Cornered drops and rivulets

Physics of Fluids

Volumn 19, Issue 4, 2007, Pages

  Snoeijer, J H ^a,b,c   Le Grand Piteira, N ^b,c   Limat, L ^b,c   Stone, H A ^d   Eggers, J ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITÉ PARIS DIDEROT   (France)

^c CNRS   (France)

^d HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTACTS (FLUID MECHANICS); STREAM FLOW; VELOCITY; VISCOUS FLOW;

CONTACT LINE; RIVULETS; VISCOUS LIQUID;

DROPS;

CONTACTS (FLUID MECHANICS); DROPS; STREAM FLOW; VELOCITY; VISCOUS FLOW;

EID: 34248138469     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2722767     Document Type: Article

References (37)

1. C. Huh and L. E. Scriven, "Hydrodynamic model of steady movement of a solid/liquid/fluid contact line," J. Colloid Interface Sci. JCISA50021-979710.1016/0021-9797(71)90188-3 35, 85 (1971).
2. P. A. Thompson and M. O. Robbins, "Simulations of contact-line motion: Slip and the dynamic contact angle," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.63.766 63, 766 (1989).
3. P. G. de Gennes, "Wetting: Statics and dynamics," Rev. Mod. Phys. RMPHAT0034-686110.1103/RevModPhys.57.827 57, 827 (1985).
4. L. M. Hocking, "Rival contact-angle models and the spreading of drops," J. Fluid Mech. JFLSA70022-112010.1017/S0022112092004579 239, 671 (1992).
5. T. Podgorski, J. M. Flesselles, and L. Limat, "Corners, cusps, and pearls in running drops," Phys. Rev. Lett.PRLTAO0031-900710.1103/ PhysRevLett.87.036102 87, 036102 (2001).
6. N. Le Grand, A. Daerr, and L. Limat, "Shape and motion of drops sliding down an inclined plane," J. Fluid Mech.JFLSA70022-112010.1017/S0022112005006105 541, 293 (2005).
7. We first became aware of simulations of this type through a presentation of R. V. Roy, "Stability and nonlinear evolution of capillary ridges and rivulets," Euromech Fluid Mechanics Conference, Toulouse, 2003.
8. L. W. Schwartz, D. Roux, and J. J. Cooper-White, "On the shapes of droplets that are sliding on a vertical wall," Physica D PDNPDT0167-278910.1016/j.physd.2005.07.001 209, 236 (2005).
9. P. G. Simpkins and V. J. Kuck, "On air entrainment in coatings," J. Colloid Interface Sci. JCISA50021-979710.1016/ S0021-9797(03)00347-3 263, 562 (2003).
10. D. Quéré, "On the minimal velocity of forced spreading in partial wetting (in French)," C. R. Acad. Sci., Ser. II: Mec., Phys., Chim., Sci. Terre Univers CRAMED0764-4450 313, 313 (1991).
11. R. V. Sedev and J. G. Petrov, "The critical condition for transition from steady wetting to film entrainment," Colloids Surf. COSUD30166-662210.1016/0166-6622(91)80041-L 53, 147 (1991).
12. J. H. Snoeijer, G. Delon, M. Fermigier, and B. Andreotti, "Avoided critical behavior in dynamically forced wetting," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.96.174504 96, 174504 (2006).
13. L. D. Landau and B. V. Levich, "Dragging of a liquid by a moving plate," Acta Physicochim. URSSACPYAR0365-1460 17, 42 (1942).
14. B. V. Derjaguin, "On the thickness of a layer of liquid remaining on the walls of vessels after their emptying, and the theory of the application of photoemulsion after coating on the cine film," Acta Physicochim. URSSACPYAR0365-1460 20, 349 (1943).
15. J. Eggers, "Existence of receding and advancing contact lines," Phys. Fluids PHFLE61070-663110.1063/1.2009007 17, 082106 (2005).
16. P. G. de Gennes, "Deposition of Langmuir-Blodget layers," Colloid Polym. Sci. CPMSB60303-402X10.1007/BF01419552 264, 463 (1986).
17. T. D. Blake and K. J. Ruschak, "A maximum speed of wetting," Nature (London)NATUAS0028-083610.1038/282489a0 282, 489 (1979).
18. S. Kistler, Wettability, edited by J. C. Berg (Marcel Dekker, New York, 1993).
19. J. G. Petrov and R. V. Sedev, "On the existence of a maximum speed of wetting," Colloids Surf. COSUD30166-662210.1016/ 0166-6622(85)80030-5 13, 313 (1985).
20. H. A. Stone, L. Limat, S. K. Wilson, J. M. Flesselles, and T. Podgorski, "Corner singularity of a contact line moving on a solid substrate," C. R. Phys. CRPOBN1631-070510.1016/ S1631-0705(02)01288-4 3, 103 (2002).
21. L. Limat and H. A. Stone, "Three-dimensional lubrication model of a contact line corner singularity," Europhys. Lett. EULEEJ0295-507510.1209/epl/i2003-10096-0 65, 365 (2004).
22. J. H. Snoeijer, E. Rio, N. Le Grand, and L. Limat, "Self-similar flow and contact line geometry at the rear of cornered drops," Phys. Fluids PHFLE61070-663110.1063/1.1946607 17, 072101 (2005).
23. M. Ben Amar, L. Cummings, and Y. Pomeau, "Transition of a moving contact line from smooth to angular," Phys. Fluids PHFLE61070-663110.1063/1.1604778 15, 2949 (2003).
24. E. Rio, A. Daerr, B. Andreotti, and L. Limat, "Boundary conditions in the vicinity of a dynamic contact line: Experimental investigation of viscous drops sliding down an inclined plane," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.94.024503 94, 024503 (2005).
25. A. Oron, S. H. Davis, and S. G. Bankoff, "Long-scale evolution of thin liquid films," Rev. Mod. Phys. RMPHAT0034-686110.1103/ RevModPhys.69.931 69, 931 (1997).
26. C. L. Navier, "Sur les lois du mouvement des fluides," Mem. Acad. Sci. Inst. Fr. MEAFA70368-9263 6, 389 (1827).
27. E. Lauga, M. P. Brenner, and H. A. Stone, Handbook of Experimental Fluid Dynamics (Springer, Berlin, to be published).
28. C. Cottin-Bizonne, B. Cross, A. Steinberger, and E. Charlaix, "Boundary slip on smooth hydrophobic surfaces: Intrinsic effects and possible artifacts," Phys. Rev. Lett. PRLTAO0031-900710.1103/ PhysRevLett.94.056102 94, 056102 (2005).
29. M. Eres, L. Schwartz, and R. Roy, "Fingering phenomena for driven coating films," Phys. Fluids PHFLE61070-663110.1063/1.870382 12, 1278 (2000).
30. J. Eggers, "Toward a description of contact line motion at higher capillary numbers," Phys. Fluids PHFLE61070-663110.1063/1.1776071 16, 3491 (2004).
31. J. M. Davis, "Asymptotic analysis of liquid films dip-coated onto chemically micropatterned surfaces," Phys. Fluids PHFLE61070-663110.1063/1.1850751 17, 038101 (2005).
32. O. V. Voinov, "Hydrodynamics of wetting [English translation]," Fluid Dyn. FLDYAH0015-462810.1007/BF01012963 11, 714 (1976).
33. R. G. Cox, "The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow," J. Fluid Mech. JFLSA70022-112010.1017/S0022112086000332 168, 169 (1986).
34. L. M. Hocking, "The spreading of a thin drop by gravity and capillarity," Q. J. Mech. Appl. Math. QJMMAV0033-561410.1093/qjmam/ 36.1.55 36, 55 (1983).
35. This idea first occurred to one of us (L.L.) and was presented in "Shape of drops sliding down an inclined surface," in Proceedings of the 4th European Coating Symposium, Bruxelles, 1-4 October 2002.
36. E. B. Dussan V. and R. T.-P. Chow, "On the ability of drops or bubbles to stick to nonhorizintal surfaces of solids," J. Fluid Mech. JFLSA70022-112010.1017/S002211208300227X 137, 1 (1979).
37. P. C. Duineveld, "The stability of ink-jet printed lines of liquid with zero receding contact angle on a homogeneous substrate," J. Fluid Mech. JFLSA70022-112010.1017/S0022112002003117 477, 175 (2003).