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Contact-line instability of dewetting thin films. (English) Zbl 1077.76027

Summary: We investigate the linear stability of dewetting thin polymer films on hydrophobised substrates driven by van der Waals forces, using a lubrication model. We focus on the role of slippage in the emerging instability at the three-phase contact-line and compare our results to the corresponding no-slip case. Our analysis shows that generically, small perturbations of the receding front are amplified, but in the slippage case by orders of magnitude larger than in the no-slip case. Moreover, while the perturbations become symmetrical in the no-slip case, they are asymmetrical in the slippage case. We furthermore extend our lubrication model to include effects of nonlinear curvature.

MSC:

76E17 Interfacial stability and instability in hydrodynamic stability
76A20 Thin fluid films
76D08 Lubrication theory
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[1] Bertozzi, A. L.; Brenner, M. P., Linear stability and transient growth in driven contact-lines, Phys. Fluids, 9, 3, 530-539 (1997) · Zbl 1185.76627
[2] Bertozzi, A. L.; Münch, A.; Fanton, X.; Cazabat, A. M., contact-line stability and ‘undercompressive shocks’ in driven thin film flow, Phys. Rev. Lett., 81, 23, 5169-5172 (1998)
[3] Brenner, M. P.; Gueyffier, D., On the bursting of liquid films, Phys. Fluids, 11, 3, 737-739 (1999) · Zbl 1147.76338
[4] Brochard-Wyart, F.; de Gennes, P.-G.; Hervert, H.; Redon, C., Wetting and slippage of polymer melts on semi-ideal surfaces, Langmuir, 10, 1566-1572 (1994)
[5] Brochard-Wyart, F.; Redon, C., Dynamics of liquid rim instabilities, Langmuir, 8, 2324-2329 (1992)
[6] Brzoska, J. B.; Brochard-Wyart, F.; Rondelez, F., Exponential growth of fingering intabilities of spreading films under horizontal thermal gradients, Europhys. Lett., 19, 97-102 (1992)
[7] Butler, K. B.; Farrell, B. F., Optimal perturbations and streak spacing in wall bounded shear flow, PoF A, 5, 774 (1993)
[8] Cazabat, A. M.; Heslot, F.; Troian, S. M.; Carles, P., Finger instability of this spreading films driven by temperature gradients, Nature, 346, 6287, 824-826 (1990)
[9] Davis, J. M.; Troian, S., On a generalized approach to the linear stability of spatially nonuniform thin film flows, PoF, 15, 1344 (2003) · Zbl 1186.76130
[10] Garnier, N.; Grigoriev, R. O.; Schatz, M. F., Optical manipulation of microscale fluid flow, Phys. Rev. Lett., 91 (2003), (Art. No. 054501)
[11] Ghatak, A.; Khanna, R.; Sharma, A., Dynamics and morphology of holes in dewetting of thin films, J. Colloid Interface Sci., 212, 483-494 (1999)
[12] R. Grigoriev, Transient growth in driven constact lines. Physica D, this issue (2004).; R. Grigoriev, Transient growth in driven constact lines. Physica D, this issue (2004).
[13] Hoffmann, K.-H.; Wagner, B.; Münch, A., On the generation and spreading of finger instabilities in film coating processes, Lect. Notes Comp. Sci. Eng., 8, 245-254 (1999)
[14] Huppert, H., Flow and instability of a viscous current down a slope, Nature, 300, 427-429 (1982)
[15] Jacobs, K.; Seemann, R.; Schatz, G.; Herminghaus, S., Growth of holes in liquid films with partial slippage, Langmuir, 14, 4961-4963 (1998)
[16] Kataoka, D. E.; Troian, S. M., A theoretical study of instabilities at the advancing front of thermally driven coating films, J. Colloid Interface Sci., 192, 350-362 (1997)
[17] Konnur, R.; Kargupta, K.; Sharma, A., Instability and morphology of thin liquid films on chemically heterogeneous substrates, Phys. Rev. Lett., 84, 5, 931-934 (2000)
[18] López, P. G.; Bankoff, S. G.; Miksis, M. J., Non-isothermal spreading of a thin liquid film on an inclined plane, J. Fluid Mech., 11, 1-39 (1996)
[19] Masson, J.-L.; Olufokunbi, O.; Green, P. F., Flow instabilities in entangled polymer films, Macromolecules, 35, 6992-6996 (2002)
[20] Münch, A., Dewetting rates of thin liquid films, J. Phys.: Condensed Matter (2004)
[21] A. Münch, C. Neto, R. Seemann, K. Jacobs, Fingering instability in dewetting films induced by slippage, in preparation.; A. Münch, C. Neto, R. Seemann, K. Jacobs, Fingering instability in dewetting films induced by slippage, in preparation.
[22] Münch, A.; Wagner, B. A., Numerical and asymptotic results on the linear stability of a thin film spreading down a slope of small inclination, Eur. J. Appl. Math., 10, 297-318 (1999) · Zbl 0948.76022
[23] C. Neto, Private Communications.; C. Neto, Private Communications.
[24] C. Neto, K. Jacobs, Physica A, submitted for publication.; C. Neto, K. Jacobs, Physica A, submitted for publication.
[25] Redon, C.; Brochard-Wyart, F.; Rondelez, F., Dynamics of dewetting, Phys. Rev. Lett., 66, 6, 715-718 (1991)
[26] Redon, C.; Brzoska, J. B.; Brochard-Wyart, F., Dewetting and slippage of microscopic polymer films, Macromolecules, 27, 468-471 (1994)
[27] Reiter, G., Dewetting of thin polymer films, Phys. Rev. Lett., 68, 1, 75-78 (1992)
[28] Reiter, G.; Khanna, R., Kinetics of autophobic dewetting of polymer films, Langmuir, 16, 6351-6357 (2000)
[29] Reiter, G.; Sharma, A., Auto-optimization of dewetting rates by rim instabilities in slipping polymer films, Phys. Rev. Lett., 80, 16 (2001)
[30] Reiter, G.; Sharma, A.; Casoli, A.; David, M.-O.; Khanna, R.; Auroy, P., Thin film instability induced by long-range forces, Langmuir, 15, 2551-2558 (1999)
[31] Seemann, R.; Herminghaus, S.; Jacobs, K., Dewetting patterns and molecular forces: a reconciliation, Phys. Rev. Lett., 86, 24, 5534-5537 (2001)
[32] Seemann, R.; Herminghaus, S.; Jacobs, K., Gaining control of pattern formation of dewetting films, J. Phys.: Condensed Matter, 13, 4925-4938 (2001)
[33] Sharma, A.; Khanna, R., Pattern formation in unstabile thin liquid films, Phys. Rev. Lett., 81, 16, 3463-3466 (1998)
[34] Sharma, A.; Khanna, R., Pattern formation in unstable thin liquid films under influence of antagonistic short- and long-range forces, J. Chem. Phys., 110, 10, 4929-4936 (1999)
[35] Sharma, A.; Reiter, G., Instability of thin polymer films on coated substrates: rupture, dewetting and drop formation, J. Colloid Interface Sci., 178, 383-389 (1996)
[36] N. Silvi, E.D.V. On the rewetting of an inclined solid surface by a liquid. Phys. Fluids, 28 (1985) 5-7.; N. Silvi, E.D.V. On the rewetting of an inclined solid surface by a liquid. Phys. Fluids, 28 (1985) 5-7.
[37] Trefethen, L. N.; Trefethen, A. E.; Reddy, S. C.; Driscoll, T. A., Hydrodynamics stability without eigenvalues, Science, 261, 578 (1993) · Zbl 1226.76013
[38] Troian, S. M.; Herbolzheimer, E.; Safran, S. A.; Joanny, J., Fingering instabilities of driven spreading films, Europhys. Lett., 10, 1, 25-30 (1989)
[39] Warner, M. R.E.; Craster, R. V.; Matar, O. K., Fingering phenomena associated with insoluble surfactant spreading on thin liquid films, JFM, 4510, 169-200 (2004) · Zbl 1066.76032
[40] Xie, R.; Karim, A.; Douglas, J. F.; Han, C. C.; Weiss, R. A., Spinodal dewetting of thin polymer films, Phys. Rev. Lett., 81, 6, 1251-1254 (1998)
[41] Zhornitskaya, L.; Bertozzi, A. L., Positivity preserving numerical schemes for lubrication-type equations, SIAM J. Numer. Anal., 37, 2, 523-555 (2000) · Zbl 0961.76060
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