Thin film lubrication dynamics of a binary mixture: Example of an oscillatory instability

Bestehorn, Michael; Borcia, Ion Dan

doi:10.1063/1.3489434

Cited by 15 publications

(22 citation statements)

References 35 publications

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“…Sufficiently strong vibration destabilizes the flat interface, leading to the formation of standing surface waves. The phenomenon has received much attention in the past and has now been extensively studied for various geometries of the system, including two semi-infinite liquid phases [2], two liquid films of finite or infinite thickness confined between two solid plates [3][4][5][6][7][8], one finite thickness liquid layer, supported by a solid plate and exposed to a gas phase [9][10][11][12][13][14][15][16][17][18], and a single unsupported soaplike viscoelastic liquid film [19].…”

Section: Introductionmentioning

confidence: 99%

Faraday instability of a two-layer liquid film with a free upper surface

Pototsky

Bestehorn

2016

Phys. Rev. Fluids

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We study the linear stability of a laterally extended flat two-layer liquid film under the influence of external vertical vibration. The first liquid layer rests on a vibrating solid plate and is overlaid by a second layer of immiscible fluid with deformable upper surface. Surface waves, excited as the result of the Faraday instability, can be characterized by a time-dependent relative amplitude of the displacements of the liquid-liquid and the liquid-gas interfaces. The in-phase displacements are associated with a zigzag (barotropic) mode and the antiphase displacement corresponds to the varicose thinning mode. We numerically determine the stability threshold in the vibrated two-layer film and compute the dispersion relation together with the decay rates of the surface waves in the absence of vibration. The in-phase and the antiphase displacements are strongly coupled in the vibrated system. The interplay between the Faraday and the Rayleigh-Taylor instabilities in the system with heavier fluid on top of a lighter fluid is analyzed.

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Section: Introductionmentioning

confidence: 99%

Faraday instability of a two-layer liquid film with a free upper surface

Pototsky

Bestehorn

2016

Phys. Rev. Fluids

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“…Accordingly, the derived model does not include the equation for concentration (7). This is a significant difference from the other long-wave model of a binary liquid film [12] and the stability analysis of an evaporating binary liquid layer [9].…”

Section: Long-wave Modelmentioning

confidence: 95%

“…Note that the effects of vapor recoil, stress induced by the vapor motion, heat flux in the gas phase and viscous dissipation are neglected in Eqs. (12) and (13). As in Ref.…”

Section: Governing Equationsmentioning

confidence: 96%

Stability of a condensing liquid film in a binary vapor mixture system

Kanatani¹

2013

International Journal of Heat and Mass Transfer

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We study stability of a condensing liquid film of a binary vapor mixture. When a binary vapor mixture of some kind is cooled on a substrate, a condensing liquid film emerges to take an inhomogeneous form such as a droplet one due to the solutal Marangoni effect. In order to analyze this phenomenon, we apply the long-wave approximation to the condensing liquid film and derive a nonlinear partial differential equation describing the spatio-temporal evolution of the film thickness. An interfacial boundary condition taking account of an effect of mass gain of the liquid film is adopted. Based on this model, we perform a linear stability analysis around a flat-film solution. We obtain an evolution equation of the amplitude of a disturbance, from which the cutoff and fastest growth wavenumbers are deduced. The maximum value of the cutoff wavenumber relative to the film thickness and its film thickness are estimated for water-ethanol mixture at atmospheric pressure. We numerically verify the long-wave nature of the instability of the condensate liquid film in this system. A significant difference in their values is found for low-ethanol fractions of the ambient vapor whether or not the temperature dependence of the mass transfer coefficient is considered. The wavenumber of a pattern of the liquid film observed in the experiment has the same parameter dependence as that of the fastest growth wavenumber.

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“…This phenomenon, known as thermodiffusion or Soret effects, 23,24 may lead to a solutal flow contribution in a direction that could counteract the thermal Marangoni flow. 25 The dominant mechanism that governs the instability is then determined by the relative time scales of the two processes. Aside from these factors, it is well established that long range molecular forces, such as van der Waals attraction, lead to the rupture of ultrathin liquid films (≤100 nm) in finite time.…”

Section: Introductionmentioning

confidence: 99%

“…A host of long wavelength instability problems for binary liquid films including the interplay of Marangoni and Soret effects have been studied by Oron, Nepomnyashchy, and co-workers. [47][48][49][50][51][52][53][54][55] Two other notably important contributions which address these issues with the inclusion of gravity in the lubrication limit are the works by Bestehorn and Borcia 25 (linear stability analysis) and Borcia et al 56 (fully nonlinear simulations). Our present work differs from these in two different ways.…”

Section: Introductionmentioning

confidence: 99%

Thermodiffusion as a means to manipulate liquid film dynamics on chemically patterned surfaces

Kalpathy

Shreyes

2017

The Journal of Chemical Physics

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The model problem examined here is the stability of a thin liquid film consisting of two miscible components, resting on a chemically patterned solid substrate and heated from below. In addition to surface tension gradients, the temperature variations also induce gradients in the concentration of the film by virtue of thermodiffusion/Soret effects. We study the stability and dewetting behaviour due to the coupled interplay between thermal gradients, Soret effects, long-range van der Waals forces, and wettability gradient-driven flows. Linear stability analysis is first employed to predict growth rates and the critical Marangoni number for chemically homogeneous surfaces. Then, nonlinear simulations are performed to unravel the interfacial dynamics and possible locations of the film rupture on chemically patterned substrates. Results suggest that appropriate tuning of the Soret parameter and its direction, in conjunction with either heating or cooling, can help manipulate the location and time scales of the film rupture. The Soret effect can either potentially aid or oppose film instability depending on whether the thermal and solutal contributions to flow are cooperative or opposed to each other.

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Thin film lubrication dynamics of a binary mixture: Example of an oscillatory instability

Cited by 15 publications

References 35 publications

Faraday instability of a two-layer liquid film with a free upper surface

Faraday instability of a two-layer liquid film with a free upper surface

Stability of a condensing liquid film in a binary vapor mixture system

Thermodiffusion as a means to manipulate liquid film dynamics on chemically patterned surfaces

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