Hostname: page-component-84b7d79bbc-lrf7s Total loading time: 0 Render date: 2024-08-05T07:10:08.310Z Has data issue: false hasContentIssue false
  • English
  • Français

Moving contact line on chemically patterned surfaces

Published online by Cambridge University Press:  23 May 2008

XIAO-PING WANG ,
TIEZHENG QIAN  and
PING SHENG
XIAO-PING WANG
Affiliation:
Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
TIEZHENG QIAN
Affiliation:
Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
PING SHENG
Affiliation:
Department of Physics and Institute of Nano Science and Technology, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
Get access Rights & Permissions [Opens in a new window]

Abstract

We simulate the moving contact line in two-dimensional chemically patterned channels using a diffuse-interface model with the generalized Navier boundary condition. The motion of the fluid–fluid interface in confined immiscible two-phase flows is modulated by the chemical pattern on the top and bottom surfaces, leading to a stick–slip behaviour of the contact line. The extra dissipation induced by this oscillatory contact-line motion is significant and increases rapidly with the wettability contrast of the pattern. A critical value of the wettability contrast is identified above which the effect of diffusion becomes important, leading to the interesting behaviour of fluid–fluid interface breaking, with the transport of the non-wetting fluid being assisted and mediated by rapid diffusion through the wetting fluid. Near the critical value, the time-averaged extra dissipation scales as U, the displacement velocity. By decreasing the period of the pattern, we show the solid surface to be characterized by an effective contact angle whose value depends on the material characteristics and composition of the patterned surfaces.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 605 , 25 June 2008 , pp. 59 - 78
Copyright
Copyright © Cambridge University Press 2008

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.)

References

REFERENCES

Barrat, J.-L. & Bocquet, L. 1999 Large slip effect at a nonwetting fluid–solid interface. Phys. Rev. Lett. 82, 4671.CrossRefGoogle Scholar
Blake, T. D. & Haynes, J. M. 1969 Kinetics of liquid/liquid displacement. J. Colloid Interface Sci. 30, 421–423.CrossRefGoogle Scholar
Briant, A. J. & Yeomans, J. M. 2004 Lattice Boltzmann simulations of contact line motion. II. Binary fluids. Phys. Rev. E 69, 031603.Google ScholarPubMed
Cahn, J. W. & Hilliard, J. E. 1958 Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28, 258–267.CrossRefGoogle Scholar
Chella, R. & Vinals, J. 1996 Mixing of a two-phase fluid by cavity flow. Phys. Rev. E 53, 3832–3840.Google ScholarPubMed
Chen, H. Y., Jasnow, D. & Vinals, J. 2000 Interface and contact line motion in a two phase fluid under shear flow. Phys. Rev. Lett. 85, 1686–1689.CrossRefGoogle Scholar
Cubaud, T. & Fermigier, M. 2004 Advancing contact lines on chemically patterned surfaces. J. Colloid Interface Sci. 269, 171–177.CrossRefGoogle ScholarPubMed
Darhuber, A. A., Troian, S. M., Miller, S. M. & Wagner, S. 2000 Morphology of liquid microstructures on chemically patterned surfaces. J. Appl. Phys. 87, 7768.CrossRefGoogle Scholar
Dussan, V., E. B., & Davis, S. H. 1974 On the motion of a fluid–fluid interface along a solid surface. J. Fluid Mech. 65, 71–95.CrossRefGoogle Scholar
Dussan, V., E. B., 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines. Annu. Rev. Fluid Mech. 11, 371.CrossRefGoogle Scholar
de Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827.CrossRefGoogle Scholar
Gau, H., Herminghaus, S., Lenz, P. & Lipowsky, R. 1999 Liquid morphologies on structured surfaces. Science 283, 46–49.CrossRefGoogle ScholarPubMed
Hocking, L. M. 1977 A moving fluid interface. Part 2. The removal of the force singularity by a slip flow. J. Fluid Mech. 79, 209–229.CrossRefGoogle Scholar
Huh, C. & Mason, S. G. 1977 The steady movement of a liquid meniscus in a capillary tube. J. Fluid Mech. 81, 401–419.CrossRefGoogle Scholar
Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35, 85–101.CrossRefGoogle Scholar
Jacqmin, D. 2000 Contact-line dynamics of a diffuse fluid interface. J. Fluid Mech. 402, 57–88.CrossRefGoogle Scholar
Kusumaatmaja, H., Lopolds, J., Dupuis, A. & Yeomans, J. M. 2006 Drop dynamics on chemically patterned surfaces. Europhys. Lett. 73, 740–746.CrossRefGoogle Scholar
Kuksenok, O., Jasonw, D., Yeomans, J., & Balazs, A. 2003 Periodic droplet formation in chemically patterned microchannels. Phys. Rev. Lett. 91, 108303.CrossRefGoogle ScholarPubMed
Landau, L. D. & Lifshitz, E. M. 1997 Statistical Physics (Part 1). Oxford University Press.Google Scholar
Luo, X, Wang, X. P., Qian, T. Z. & Sheng, P. 2006 Moving contact line over undulating surfaces. Solid State Commun. 139 623–629.CrossRefGoogle Scholar
Onsager, L. 1931 a Reciprocal relations in irreversible processes. I. Phys. Rev. 37, 405–426.CrossRefGoogle Scholar
Onsager, L. 1931 b Reciprocal relations in irreversible processes. II.. Phys. Rev. 38, 2265–2279.CrossRefGoogle Scholar
Onsager, L. & Machlup, S. 1953 Fluctuations and irreversible processes. Phys. Rev. 91, 1505–1512.CrossRefGoogle Scholar
Pismen, L. M. & Pomeau, Y. 2000 Disjoining potential and spreading of thin liquid layers in the diffuse-interface model coupled to hydrodynamics. Phys. Rev. E 62, 2480–2492.Google ScholarPubMed
Qian, T. Z., Wang, X. P. & Sheng, P. 2003 Molecular scale contact line hydrodynamics of immiscible flows. Phys. Rev. E 68, 016306.Google ScholarPubMed
Qian, T. Z., Wang, X. P. & Sheng, P. 2004 Power-law slip profile of the moving contact line in two-phase immiscible flows. Phys. Rev. Lett. 93, 094501.CrossRefGoogle ScholarPubMed
Qian, T. Z., Wang, X. P. & Sheng, P. 2006 A variational approach to the moving contact line hydrodynamics, J. Fluid Mech. 564, 333–360.CrossRefGoogle Scholar
Seppecher, P. 1996 Moving contact lines in the Cahn-Hilliard theory. Intl J. Engng Sci. 34, 977–992.CrossRefGoogle Scholar
Zhou, M. Y. & Sheng, P. 1990 Dynamics of immiscible-fluid displacement in a capillary tube. Phys. Rev. Lett. 64, 882–885.CrossRefGoogle Scholar