Stability of liquid film flow laden with the soluble surfactant sodium dodecyl sulphate: predictions versus experimental data

Gravity-driven liquid film flows laden with a soluble surfactant are considered, and aqueous solutions of sodium dodecyl sulphate (SDS) are taken as a case-study. Literature measurements of the critical Reynolds number for the onset of instability are set in perspective with predictions of linear st...

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 894
Main Authors Katsiavria, A., Bontozoglou, V.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 10.07.2020
Subjects
Adsorption
Aqueous solutions
Boundary conditions
Compressibility
Computational fluid dynamics
Eigenvalues
Equilibrium
Flow stability
Fluid flow
Gravity
JFM Papers
Kinematics
Mass transfer
Momentum
Monolayers
Predictions
Reynolds number
Sodium
Sodium dodecyl sulfate
Sodium lauryl sulfate
Stabilizing
Sulfates
Surfactants
Theories
Velocity
Wavelength
capillary flows
thin films
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Summary:Gravity-driven liquid film flows laden with a soluble surfactant are considered, and aqueous solutions of sodium dodecyl sulphate (SDS) are taken as a case-study. Literature measurements of the critical Reynolds number for the onset of instability are set in perspective with predictions of linear stability theory. The theory is based on a Frumkin model of adsorption equilibrium, modified by the inclusion of finite compressibility of the adsorbed monolayer. Quantitative comparison between data and theory is first attempted in the limit of infinite wavelength. Though wave characteristics are satisfactorily predicted, the theoretical critical Reynolds number is an order of magnitude below measurements. This discrepancy is understood in terms of the large difference between momentum and mass diffusivities and indicates that the assumption of infinite wavelength is far more restrictive for the mass transfer than for the flow problem. Finite-wavelength effects are taken into account by numerical solution of the Orr–Sommerfeld eigenvalue problem, leading to predictions of maximum stabilization in good agreement with the measurements. Introduction of realistic values of monolayer compressibility improves further the agreement at high surfactant loadings. Finally, a strong stabilizing effect of salinity is confirmed.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2020.283