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On the wetting dynamics in a Couette flow

  • Peng Gao (a1) and Xi-Yun Lu (a1)

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.

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Email address for correspondence: gaopeng@ustc.edu.cn

References

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Blake, T. D. & Ruschak, K. J. 1979 Maximum speed of wetting. Nature 282, 489491.
Chan, T. S., Snoeijer, J. H. & Eggers, J. 2012 Theory of the forced wetting transition. Phys. Fluids 24, 072104.
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.
Cox, R. G. 1986 The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech. 168, 169194.
Derjaguin, B. V. & Levi, S. M. 1964 Film Coating Theory. Focal.
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.
Dussan, E. B. & Davis, S. H. 1974 Motion of a fluid–fluid interface along a solid surface. J. Fluid Mech. 65, 7195.
Eggers, J. 2004a Hydrodynamic theory of forced dewetting. Phys. Rev. Lett. 93, 094502.
Eggers, J. 2004b Toward a description of contact line motion at higher capillary numbers. Phys. Fluids 16, 34913494.
Eggers, J. 2005 Existence of receding and advancing contact lines. Phys. Fluids 17, 082106.
de Gennes, P. G. 1986 Deposition of Langmuir–Blodgett layers. Colloid Polym. Sci. 264, 463465.
Hocking, L. M. 1981 Sliding and spreading of thin two-dimensional drops. Q. J. Mech. Appl. Maths 34, 3755.
Hocking, L. M. 1983 The spreading of a thin drop by gravity and capillarity. Q. J. Mech. Appl. Maths 36, 5569.
Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35, 85101.
Jacqmin, D. 2004 Onset of wetting failure in liquid–liquid systems. J. Fluid Mech. 517, 209228.
Oron, A., Davis, S. H. & Bankoff, G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931980.
Qian, T., Wang, X.-P. & Sheng, P. 2006 A variational approach to moving contact line hydrodynamics. J. Fluid Mech. 564, 333360.
Ren, W. & E, W. 2007 Boundary conditions for the moving contact line problem. Phys. Fluids 19, 022101.
Sbragaglia, M., Sugiyama, K. & Biferale, L. 2008 Wetting failure and contact line dynamics in a Couette flow. J. Fluid Mech. 614, 471493.
Sedev, R. V. & Petrov, J. G. 1991 The critical condition for transition from steady wetting to film entrainment. Colloids Surf. 53, 147156.
Snoeijer, J. H. & Andreotti, B. 2013 Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45, 269292.
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.
Snoeijer, J. H., Delon, G., Fermigier, M. & Andreotti, B. 2006 Avoided critical behavior in dynamically forced wetting. Phys. Rev. Lett. 96, 174504.
Thompson, P. A. & Robbins, M. O. 1989 Simulations of contact-line motion: slip and the dynamic contact angle. Phys. Rev. Lett. 63, 766769.
Voinov, O. V. 1976 Hydrodynamics of wetting. Fluid Dyn. 11, 714721.
Voinov, O. V. 2000 Wetting: inverse dynamic problem and equations for microscopic parameters. J. Colloid Interface Sci. 226, 515.
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On the wetting dynamics in a Couette flow

  • Peng Gao (a1) and Xi-Yun Lu (a1)

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