On the instabilities of vertical falling liquid films in the presence of surface-active solute

Ji, Wei; Setterwall, Fredrik

doi:10.1017/s0022112094003721

Cited by 49 publications

(36 citation statements)

References 10 publications

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“…This result was obtained for a vertically falling film by Anshus and Acrivos [9], who also showed that the wavelength of the most dangerous mode is significantly increased by surfactant. Ji and Setterwall [10] discussed the effect of soluble surfactant and demonstrated the existence of an unstable Marangoni mode for a vertical film. Pozrikidis [11] relaxed the long-wave assumption adopted by previous workers and showed that for a single film in the inertialess, zero Reynolds number limit, there are two normal modes, the first of which corresponds to that found by Yih [4] and the second of which is a Marangoni mode contributed by the surfactant.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Inertialess multilayer film flow with surfactant: Stability and traveling waves

Thompson

Blyth

2016

Phys. Rev. Fluids

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“…Since then, the flow in falling liquid films has been studied extensively through experimental measurements [10,45], low-dimensional modelling [46,47], and full numerical simulations [48]. The effects of many factors that influence the flow in falling films have been investigated, such as the effects of thermocapillarity [49], electric fields [50,51], and surfactants [52,53]. Different processes that may be involved in falling films have also been studied, such as heat transfer [54], mass transfer [55], chemical reactions [56], and phase change [57].…”

Section: Introductionmentioning

confidence: 99%

Impact of droplets on inclined flowing liquid films

2015

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The impact of droplets on an inclined falling liquid film is studied experimentally using highspeed imaging. The falling film is created on a flat substrate with controllable thicknesses and flow rates. Droplets with different sizes and speeds are used to study the impact process under various Ohnesorge and Weber numbers, and film Reynolds numbers. A number of phenomena associated with droplet impact are identified and analysed, such as bouncing, partial coalescence, total coalescence, and splashing. The effects of droplet size, speed, as well the film flow rate are studied culminating in the generation of an impact regime map. The analysis of the lubrication force acted on the droplet via the gas layer shows that a higher flow rate in the liquid film produces a larger lubrication force, slows down the drainage process, and increases the probability of droplet bouncing. Our results demonstrate that the flowing film has a profound effect on the droplet impact process and associated phenomena, which are markedly more complex than those accompanying impact on initially quiescent films.

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“…Mass transfer rates, as well as the kinetics of adsorption, have been shown to be critical in the special case of a volatile soluble surfactant, which actually enhances instability (Ji & Setterwall 1994;Shkadov, Velarde & Shkadova 2004). Enhancement of instability was also shown by Yiantsios & Higgins (2010) to be possible under conditions of evaporating thin films in the presence of non-volatile soluble surfactants.…”

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confidence: 99%

The role of surfactants on the mechanism of the long-wave instability in liquid film flows

Karapetsas

Bontozoglou

2014

J. Fluid Mech.

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The analysis for the physical mechanism of the long-wave instability in liquid film flow is extended to take into account the presence of a surfactant of arbitrary solubility. The Navier–Stokes equations are supplemented by mass balances for the concentrations at the interface and in the bulk, by a Langmuir model for adsorption kinetics at the interface, and are expanded in the limit of long-wave disturbances. The longitudinal flow perturbation, known to result from the perturbation shear stress which develops along the deformed interface, is shown to contribute a convective flux that triggers an interfacial concentration gradient. This gradient is, at leading order, in phase with the interfacial deformation, and as a result produces Marangoni stresses that stabilize the flow. The strength of the interfacial concentration gradient is shown to be maximum for an insoluble surfactant and to decrease with increasing surfactant solubility. The decrease is explained in terms of the spatial phase of mass transfer between interface and bulk, which mitigates the interfacial flux by the flow perturbation and leads to the attenuation of Marangoni stresses. Higher-order terms are derived, which provide corrections for disturbances of finite wavelength

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On the instabilities of vertical falling liquid films in the presence of surface-active solute

Cited by 49 publications

References 10 publications

Inertialess multilayer film flow with surfactant: Stability and traveling waves

Inertialess multilayer film flow with surfactant: Stability and traveling waves

Impact of droplets on inclined flowing liquid films

The role of surfactants on the mechanism of the long-wave instability in liquid film flows

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