Nonlinear dynamics of two-layer channel flow with soluble surfactant below or above the critical micelle concentration

Kalogirou, Anna; Blyth, Mark

doi:10.1017/jfm.2020.480

Cited by 5 publications

(6 citation statements)

References 56 publications

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“…Recently the present authors showed that for the inertialess channel flow problem, the ability of the surfactant to dissolve in one of the fluids can either enhance or suppress interfacial instability for certain fluids and/or surfactant properties [9,10]. Studies of the related problem of film flow down an inclined substrate have found surfactant solubility to have a destabilising effect [11][12][13].…”

Section: Introductionmentioning

confidence: 86%

“…where H = 1 + h 2 x and the notation [F i ] 1 2 = F 1 − F 2 is used. The surface tension in conditions (3) is given by the Langmuir equation of state which is γ = 1 + Ma ln (1 − Γ ) [16,18] and is seen to depend on the interfacial surfactant concentration Γ , the evolution of which is described by the convection-diffusion equation [10,19] 1…”

Section: Linear Stability Analysismentioning

confidence: 99%

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Instabilities at a sheared interface over a liquid laden with soluble surfactant

Kalogirou

Blyth

2021

J Eng Math

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The linear stability of a semi-infinite fluid undergoing a shearing motion over a fluid layer that is laden with soluble surfactant and that is bounded below by a plane wall is investigated under conditions of Stokes flow. While it is known that this configuration is unstable in the presence of an insoluble surfactant, it is shown via a linear stability analysis that surfactant solubility has a stabilising effect on the flow. As the solubility increases, large-wavelength perturbations are stabilised first, leaving open the possibility of mid-wave instability for moderate surfactant solubilities, and the flow is fully stabilised when the solubility exceeds a threshold value. The predictions of the linear stability analysis are supported by an energy budget analysis which is also used to determine the key physical effects responsible for the (de)stabilisation. Asymptotic expansions performed for long-wavelength perturbations turn out to be non-uniform in the insoluble surfactant limit. In keeping with the findings for insoluble surfactant obtained by Pozrikidis & Hill (IMA J Appl Math 76:859–875, 2011), the presence of the wall is found to be a crucial factor in the instability.

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Section: Introductionmentioning

confidence: 86%

Section: Linear Stability Analysismentioning

confidence: 99%

Instabilities at a sheared interface over a liquid laden with soluble surfactant

Kalogirou

Blyth

2021

J Eng Math

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“…Consequently, exploiting the disparity between the and length scales, we perform a lubrication analysis to derive the following model system that will allow us to study the nonlinear spatio-temporal interfacial dynamics (see Appendix A for a detailed derivation): where , , , are all functions of and are defined by The functions and are positive provided that , while the functions and can each be of either sign depending on the values of , and . The lubrication model presented above is similar to the model of Tilley, Davis & Bankoff (1994) and it reduces to those obtained in related studies on channel flows with surfactant (Blyth & Pozrikidis 2004; Frenkel & Halpern 2017; Kalogirou & Blyth 2020), in the case when surfactant is neglected.…”

Section: Mathematical Modelmentioning

confidence: 88%

“…We note that the flow rate can be found by satisfying a periodicity condition on the pressure (Ooms et al. 1985; Blyth & Pozrikidis 2004; Kalogirou & Blyth 2020), e.g. or equivalently fixing the pressure drop in the streamwise direction to be zero over a specified domain of length .…”

Section: Figure 14mentioning

confidence: 99%

Nonlinear dynamics of unstably stratified two-layer shear flow in a horizontal channel

Kalogirou

Blyth²

2023

J. Fluid Mech.

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The Rayleigh–Taylor instability at the interface of two sheared fluid layers in a horizontal channel is investigated in the absence of inertia. The dynamics of the flow is described by a nonlinear lubrication equation which is solved numerically for adverse density stratifications. The early-time dynamics features a number of finger-like protrusions of different heights at the interface. The fingers travel at different speeds leading to a sequence of merging events after which the interface eventually settles to a near-saturated state, comprising only one finger that includes most of the lower fluid. For sufficiently large density stratifications, the final state spans the height of the channel and includes two thin fluid films at each wall, both of which undergo chaotic dynamics, but finite-time touch-down/touch-up is shown to be precluded by the shear flow. An asymptotic analysis in the large-Bond-number limit (intense density stratification) reveals the finer structure of the final state including Landau–Levich-type connection regions. The asymptotic solutions are compared with numerical results of the lubrication model as well as direct numerical simulations, and excellent agreement is observed between the three in terms of interfacial structure, wave speed and film thicknesses.

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“…(2020) considered both the solutocapillary effect of soluble surfactant and the thermocapillary effect, and reached the same conclusion. Kalogirou & Blyth (2019, 2020, 2021) investigated a two-layer shear flow with soluble surfactant dissolving in the lower layer. They reported that solubility and sorption kinetics could influence interfacial dynamics and the effect of soluble surfactant on the instability could be either stabilizing or destabilizing.…”

Section: Introductionmentioning

confidence: 99%

The role of soluble surfactant in the linear instability of a film coating inside a tube

Li,

Chen,

Cheng

et al. 2023

J. Fluid Mech.

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This study investigates the linear instability of a thin-film coating inside a rigid tube. The flow is assumed to be inertialess and driven by an axial body force (e.g. gravity), an interfacial shearing force, or their combinations. The interface and the bulk of the film are laden with soluble surfactant. The properties of the soluble surfactant, i.e. solubility, sorption kinetics and bulk diffusivity, modulate the interfacial dynamics of the film. The influence of these properties on the linear instability of the film is comprehensively investigated via long-wave approximation analysis and numerical calculation. Two modes, namely the interface mode and the surfactant mode, are identified to dominate the instability. For a quiescent film, it is found that solubility, sorption kinetics and bulk diffusivity act to improve the uniformity of the surface surfactant and mitigate the stabilizing effect of the Marangoni force. For the film driven by the axial body/interfacial shearing force, the results reveal that solubility plays contrasting roles in the interface mode and the surfactant mode. A window with intermediate solubility is detected where the film can be linearly stabilized. Moreover, sorption kinetics is found to destabilize the perturbations with long wavelength whereas it stabilizes the perturbations with finite wavelength. The bulk diffusivity of the surfactant has a non-monotonic influence on the flow instability, and the film can be relatively stable at both strong and weak diffusivity.

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Nonlinear dynamics of two-layer channel flow with soluble surfactant below or above the critical micelle concentration

Abstract: Abstract

Cited by 5 publications

References 56 publications

Instabilities at a sheared interface over a liquid laden with soluble surfactant

Instabilities at a sheared interface over a liquid laden with soluble surfactant

Nonlinear dynamics of unstably stratified two-layer shear flow in a horizontal channel

The role of soluble surfactant in the linear instability of a film coating inside a tube

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