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Sliding instability of draining fluid films

Published online by Cambridge University Press:  19 October 2018

Georg F. Dietze Open the ORCID record for Georg F. Dietze [Opens in a new window] ,
Jason R. Picardo Open the ORCID record for Jason R. Picardo [Opens in a new window]  and
R. Narayanan
Georg F. Dietze*
Affiliation:
Laboratoire FAST, Univ. Paris-Sud, CNRS, Université Paris-Saclay, F-91405, Orsay, France
Jason R. Picardo
Affiliation:
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore, 560089, India
R. Narayanan
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
*
†Email address for correspondence: dietze@fast.u-psud.fr
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Abstract

The aim of this paper is to show that the spontaneous sliding of drops forming from an interfacial instability on the surface of a wall-bounded fluid film is caused by a symmetry-breaking secondary instability. As an example, we consider a water film suspended from a ceiling that drains into drops due to the Rayleigh–Taylor instability. Loss of symmetry is observed after the film has attained a quasi-steady state, following the buckling of the thin residual film separating two drops, whereby two extremely thin secondary troughs are generated. Instability emanates from these secondary troughs, which are very sensitive to surface curvature perturbations because drainage there is dominated by capillary pressure gradients. We have performed two types of linear stability analysis. Firstly, applying the frozen-time approximation to the quasi-steady base state and assuming exponential temporal growth, we have identified a single, asymmetric, unstable eigenmode, constituting a concerted sliding motion of the large drops and secondary troughs. Secondly, applying transient stability analysis to the time-dependent base state, we have found that the latter is unstable at all times after the residual film has buckled, and that localized pulses at the secondary troughs are most effective in triggering the aforementioned sliding eigenmode. The onset of sliding is controlled by the level of ambient noise, but, in the range studied, always occurs in the quasi-steady regime of the base state. The sliding instability is also observed in a very thin gas film underneath a liquid layer, which we have checked for physical properties encountered underneath Leidenfrost drops. In contrast, adding Marangoni stresses to the problem substantially modifies the draining mechanism and can suppress the sliding instability.

JFM classification

Interfacial Flows (free surface): Capillary flows Instability: Instability Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 857 , 25 December 2018 , pp. 111 - 141
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Copyright
© 2018 Cambridge University Press 

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Dietze et al. supplementary movie 1

Evolution of the suspended water film toward a quasi-steady state (h0=1 mm, Bo=0.134). The movie shows the evolution from panel 2a to panel 2f in slow motion, allowing to observe the three stages detailed in panels 3c, 3d, and 3e. The ordinate has been rescaled logarithmically to better highlight the secondary troughs.

Download Dietze et al. supplementary movie 1(Video)
Video 622.9 KB

Dietze et al. supplementary movie 2

Loss of symmetry and sliding of the suspended water film (h0=1 mm, Bo=0.134). The movie shows the evolution between panels 2a and 2i, whereby the framerate has been increased with respect to movie 1 in order to focus on the loss of symmetry and sliding detailed in panel 3f and figure 4. The ordinate has been rescaled logarithmically to better highlight the secondary troughs.

Download Dietze et al. supplementary movie 2(Video)
Video 853.8 KB

Dietze et al. supplementary movie 3

Evolution of the suspended water film with additional Marangoni stresses (h0=1 mm, Bo=0.134, Ma=-0.2). The movie shows the buckling cascade of figure 11 in action. The ordinate has been rescaled logarithmically to better highlight the evolution of the troughs.

Download Dietze et al. supplementary movie 3(Video)
Video 2.6 MB
Supplementary material: File

Dietze et al. supplementary data

Supplementary data

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