Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-23T08:04:57.877Z Has data issue: false hasContentIssue false

On the wetting dynamics in a Couette flow

Published online by Cambridge University Press:  08 May 2013

Peng Gao*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
*
Email address for correspondence: gaopeng@ustc.edu.cn

Abstract

The dynamics of moving contact lines in a two-phase Couette flow is investigated by using a matched asymptotic procedure. The walls are assumed to be partially wetting, and the microscopic contact angle is finite but sufficiently small so that the lubrication approach can be used. Explicit formulas are derived to characterize the shear-induced interface deformation and the critical capillary number for the onset of wetting transition. It is found that the apparent contact angle vanishes for liquid–air systems and remains finite for liquid–liquid systems when the wetting transition occurs.

Type
Rapids
Copyright
©2013 Cambridge University Press 

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

Blake, T. D. & Ruschak, K. J. 1979 Maximum speed of wetting. Nature 282, 489491.CrossRefGoogle Scholar
Chan, T. S., Snoeijer, J. H. & Eggers, J. 2012 Theory of the forced wetting transition. Phys. Fluids 24, 072104.CrossRefGoogle Scholar
Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J. & Knuth, D. E. 1996 On the Lambert W function. Adv. Comput. Math. 5, 329359.CrossRefGoogle Scholar
Cox, R. G. 1986 The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech. 168, 169194.CrossRefGoogle Scholar
Derjaguin, B. V. & Levi, S. M. 1964 Film Coating Theory. Focal.Google Scholar
Duffy, B. R. & Wilson, S. K. 1997 A third-order differential equation arising in thin-film flows and relevant to Tanner’s law. Appl. Math. Lett. 10, 6368.CrossRefGoogle Scholar
Dussan, E. B. & Davis, S. H. 1974 Motion of a fluid–fluid interface along a solid surface. J. Fluid Mech. 65, 7195.CrossRefGoogle Scholar
Eggers, J. 2004a Hydrodynamic theory of forced dewetting. Phys. Rev. Lett. 93, 094502.CrossRefGoogle ScholarPubMed
Eggers, J. 2004b Toward a description of contact line motion at higher capillary numbers. Phys. Fluids 16, 34913494.CrossRefGoogle Scholar
Eggers, J. 2005 Existence of receding and advancing contact lines. Phys. Fluids 17, 082106.CrossRefGoogle Scholar
de Gennes, P. G. 1986 Deposition of Langmuir–Blodgett layers. Colloid Polym. Sci. 264, 463465.CrossRefGoogle Scholar
Hocking, L. M. 1981 Sliding and spreading of thin two-dimensional drops. Q. J. Mech. Appl. Maths 34, 3755.CrossRefGoogle Scholar
Hocking, L. M. 1983 The spreading of a thin drop by gravity and capillarity. Q. J. Mech. Appl. Maths 36, 5569.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, 85101.CrossRefGoogle Scholar
Jacqmin, D. 2004 Onset of wetting failure in liquid–liquid systems. J. Fluid Mech. 517, 209228.CrossRefGoogle Scholar
Oron, A., Davis, S. H. & Bankoff, G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931980.CrossRefGoogle Scholar
Qian, T., Wang, X.-P. & Sheng, P. 2006 A variational approach to moving contact line hydrodynamics. J. Fluid Mech. 564, 333360.CrossRefGoogle Scholar
Ren, W. & E, W. 2007 Boundary conditions for the moving contact line problem. Phys. Fluids 19, 022101.CrossRefGoogle Scholar
Sbragaglia, M., Sugiyama, K. & Biferale, L. 2008 Wetting failure and contact line dynamics in a Couette flow. J. Fluid Mech. 614, 471493.CrossRefGoogle Scholar
Sedev, R. V. & Petrov, J. G. 1991 The critical condition for transition from steady wetting to film entrainment. Colloids Surf. 53, 147156.CrossRefGoogle Scholar
Snoeijer, J. H. & Andreotti, B. 2013 Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45, 269292.CrossRefGoogle Scholar
Snoeijer, J. H., Andreotti, B., Delon, G. & Fermigier, M. 2007 Relaxation of a dewetting contact line. Part 1. A full-scale hydrodynamic calculation. J. Fluid Mech. 579, 6383.CrossRefGoogle Scholar
Snoeijer, J. H., Delon, G., Fermigier, M. & Andreotti, B. 2006 Avoided critical behavior in dynamically forced wetting. Phys. Rev. Lett. 96, 174504.CrossRefGoogle ScholarPubMed
Thompson, P. A. & Robbins, M. O. 1989 Simulations of contact-line motion: slip and the dynamic contact angle. Phys. Rev. Lett. 63, 766769.CrossRefGoogle ScholarPubMed
Voinov, O. V. 1976 Hydrodynamics of wetting. Fluid Dyn. 11, 714721.CrossRefGoogle Scholar
Voinov, O. V. 2000 Wetting: inverse dynamic problem and equations for microscopic parameters. J. Colloid Interface Sci. 226, 515.CrossRefGoogle ScholarPubMed