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

Published online by Cambridge University Press:  03 June 2015

A. L. Kupershtokh ,
E. V. Ermanyuk  and
N. V. Gavrilov
A. L. Kupershtokh*
Affiliation:
Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk 630090, Russia National Research Novosibirsk State University, Novosibirsk 630090, Russia
E. V. Ermanyuk
Affiliation:
Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk 630090, Russia Laboratoire de physique ENS de Lyon, France
N. V. Gavrilov
Affiliation:
Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk 630090, Russia
*
*Corresponding author. Email addresses: skn@hydro.nsc.ru (A. L. Kupershtokh), ermanyuk@gmail.com (E. V. Ermanyuk), gavrilov@hydro.nsc.ru (N. V. Gavrilov)
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Abstract

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.

Keywords

76M2876T3076M2565Z05Lattice Boltzmann equation methodphase transitionliquid filmsdynamics of multiphase mediaMarangoni effectcomputer simulations
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 5 , May 2015 , pp. 1301 - 1319
Copyright
Copyright © Global-Science Press 2015 

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References

[1]Scheludko, A., Thin liquid films, Adv. Colloid Interface Sci. 1 (1967) 391–464.Google Scholar
[2]Scheludko, A.Manev, E., Critical thickness of rupture of chlorbenzene and aniline films, Trans. Faraday Soc. 64 (1968) 1123–1134.Google Scholar
[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) 1262–1273.Google Scholar
[4]Craster, R.V.Matar, O.K., Dynamics and stability of thin liquid films, Rev. Mod. Phys. 81 (3) (2009) 1131–1198.Google Scholar
[5]Bonn, D.Eggers, J.Indekeu, J.Meunier, J.Rolley, E., Wetting and spreading, Rev. Mod. Phys. 81 (2) (2009) 739–805.Google Scholar
[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) 340–350.Google Scholar
[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) 130–138.Google Scholar
[8]Qian, Y.-H.Chen, S., Finite size effect in lattice-BGK models, International Journal of Modern Physics C 8 (4) (1997) 763–771.Google Scholar
[9]Zhang, R.Chen, H., Lattice Boltzmann method for simulations of liquid-vapor thermal flows, Phys. Rev. E. 67 (6) (2003) 066711.Google Scholar
[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) 965–974.Google Scholar
[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) 29–42.Google Scholar
[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) 303–311.Google Scholar
[13]Qian, Y.H.d’Humiéres, D., Lallemand, P., Lattice BGK models for Navier – Stokes equation, Europhys. Lett. 17 (6) (1992) 479–484.Google Scholar
[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) 511–525.Google Scholar
[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. 241–246.Google Scholar
[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) 75–96.Google Scholar
[17]Kupershtokh, A.L., Criterion of numerical instability of liquid state in LBE simulations, Computers and Mathematics with Applications 59 (7) (2010) 2236–2245.Google Scholar
[18]Koelman, J.M.V.A., A simple lattice Boltzmann scheme for Navier–Stokes fluid flow, Europhys. Lett. 15 (6) (1991) 603–607.Google Scholar
[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) 210–236.Google Scholar
[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) 3537–3548.Google Scholar
[21]Bird, J.C.de Ruiter, R., Courbin, L., Stone, H.A., Daughter bubble cascades produced by folding of ruptured thin films, Nature 465 (2010) 759–762.Google Scholar