Skip to main content Accessibility help

Sliding instability of draining fluid films

  • Georg F. Dietze (a1), Jason R. Picardo (a2) and R. Narayanan (a3)


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.


Corresponding author

Email address for correspondence:


Hide All
Alexeev, A. & Oron, A. 2007 Suppression of the Rayleigh–Taylor instability of thin liquid films by the Marangoni effect. Phys. Fluids 19 (8), 082101.
Balestra, G., Brun, P.-T. & Gallaire, F. 2016 Rayleigh–Taylor instability under curved substrates: an optimal transient growth analysis. Phys. Rev. Fluids 1, 083902.
Bonn, D. 2009 Wetting and spreading. Rev. Mod. Phys. 81 (2), 739805.
Boos, W. & Thess, A. 1999 Cascade of structures in long-wavelength marangoni instability. Phys. Fluids 11 (6), 14841494.
Boyd, J. P. 1989 Chebyshev and Fourier Spectral Methods. Springer.
Burton, J. C., Sharpe, A. L., van der Veen, R. C. A., Franco, A. & Nagel, S. R. 2012 Geometry of the vapor layer under a Leidenfrost drop. Phys. Rev. Lett. 109, 074301.
Chang, H. C., Demekhin, E. A. & Kalaidin, E. 1996 Simulation of noise-driven wave dynamics on a falling film. AIChE J. 42 (6), 15531568.
Dietze, G. F. & Ruyer-Quil, C. 2013 Wavy liquid films in interaction with a confined laminar gas flow. J. Fluid Mech. 722, 348393.
Dietze, G. F. & Ruyer-Quil, C. 2015 Films in narrow tubes. J. Fluid Mech. 762, 68109.
Duruk, S. & Oron, A. 2016 Nonlinear dynamics of a thin liquid film deposited on a laterally oscillating corrugated surface in the high-frequency limit. Phys. Fluids 28 (11), 112101.
Frumkin, V. & Oron, A. 2016 Liquid film flow along a substrate with an asymmetric topography sustained by the thermocapillary effect. Phys. Fluids 28 (8), 082107.
Glasner, K. 2007 The dynamics of pendant droplets on a one-dimensional surface. Phys. Fluids 19 (10), 102104.
Hammond, P. S. 1983 Nonlinear adjustment of a thin annular film of viscous fluid surrounding a thread of another within a circular cylindrical pipe. J. Fluid Mech. 137, 363384.
Israelachvili, J. 2011 Intermolecular and Surface Forces. Academic Press.
Landau, L. D. & Levich, B. 1942 Dragging of liquid by a moving plate. Acta Physicochim. USSR 17, 4254.
Linke, H., Alemán, B. J., Melling, L. D., Taormina, M. J., Francis, M. J., Dow-Hygelund, C. C., Narayanan, V., Taylor, R. P. & Stout, A. 2006 Self-propelled Leidenfrost droplets. Phys. Rev. Lett. 96, 154502.
Lister, J. R., Morrison, N. F. & Rallison, J. M. 2006a Sedimentation of a two-dimensional drop towards a rigid horizontal plate. J. Fluid Mech. 552, 345351.
Lister, J. R., Rallison, J. M., King, A. A., Cummings, L. J. & Jensen, O. E. 2006b Capillary drainage of an annular film: the dynamics of collars and lobes. J. Fluid Mech. 552, 311343.
Ma, X., Liétor-Santos, J.-J. & Burton, J. C. 2015 The many faces of a Leidenfrost drop. Phys. Fluids 27, 091109.
Ma, X., Liétor-Santos, J.-J. & Burton, J. C. 2017 Star-shaped oscillations of Leidenfrost drops. Phys. Rev. Fluids 2, 031602(R).
Oron, A. 2000 Nonlinear dynamics of three-dimensional long-wave Marangoni instability in thin liquid films. Phys. Fluids 12 (7), 16331645.
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228, 58385866.
Quéré, D. 2013 Leidenfrost dynamics. Annu. Rev. Fluid Mech. 45, 197215.
Ruyer-Quil, C. & Manneville, P. 2002 Further accuracy and convergence results on the modeling of flows down inclined planes by weighted-residual approximations. Phys. Fluids 14 (1), 170183.
Schmid, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129162.
Yiantsios, S. G. & Higgins, B. G. 1989 Rayleigh–Taylor instability in thin viscous films. Phys. Fluids 1, 14841501.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Type Description Title

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.

 Video (623 KB)
623 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.

 Video (854 KB)
854 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.

 Video (2.6 MB)
2.6 MB
Supplementary materials

Dietze et al. supplementary data
Supplementary data

 Unknown (12 KB)
12 KB


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed