of ⌫, the designation of the two modes as GL and LS depends on whether the low-k or high-k behavior is used for labeling. In this work, we use the nomenclature based on low-k asymptotic behavior of the two roots to classify them as GL and LS.…”

Section: Neo-hookean Solidmentioning

confidence: 99%

Stability of gravity-driven free-surface flow past a deformable solid at zero and finite Reynolds number

Gaurav

Shankar

2007

Physics of Fluids

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The linear stability of Newtonian liquid flow down an inclined plane lined with a deformable elastic solid layer is analyzed at zero and finite Reynolds number. There are two qualitatively different interfacial modes in this composite system: the free-surface or gas-liquid ͑"GL"͒ mode which becomes unstable at low wave numbers and nonzero Reynolds number in flow down a rigid plane, and the liquid-solid ͑"LS"͒ mode which could become unstable even in the absence of inertia at finite wave numbers when the solid layer is deformable. The objectives of this work are to examine the effect of solid layer deformability on the GL and LS modes at zero and finite inertia, and to critically assess prior predictions concerning GL mode instability suppression at finite inertia obtained using the linear elastic model by comparison with the more rigorous neo-Hookean model for the solid. In the creeping-flow limit where the GL mode instability is absent in a rigid incline, we show that for both solid models, the GL and LS modes become unstable at finite wavelengths when the solid layer becomes sufficiently soft. At finite wavelengths, the labeling of the two interfacial modes as GL and LS becomes arbitrary because these two modes get "switched" when the solid layer becomes sufficiently deformable. The critical strain required for instability becomes independent of the solid thickness ͑at high enough values of thickness͒ for both GL and LS modes in the linear elastic solid, while it decreases with the thickness of the neo-Hookean solid. At finite Reynolds number, it is shown for both the solid models that the free-surface instability in flow down a rigid plane can be suppressed at all wavelengths by the deformability of the solid layer. The neutral curves associated with this instability suppression are identical for both linear elastic and neo-Hookean models. When the solid becomes even more deformable, both the GL and LS modes become unstable for finite wave numbers at nonzero inertia, but the corresponding neutral curves obtained from the two solid models differ significantly in detail. At finite inertia, for both the solid models, there is a significant window in the shear modulus of the solid for moderate values of solid thickness where both the GL and LS modes are stable at all wave numbers. Thus, using the neo-Hookean model, the present study reaffirms the prediction that soft elastomeric coatings offer a passive route to suppress and control interfacial instabilities.

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Section: Neo-hookean Solidmentioning

confidence: 99%

Stability of gravity-driven free-surface flow past a deformable solid at zero and finite Reynolds number

Gaurav

Shankar

2007

Physics of Fluids

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“…Until now, the investigation of the above-mentioned instability mechanism was done in a one-layer approach (Rednikov et al, 2000). However, there is no doubt that this type of instability can be important in two-layer systems.…”

Section: Mode Mixing Of Interfacial and Internal Wavesmentioning

confidence: 99%

Interfacial Convection in Multilayer Systems

2006

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“…As ε is also an ordering parameter, the substitution of expansions [21]- [24] into [12]- [20] yields a hierarchy of equations for Q 0 , Q 1 , and Q 2 that demand specific solvability conditions (Fredholm alternative).…”

Section: Instability Thresholdmentioning

confidence: 99%