2016
DOI: 10.1017/jfm.2016.96
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Surface viscosity and Marangoni stresses at surfactant laden interfaces

Abstract: We calculate here the force on a probe at a viscous, compressible interface, laden with soluble surfactant that equilibrates on a finite time scale. The motion of the probe through the interface drives variations in the surfactant concentration at the interface that in turn leads to a Marangoni flow that contributes to the force on the probe. We demonstrate that the Marangoni force on the probe depends non-trivially on the surface shear and dilatational viscosities of the interface indicating the difficulty in… Show more

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Cited by 68 publications
(57 citation statements)
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“…Since emphasis is put on the dilute regime, the reference Gibbs elasticity is set by the equilibrium value E 0 = Γ 0 k B T . Following [26], we define the dimensionless surface compressibility as the ratio of viscous over surface tension gradient forces…”
Section: General Considerationsmentioning
confidence: 99%
“…Since emphasis is put on the dilute regime, the reference Gibbs elasticity is set by the equilibrium value E 0 = Γ 0 k B T . Following [26], we define the dimensionless surface compressibility as the ratio of viscous over surface tension gradient forces…”
Section: General Considerationsmentioning
confidence: 99%
“…The denominator η (s)γ s is the magnitude of the surface stresses of rheological origin, here taken for a shear flow at a shear rateγ s . Three non-dimensional groups will appear in the stress boundary condition for a planar interface undergoing a complex surface deformation, either Bo s , Bo d number and M a, or the combination Bo s , Θ, M a [35,47,49]. When the interface is curved, effects of capillarity (captured by a Capillary number) and bending will additionally contribute.…”
Section: Accepted Manuscriptmentioning
confidence: 99%
“…We neglected surfactant compressibility but could incorporate it explicitly by tracking the surfactant concentration field in a mass conservation equation. This could be further generalized by accounting for the kinetics of adsorption and desorption of species to and from the bulk, in the case of soluble surfactants [43] and nanoparticles [44][45][46]. Surface dilatational viscosities, which would generally also be -dependent, may also play a significant role in flows with a compressional contribution.…”
Section: Implications and Conclusionmentioning
confidence: 99%