- Rapid Communication
- Access by Xinjiang University
Nonlinear rupture of thin liquid films on solid surfaces
Phys. Rev. E 71, 040601(R) – Published 5 April, 2005
DOI: https://doi.org/10.1103/PhysRevE.71.040601
Abstract
In this letter we investigate the rupture instability of thin liquid films by means of a bifurcation analysis in the vicinity of the short-scale instability threshold. The rupture time estimate obtained in closed form as a function of the relevant dimensionless groups is in striking agreement with the results of the numerical simulations of the original nonlinear evolution equations. This suggests that the weakly nonlinear theory adequately captures the underlying physics of the instability. When antagonistic (attractive/repulsive) molecular forces are considered, nonlinear saturation of the instability becomes possible. We show that the stability boundaries are determined by the van der Waals potential alone.
Article Text
References (17)
- B. V. Deryagin, Colloid J. USSR 10, 25 (1955); A. Sheludko, Adv. Colloid Interface Sci. 1, 391 (1967).
- A. Vrij, Discuss. Faraday Soc. 42, 43 (1966); E. Ruckenstein and R. K. Jain, J. Chem. Soc., Faraday Trans. 2 42, 23 (1974).
- J. T. G. Overbeek, J. Chem. Phys. 64, 1178 (1960).
- M. B. Williams and S. H. Davis, J. Colloid Interface Sci. 90, 220 (1982).
- A. Oron, S. H. Davis, and S. G. Bankoff, Rev. Mod. Phys. 69, 931 (1997).
- J. P. Burelbach, S. G. Bankoff, and S. H. Davis, J. Fluid Mech. 195, 463 (1988); R. V. Craster and O. K. Matar, ibid. 425, 235 (2000).
- A. De Wit, D. Gallez, and C. I. Christov, Phys. Fluids 6, 3256 (1994); O. E. Jensen and J. B. Grotberg, J. Fluid Mech. 240, 259 (1992).
- T. Erneux and S. H. Davis, Phys. Fluids A 5, 1117 (1993).
- B. Y. Rubinstein and A. M. Leshansky, Langmuir 16, 2049 (2000); B. Y. Rubinstein and S. G. Bankoff, ibid. 17, 1306 (2001).
- Y. L. Zhang, R. V. Craster, and O. K. Matar, J. Colloid Interface Sci. 264, 160 (2003).
- R. Konnur, K. Kargupta, and A. Sharma, Phys. Rev. Lett. 84, 931 (2000); A. Sharma, Eur. Phys. J. E 12, 397 (2003).
- K. Kargupta and A. Sharma, Phys. Rev. Lett. 86, 4536 (2001).
- G. Becker, G. Grün, R. Seemann, H. Mantz, K. Jacobs, K. R. Merke, and R. Blossey, Nat. Mater. 2, 59 (2003).
- R. Seemann, S. Herminghaus, and K. Jacobs, Phys. Rev. Lett. 86, 5534 (2001).
- B. Y. Rubinstein and L. M. Pismen, Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 983 (1999).
- Reprinted from Y. L. Zhang, R. V. Craster, and O. K. Matar, J. Colloid Interface Sci. 264, 167 (2003), with permission from Elsevier.
The Galerkin method can be applied for derivation of the amplitude equation for the “most dangerous” linear mode. The resulting amplitude equation is the same as Eq. (3) with given by the linear stability and that differs from the near-critical expression Eq. (4). The preliminary analysis shows that in case with no surfactant, the nonlinear rupture time estimate is in excellent agreement with results of numerical simulations [10] for the same value of the initial amplitude . The theory of the nonlinear rupture far from the instability threshold is a subject of a separate paper.