Skip to main content Accessibility help

The Rupture of Thin Liquid Films Placed on Solid and Liquid Substrates in Gravity Body Forces

  • A. L. Kupershtokh (a1) (a2), E. V. Ermanyuk (a1) (a3) and N. V. Gavrilov (a1)


This paper presents a numerical and experimental study on hydrodynamic behavior of thin liquid films in rectangular domains. Three-dimensional computer simulations were performed using the lattice Boltzmann equation method (LBM). The liquid films laying on solid and liquid substrates are considered. The rupture of liquid films in computations is initiated via the thermocapillary (Marangoni) effect by applying an initial spatially localized temperature perturbation. The rupture scenario is found to depend on the shape of the temperature distribution and on the wettability of the solid substrate. For a wettable solid substrate, complete rupture does not occur: a residual thin liquid film remains at the substrate in the region of pseudo-rupture. For a non-wettable solid substrate, a sharp-peaked axisymmetric temperature distribution induces the rupture at the center of symmetry where the temperature is maximal. Axisymmetric temperature distribution with a flat-peaked temperature profile initiates rupture of the liquid film along a circle at some distance from the center of symmetry. The outer boundary of the rupture expands, while the inner liquid disk transforms into a toroidal figure and ultimately into an oscillating droplet.

We also apply the LBM to simulations of an evolution of one or two holes in liquid films for two-layer systems of immiscible fluids in a rectangular cell. The computed patterns are successfully compared against the results of experimental visualizations. Both the experiments and the simulations demonstrate that the initially circular holes evolved in the rectangular cell undergoing drastic changes of their shape under the effects of the surface tension and gravity. In the case of two interacting holes, the disruption of the liquid bridge separating two holes is experimentally observed and numerically simulated.


Corresponding author

*Corresponding author. Email addresses: (A. L. Kupershtokh), (E. V. Ermanyuk), (N. V. Gavrilov)


Hide All
[1]Scheludko, A., Thin liquid films, Adv. Colloid Interface Sci. 1 (1967) 391464.
[2]Scheludko, A.Manev, E., Critical thickness of rupture of chlorbenzene and aniline films, Trans. Faraday Soc. 64 (1968) 11231134.
[3]Ivanov, I.B.Radoev, B.Manev, E.Scheludko, A., The theory of the critical thickness of rupture of thin liquid films, Trans. Faraday Soc. 66 (1970) 12621273.
[4]Craster, R.V.Matar, O.K., Dynamics and stability of thin liquid films, Rev. Mod. Phys. 81 (3) (2009) 11311198.
[5]Bonn, D.Eggers, J.Indekeu, J.Meunier, J.Rolley, E., Wetting and spreading, Rev. Mod. Phys. 81 (2) (2009) 739805.
[6]Bratukhin, Yu.K.Zuev, A.L.Kostarev, K.G.Shmyrov, A.V., Stability of a steady-state discontinuity of a fluid layer on the surface of an immiscible fluid, Fluid Dynamics 44 (3) (2009) 340350.
[7]Kupershtokh, A.L., Three-dimensional simulations of two-phase liquid-vapor systems on GPU using the lattice Boltzmann method, Numerical Methods and Programming: Section 1. Numerical methods and applications 13 (2012) 130138.
[8]Qian, Y.-H.Chen, S., Finite size effect in lattice-BGK models, International Journal of Modern Physics C 8 (4) (1997) 763771.
[9]Zhang, R.Chen, H., Lattice Boltzmann method for simulations of liquid-vapor thermal flows, Phys. Rev. E. 67 (6) (2003) 066711.
[10]Kupershtokh, A.L.Medvedev, D.A.Karpov, D.I., On equations of state in a lattice Boltzmann method, Computers and Mathematics with Applications 58 (5) (2009) 965974.
[11]Kupershtokh, A.L., Simulation of flows with liquid-vapor interfaces by the lattice Boltzmann method, Vestnik NGU (Quarterly Journal of Novosibirsk State Univ.), Series: Math., Mech. and Informatics 5 (3) (2005) 2942.
[12]Kupershtokh, A.L.Karpov, D.I.Medvedev, D.A.Stamatelatos, C.Charalambakos, V.P.Pyrgioti, E.C.Agoris, D.P., Stochastic models of partial discharge activity in solid and liquid dielectrics, IET Science Measurement and Technology 1 (6) (2007) 303311.
[13]Qian, Y.H.d’Humiéres, D., Lallemand, P., Lattice BGK models for Navier – Stokes equation, Europhys. Lett. 17 (6) (1992) 479484.
[14]Bhatnagar, P.L.Gross, E.P.Krook, M.K., A model for collision process in gases. I. Small amplitude process in charged and neutral one-component system, Phys. Rev. 94 (3) (1954) 511525.
[15]Kupershtokh, A.L., New method of incorporating a body force term into the lattice Boltzmann equation, Proc. of the 5th International EHD Workshop, Poitiers, France, 2004, pp. 241246.
[16]Kupershtokh, A.L., Incorporating a body force term into the lattice Boltzmann equation, Vestnik NGU (Quarterly Journal of Novosibirsk State Univ.), Series: Math., Mech. and Informatics 4 (2) (2004) 7596.
[17]Kupershtokh, A.L., Criterion of numerical instability of liquid state in LBE simulations, Computers and Mathematics with Applications 59 (7) (2010) 22362245.
[18]Koelman, J.M.V.A., A simple lattice Boltzmann scheme for Navier–Stokes fluid flow, Europhys. Lett. 15 (6) (1991) 603607.
[19]Chen, L.Kang, Q.Mu, Y.He, Y.-L.Tao, W.-Q., A critical review of the pseudopotential multiphase lattice Boltzmann model: Methods and applications, Int. J. Heat, Mass Transfer 76 (2014) 210236.
[20]Kupershtokh, A.L., A lattice Boltzmann equation method for real fluids with the equation of state known in tabular form only in regions of liquid and vapor phases, Computers and Mathematics with Applications 61 (12) (2011) 35373548.
[21]Bird, Ruiter, R., Courbin, L., Stone, H.A., Daughter bubble cascades produced by folding of ruptured thin films, Nature 465 (2010) 759762.


The Rupture of Thin Liquid Films Placed on Solid and Liquid Substrates in Gravity Body Forces

  • A. L. Kupershtokh (a1) (a2), E. V. Ermanyuk (a1) (a3) and N. V. Gavrilov (a1)


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