Side wall effects on the instability of thin gravity-driven films—From long-wave to short-wave instability

Pollak, Thilo; Haas, André; Aksel, Nuri

doi:10.1063/1.3634042

Cited by 32 publications

(16 citation statements)

References 29 publications

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“…Conversely, when the falling film is significantly confined by sidewalls, as may be the case in experimental realizations, the lateral boundary conditions already impose a three-dimensional primary flow. Depending on the sidewall separation distance, this can cause any (quasi-)two-dimensional wave dynamics to be practically bypassed (Vlachogiannis et al 2010;Georgantaki et al 2011;Pollak, Haas & Aksel 2011).…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional flow structures in laminar falling liquid films

et al. 2014

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Full numerical simulations of the Navier-Stokes equations for four cases of vertically falling liquid films with three-dimensional surface waves have been performed. Flow conditions are based on several previous experimental studies where the streamwise and spanwise wavelengths were imposed, which we exploit by simulating periodic wave segments. The considered flows are laminar but approach conditions at which intermittent wave-induced turbulence has been observed elsewhere. Working liquids range from water to silicone oil and cover a large interval of the Kapitza number (Ka = 18-3923), which relates capillary to viscous forces. Simulations were performed on a supercomputer, using a finite-volume code and the volume of fluid and continuum surface force methods to account for the multiphase nature of the flow. Our results show that surface waves, consisting of large horseshoe-shaped wave humps concentrating most of the liquid and preceded by capillary ripples on a thin residual film, segregate the flow field into two regions: an inertia-dominated one in the large humps, where the local Reynolds number is up to five times larger than its mean value, and a visco-capillary region, where capillary and/or viscous forces dominate. In the inertial region, an intricate structure of different-scale vortices arises, which is more complicated than film thickness variations there suggest. Conversely, the flow in the visco-capillary region of large-Ka fluids is entirely governed by the local free-surface curvature through the action of capillary forces, which impose the pressure distribution in the liquid film. This results in flow separation zones underneath the capillary troughs and a spanwise cellular flow pattern in the region of capillary wave interference. In some cases, capillary waves bridge the large horseshoe humps in the spanwise direction, coupling the two aforementioned regions and leading the flow to oscillate between three-and two-dimensional wave patterns. This persists over long times, as we show by simulations with the low-dimensional model of Scheid et al. (J. Fluid Mech., vol. 562, 2006, pp. 183-222) after satisfactory comparison with our direct simulations at short times. The governing mechanism is connected to the bridging capillary waves, which drain liquid from the horseshoe humps, decreasing their amplitude and wave speed and causing them to retract in the streamwise direction. Overall, it is observed that spanwise flow structures (not accounted for in two-dimensional investigations) are particularly complex due to the absence of gravity in this direction.

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Section: Introductionmentioning

confidence: 99%

Three-dimensional flow structures in laminar falling liquid films

et al. 2014

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“…It is notable that an unequivocal experimental confirmation of the linear prediction was also delayed significantly (Liu, Paul & Gollub 1993), and that an unexpected strong effect of the channel width was reported very recently by Georgantaki et al (2011) and Pollak, Haas & Aksel (2011).…”

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confidence: 97%

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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“…17,30,43,52 The respective setup is illustrated in Figure 6. A paddle was mounted close to the inflow of the channel upstream of the topography.…”

Section: B Primary Instabilitymentioning

confidence: 99%

“…A Gaussian filter was applied to each image and the threshold was set to 80% of the image's brightest pixel. The centroid of the area of the oscillating sharp-edged spot was determined and a Fourier transformation algorithm established by Pollak et al 30 was applied. In case of an amplification of the respective disturbance in streamwise direction, the flow was denoted as convectively unstable, in the opposite case as stable.…”

Section: B Primary Instabilitymentioning

confidence: 99%

“…The effects of side walls on gravity-driven films and their linear stability were studied comprehensively in recent publications. [24][25][26][27][28][29][30] The major challenge in dealing with flows over topography is that the steady-state flow field cannot be calculated analytically from the Navier-Stokes-equations. Recent experimental and numerical findings identified an unexpectedly rich variety of complex flow phenomena.…”

Section: Introductionmentioning

confidence: 99%

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Does the topography’s specific shape matter in general for the stability of film flows?

2015

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In our experimental study on the linear stability of gravity-driven films flowing over inclined topographies, we consider a fundamental question: does the topography's specific shape matter in general for the stability of film flows? In order to understand this complex problem, we used five topographies of different shapes. For each topography, we characterized the basic flow by measuring the flow field and the free surface contour. Experiments on the flow's linear stability followed. We obtained astonishing results on how the topography's shape can manipulate both the basic flow and the linear stability of gravity-driven films. C 2015 AIP Publishing LLC.

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Side wall effects on the instability of thin gravity-driven films—From long-wave to short-wave instability

Cited by 32 publications

References 29 publications

Three-dimensional flow structures in laminar falling liquid films

Three-dimensional flow structures in laminar falling liquid films

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

Does the topography’s specific shape matter in general for the stability of film flows?

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