Hostname: page-component-7dd5485656-k8lnt Total loading time: 0 Render date: 2025-10-30T14:41:26.865Z Has data issue: false hasContentIssue false
  • English
  • Français

Competitive displacement of thin liquid films on chemically patterned substrates

Published online by Cambridge University Press:  04 January 2007

RICHARD D. LENZ  and
SATISH KUMAR
RICHARD D. LENZ
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, 151 Amundson Hall, 421 Washington Avenue SE, Minneapolis, MN 55455, USA
SATISH KUMAR
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, 151 Amundson Hall, 421 Washington Avenue SE, Minneapolis, MN 55455, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The behaviour of the interface between stratified thin liquid films bounded by parallel solid surfaces and subject to van der Waals forces which drive dewetting is studied in this work. Chemically homogeneous surfaces are considered first; this is followed by an investigation of chemically heterogeneous surfaces. The lubrication approximation is applied to obtain a single nonlinear evolution equation which describes the interfacial behaviour, and both the linear stability and nonlinear development of the interface are examined. The sensitivity of the interfacial rupture time to problem parameters such as the viscosity ratio, initial interfacial height, interfacial tension, and magnitude of the van der Waals forces is characterized in detail for the homogeneous case. This serves as a basis for a study of the heterogeneous case, where the strong dependence of the rupture time on the length scale of the heterogeneity is found to be relatively independent of changes in the remaining problem parameters. The mechanisms underlying the rupture-time behaviour are also explored in detail. The results suggest a route by which one liquid can become emulsified in the other, and may be beneficial to industrial processes such as lithographic printing which are based on wettability phenomena.

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 571 , 25 January 2007 , pp. 33 - 57
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Benney, D. J. 1966 Long waves on liquid films. J. Math. Phys. 45, 150–155.CrossRefGoogle Scholar
Bischof, J., Scherer, D., Herminghaus, S. & Leiderer, P. 1996 Dewetting modes of thin metallic films: Nucleation of holes and spinodal dewetting. Phys. Rev. Lett. 77, 1536–1539.CrossRefGoogle ScholarPubMed
Burelbach, J. P., Bankoff, S. G. & Davis, S. H. 1988 Nonlinear stability of evaporating/condensing liquid films. J. Fluid Mech. 195, 463–494.CrossRefGoogle Scholar
Danov, K. D., Paunov, V. N., Alleborn, N., Raszillier, H. & Durst, F. 1998a Stability of evaporating two-layered liquid film in the presence of surfactant–I. The equations of lubrication approximation. Chem. Engng Sci. 53, 2809–2822.CrossRefGoogle Scholar
Danov, K. D., Paunov, V. N., Stoyanov, S. D., Alleborn, N., Raszillier, H. & Durst, F. 1998b Stability of evaporating two-layered liquid film in the presence of surfactant–II. Linear analysis. Chem. Engng Sci. 53, 2823–2837.CrossRefGoogle Scholar
Decré, M. M. J. & Baret, J.-C. 2003 Gravity-driven flows of viscous liquids over two-dimensional topographies. J. Fluid Mech. 487, 147–166.CrossRefGoogle Scholar
Fisher, L. S. & Golovin, A. A. 2005 Nonlinear stability analysis of a two-layer thin liquid film: Dewetting and autophobic behaviour. J. Colloid Interface Sci. 291, 515–528.CrossRefGoogle Scholar
Hamaker, H. C. 1937 The London–van der Waals attraction between spherical particles. Physica 4, 1058–1072.CrossRefGoogle Scholar
Harrey, P. M., Evans, P. S. A., Ramsey, B. J. & Harrison, D. 1999 A novel manufacturing process for capacitors using offset lithography. In First Intl Symp. on Environmentally Conscious Design and Inverse Manufacturing, pp. 842–846. Tokyo, Japan.CrossRefGoogle Scholar
Jensen, O. E. & Grotberg, J. B. 1992 Insoluble surfactant spreading on a thin viscous film: shock evolution and film rupture. J. Fluid Mech. 240, 259–288.CrossRefGoogle Scholar
Jensen, O. E. & Grotberg, J. B. 1993 The spreading of heat or soluble surfactant along a thin liquid film. Phys. Fluids A 5, 58–68.CrossRefGoogle Scholar
Joo, S. W. & Hsieh, K.-C. 2000 Interfacial instabilities in thin stratified viscous fluids under microgravity. Fluid Dyn. Res. 26, 203–217.CrossRefGoogle Scholar
Kalliadasis, S., Bielarz, C. & Homsy, G. M. 2000 Steady free-surface thin film flows over topography. Phys. Fluids 12, 1889–1898.CrossRefGoogle Scholar
Karapanagiotis, I. & Gerberich, W. W. 2005 Polymer film rupturing in comparison with leveling and dewetting. Surf. Sci. 594, 192–202.CrossRefGoogle Scholar
Kargupta, K., Konnur, R. & Sharma, A. 2000 Instability and pattern formation in thin liquid films on chemically heterogeneous substrates. Langmuir 16, 10243–10253.CrossRefGoogle Scholar
Kargupta, K. & Sharma, A. 2002 Morphological self-organization by dewetting in thin films on chemically patterned substrates. J. Chem. Phys. 116, 3042–3051.CrossRefGoogle Scholar
Kheshgi, H. S. & Scriven, L. E. 1991 Dewetting: Nucleation and growth of dry regions. Chem. Engng Sci. 46, 519–526.CrossRefGoogle Scholar
Konnur, R., Kargupta, K. & Sharma, A. 2000 Instability and morphology of thin liquid films on chemically heterogeneous substrates. Phys. Rev. Lett. 84, 931–934.CrossRefGoogle ScholarPubMed
Kumar, S. & Matar, O. K. 2004 Dewetting of thin liquid films near soft elastomeric layers. J. Colloid Interface Sci. 273, 581–588.CrossRefGoogle ScholarPubMed
Leyland, N. S., Evans, J. R. G. & Harrison, D. J. 2002 Lithographic printing of force-sensitive resistors. J. Mater. Sci., Mater. Electron. 13, 387–390.CrossRefGoogle Scholar
MacPhee, J. 1998 Fundamentals of Lithographic Printing. GATFPress.Google Scholar
Matar, O. K. 2002 Nonlinear evolution of thin free viscous films in the presence of soluble surfactant. Phys. Fluids 14, 4216–4234.CrossRefGoogle Scholar
Matar, O. K., Gkanis, V. & Kumar, S. 2005 Nonlinear evolution of thin liquid films dewetting near soft elastomeric layers. J. Colloid Interface Sci. 286, 319–332.CrossRefGoogle ScholarPubMed
Matar, O. K. & Kumar, S. 2004 Rupture of a surfactant-covered thin liquid film on a flexible wall. SIAM J. Appl. Maths 64, 2144–2166.CrossRefGoogle Scholar
Mazouchi, A. & Homsy, G. M. 2001 Free surface Stokes flow over topography. Phys. Fluids 13, 2751–2761.CrossRefGoogle Scholar
Merkt, D., Pototsky, A., Bestehorn, M. & Thiele, U. 2005 Long-wave theory of bounded two-layer films with a free liquid-liquid interface: Short- and long-time evolution. Phys. Fluids 17, 64104–1–20.CrossRefGoogle Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931–980.CrossRefGoogle Scholar
Paunov, V. N., Danov, K. D., Alleborn, N., Raszillier, H. & Durst, F. 1998 Stability of evaporating two-layered liquid film in the presence of surfactant–III. Non-linear stability analysis. Chem. Engng Sci. 53, 2839–2857.CrossRefGoogle Scholar
Pototsky, A., Bestehorn, M., Merkt, D. & Thiele, U. 2004 Alternative pathways of dewetting for a thin liquid two-layer film. Phys. Rev. E 70, 25201–1–4.CrossRefGoogle ScholarPubMed
Pritchard, W. G., Scott, L. R. & Tavener, S. J. 1992 Numerical and asymptotic methods for certain viscous free-surface flows. Phil. Trans. R. Soc. Lond A 340, 1–45.Google Scholar
Ruckenstein, E. & Jain, R. K. 1974 Spontaneous rupture of thin liquid films. J. Chem. Soc. Faraday Trans. II 70, 132–147.CrossRefGoogle Scholar
Seemann, R., Herminghaus, S. & Jacobs, K. 2001 Gaining control of pattern formation of dewetting liquid films. J. Phys.: Condens. Matter 13, 4925–4938.Google Scholar
Sharma, A. & Jameel, A. T. 1993 Nonlinear stability, rupture, and morphological phase separation of thin fluid films on apolar and polar substrates. J. Colloid Interface Sci. 161, 190–208.CrossRefGoogle Scholar
Sharma, A. & Ruckenstein, E. 1985 Mechanism of tear film rupture and formation of dry spots on cornea. J. Colloid Interface Sci. 106, 12–27.CrossRefGoogle Scholar
Sharma, A. & Ruckenstein, E. 1986a An analytical nonlinear theory of thin film rupture and its application to wetting films. J. Colloid Interface Sci. 113, 456–479.CrossRefGoogle Scholar
Sharma, A. & Ruckenstein, E. 1986b The role of lipid abnormalities, aqueous and mucus deficiencies in the tear film breakup, and implications for tear substitutes and contact lens tolerance. J. Colloid Interface Sci. 111, 8–34.CrossRefGoogle Scholar
Sheludko, A. 1967 Thin liquid films. Adv. Colloid Interface Sci. 1, 391–464.CrossRefGoogle Scholar
Squires, T. M. & Quake, S. R. 2005 Microfluidics: Fluid physics at the nanoliter scale. Rev. Mod. Phys. 77, 977–1026.CrossRefGoogle Scholar
Stange, T. G., Evans, D. F. & Hendrickson, W. A. 1997 Nucleation and growth of defects leading to dewetting of thin polymer films. Langmuir 13, 4459–4465.CrossRefGoogle Scholar
Stillwagon, L. E. & Larson, R. G. 1988 Fundamentals of topographic substrate leveling. J. Appl. Phys. 63, 5251–5258.CrossRefGoogle Scholar
Stillwagon, L. E. & Larson, R. G. 1990 Leveling of thin films over uneven substrates during spin coating. Phys. Fluids A 2, 1937–1944.CrossRefGoogle Scholar
Vrij, A. 1966 Possible mechanism for the spontaneous rupture of thin, free liquid films. Discuss. Faraday Soc. 42, 23–33.CrossRefGoogle Scholar
Williams, M. B. & Davis, S. H. 1982 Nonlinear theory of film rupture. J. Colloid Interface Sci. 90, 220–228.CrossRefGoogle Scholar
de Wit, A., Gallez, D. & Christov, C. I. 1994 Nonlinear evolution equations for thin liquid films with insoluble surfactants. Phys. Fluids 6, 3256–3266.CrossRefGoogle Scholar
Witelski, T. P. & Bernoff, A. J. 1999 Stability of self-similar solutions for van der Waals driven thin film rupture. Phys. Fluids 11, 2443–2445.CrossRefGoogle Scholar
Yiantsios, S. G. & Higgins, B. G. 1991 Rupture of thin films: Nonlinear stability analysis. J. Colloid Interface Sci. 147, 341–350.CrossRefGoogle Scholar
Zhang, W. W. & Lister, J. R. 1999 Similarity solutions for van der Waals rupture of a thin film on a solid substrate. Phys. Fluids 11, 2454–2462.CrossRefGoogle Scholar
Zhang, Y. L., Matar, O. K. & Craster, R. V. 2003 Analysis of tear film rupture: Effect of non-Newtonian rheology. J. Colloid Interface Sci. 262, 130–148.CrossRefGoogle ScholarPubMed
Zope, M., Kargupta, K. & Sharma, A. 2001 Self-organized structures in thin liquid films on chemically heterogeneous substrates: Effect of antagonistic short and long range interactions. J. Chem. Phys. 114, 7211–7221.CrossRefGoogle Scholar