Linear waves at a surfactant-contaminated interface separating two fluids: Dispersion and dissipation of capillary-gravity waves

Girish K. Rajan, Diane M. Henderson

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Article number072104
JournalPhysics of Fluids
Volume30
Issue number7
DOIs
StatePublished - Jul 1 2018

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gravity waves
dissipation
surfactants
fluids
decay rates
contamination
oceans
capillary waves
predictions
derivation
elastic properties
viscosity

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

Cite this

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Linear waves at a surfactant-contaminated interface separating two fluids : Dispersion and dissipation of capillary-gravity waves. / Rajan, Girish K.; Henderson, Diane M.

In: Physics of Fluids, Vol. 30, No. 7, 072104, 01.07.2018.

Research output: Contribution to journalArticle

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