Effect of surfactants on the inertialess instability of a two-layer film flow

Gao, Peng; Lu, Xi‐Yun

doi:10.1017/s0022112007008646

Cited by 24 publications

(55 citation statements)

References 26 publications

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“…Previous studies have also shown that the viscosity contrast between the layers can play an important role in deciding stability. We have validated our calculations by successfully comparing our results with those of Gao and Lu [21] in the case of two layers with surfactant, and with those of Weinstein and Chen [27] for three clean layers.…”

Section: Linear Stability: Stokes Flowsupporting

confidence: 60%

“…The growth rates for these modes are shown in figure 2(c) for m 2 = 2.5. This is a facet of differential layer thicknesses; when r 2 = 1 Gao and Lu [21] noted that at most one of the four possible modes (in the presence of surfactant) can be unstable for a fixed parameter set. …”

Section: A Two-layer Flowmentioning

confidence: 99%

“…The case of two-layer flow was studied in detail by Gao and Lu [21] for layers of equal thickness. Assuming equal densities, a clean two-layer flow is stable when the more viscous layer is next to the wall, and is unstable when the less viscous film is next to the wall so that m 2 > 1.…”

Section: A Two-layer Flowmentioning

confidence: 99%

“…Assuming equal densities, a clean two-layer flow is stable when the more viscous layer is next to the wall, and is unstable when the less viscous film is next to the wall so that m 2 > 1. Gao and Lu [21] demonstrated that a stable, clean two-layer film with m 2 < 1 is destabilised by adding surfactant to the interface between the films. However, the flow remains stable when surfactant is added to the free surface, and they found no evidence that surfactant can stabilise a unstable clean configuration.…”

Section: A Two-layer Flowmentioning

confidence: 99%

“…Gao and Lu [21] studied the linear stability of twolayer flow in the presence of surfactant. They conducted a normal mode linear stability analysis in the limit of zero Reynolds number for arbitrary wavelength disturbances.…”

Section: Introductionmentioning

confidence: 99%

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Inertialess multilayer film flow with surfactant: Stability and traveling waves

Thompson

Blyth

2016

Phys. Rev. Fluids

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Multilayer film flow down an inclined plane in the presence of an insoluble surfactant is investigated with particular emphasis on determining flow stability and investigating the possibility of travelling wave solutions. The investigation is conducted for two or three layers under conditions of Stokes flow and, separately, on the basis of a long-wave assumption. A normal mode linear stability analysis for Stokes flow shows that adding surfactant to one of the film surfaces can destabilise an otherwise stable flow configuration. For the long-wave system, periodic travelling-wave branches are detected and traced, revealing solutions with pulse-like solitary waves on each film surface travelling in phase with each other, travelling waves with capillary ridge structures, and solutions with two of the film surfaces almost in contact. Time-periodic travelling wave solutions are also found. The stability of the travelling waves is determined by solving initial value problems and by computing eigenvalue spectra. Boundary element simulations for Stokes flow confirm the existence of travelling waves outside of the longwave regime.

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Section: Linear Stability: Stokes Flowsupporting

confidence: 60%

Section: A Two-layer Flowmentioning

confidence: 99%

Section: A Two-layer Flowmentioning

confidence: 99%

Section: A Two-layer Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Inertialess multilayer film flow with surfactant: Stability and traveling waves

Thompson

Blyth

2016

Phys. Rev. Fluids

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Investigating the influence of surface shear stress on the stability of gravity‐driven multilayer liquid flow

Tomar

2024

Can J Chem Eng

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We conducted a linear stability analysis on the behaviour of two gravity‐driven Newtonian liquid layers flowing down an inclined rigid plane, subjected to external shear stress at the free surface, in both the direction of and opposite to gravity. A long wave asymptotic analysis was conducted to examine the influence of several parameters, including liquid film thickness (β), viscosity ratio (μr), and external shear stress (τ), on the interfacial modes of both gas–liquid (GL) and liquid–liquid (LL). For viscosity ratios (μr) < 1 and Reynolds number (Re) = 0, the observations indicate that the LL mode exhibits instability attributed to O(k) instability. This phenomenon is manifest when an external shear stress is applied at the GL interface, specifically within a defined range of negative shear stress values. When and , the investigation reveals the presence of two complex conjugate roots when external shear stress opposes the direction of gravity. One of these roots, referred to as the positive root, is associated with the leading (or zero) order instability that renders the GL mode unstable. The other root corresponds to the leading (or zero) order stability, contributing to the stability of the LL mode. In contrast, when external shear stress acts along the gravity direction, we observe that the GL mode is stable while the LL mode becomes unstable due to O(k) instability for various values of β. This finding highlights the importance of the direction of external shear stress in determining the interfacial mode's stability behaviour.

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Effects of velocity slip on the inertialess instability of a contaminated two-layer film flow

Anjalaiah

Usha

2015

Acta Mech

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This manuscript provides a theoretical stability analysis for the configuration of two-layer immiscible flow down an inclined plane with velocity slip along the incline in the limit of zero Reynolds number. Surfactants may be present at the air-liquid interface, liquid-liquid interface, or both. In addition to an Orr-Sommerfeld analysis (again at zero Reynolds number), a long wavelength stability analysis is performed and the results are shown to be consistent. The interface mode, namely the mode of instability that arises because of viscosity stratification, is examined. Stability results (growth rates as a function of slip parameter and neutral stability boundaries) for various configurations of viscosity, surfactant placement, and layer thickness are compared with those of the previous literature and found to agree. It is found that velocity slip along the inclined plane reduces the maximum growth rate of instabilities in configurations where they occur, and the range of unstable wave numbers shrinks as well, indicating that slip has a promise for stabilization. This suggests that there is a possibility of using this favourably as a control option for two-layer flows in the absence or presence of surfactants, in relevant applications by designing the substrate to be a porous substrate with small permeability or a slippery substrate or a rough substrate or a hydrophobic substrate which can be modelled as substrates with velocity slip.

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Effect of surfactants on the inertialess instability of a two-layer film flow

Cited by 24 publications

References 26 publications

Inertialess multilayer film flow with surfactant: Stability and traveling waves

Inertialess multilayer film flow with surfactant: Stability and traveling waves

Investigating the influence of surface shear stress on the stability of gravity‐driven multilayer liquid flow

Effects of velocity slip on the inertialess instability of a contaminated two-layer film flow

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