Localized Marangoni forcing in driven thin films

Physica D: Nonlinear Phenomena

Volumn 209, Issue 1-4 SPEC. ISS., 2005, Pages 117-134

  Haskett, Ryan P ^a   Witelski, Thomas P ^a   Sur, Jeanman ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

Fluid dynamics; Lubrication theory; Marangoni forcing; Thermocapillary valve; Thin films

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONTROL THEORY; FLOW OF FLUIDS; FLUID DYNAMICS; HYDRAULIC MACHINERY;

LUBRICATION THEORY; MARANGONI FORCING; THERMOCAPILLARY VALVE; VISCOUS FLUIDS;

THIN FILMS;

EID: 24144440739     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2005.06.019     Document Type: Conference Paper

References (36)

1. H.A. Stone, A.D. Stroock, and A. Ajdari Engineering flows in small devices Annu. Rev. Fluid Mechan. 36 2004 381 411
2. N. Garnier, R.O. Grigoriev, M.F. Schatz, Optical manipulation of microscale fluid flow, Phys. Rev. Lett. 91 (5) (2003) 4501:1-4.
3. A. Oron, S.H. Davis, and S.G. Bankoff Long-scale evolution of thin liquid films Rev. Modern Phys. 69 3 1997 931 980
4. T.G. Myers Thin films with high surface tension SIAM Rev. 40 3 1998 441 462
5. H.E. Huppert Flow and instability of a viscous current down a slope Nature 300 1982 427 429
6. A.M. Cazabat, F. Heslot, S.M. Troian, and P. Carles Fingering instability of thin spreading films driven by temperature gradients Nature 346 1990 824
7. M.J. Tan, S.G. Bankoff, and S.H. Davis Steady thermocapillary flows of thin liquid layers. i. Theory Phys. Fluids A 2 3 1990 313 321
8. J.P. Burelbach, S.G. Bankoff, and S.H. Davis Steady thermocapillary flows of thin liquid layers. II. Experiment Phys. Fluids A 2 3 1990 322 333
9. X. Fanton, A.M. Cazabat, and D. Quéré Thickness and shape of films driven by a Marangoni flow Langmuir 12 1996 5875 5880
10. A.L. Bertozzi, A. Münch, X. Fanton, and A.M. Cazabat Contact line stability and "Undercompressive Shocks" in driven thin film flow Phys. Rev. Lett. 81 23 1998 5169 5172
11. L.W. Schwartz On the asymptotic analysis of surface-stress-driven thin-layer flow J. Eng. Math. 39 1-4 2001 171 188
12. A. Münch The thickness of a Marangoni-driven thin liquid film emerging from a meniscus SIAM J. Appl. Math. 62 6 2002 2045 2063
13. I.S. McKinley, and S.K. Wilson The linear stability of a ridge of fluid subject to a jet of air Phys. Fluids 13 4 2001 872 883
14. J.J. Kriegsmann, M.J. Miksis, and J. Vanden-Broeck Pressure driven disturbances on a thin viscous film Phys. Fluids 10 6 1998 1249 1255
15. Y. Jiang, H. Badr, and J.M. Floryan Thermocapillary convection with moving contact points Phys. Fluids 15 2 2003 442 454
16. V.S. Ajaev, and D.A. Willis Thermocapillary flow and rupture in films of molten metal on a substrate Phys. Fluids 15 10 2003 3144 3150
17. B. Scheid, A. Oron, P. Colinet, U. Thiele, and J.-C. Legros Nonlinear evolution of nonuniformly heated falling liquid films Phys. Fluids 14 12 2002 4130 4151
18. S. Kalliadasis, A. Kiyashko, and E.A. Demekhin Marangoni instability of a thin liquid film heated from below by a local heat source J. Fluid Mech. 457 2003 377 408
19. A. Oron Nonlinear dynamics of irradiated thin volatile liquid films Phys. Fluids 12 1 2000 29 41
20. J.M. Skotheim, U. Thiele, and B. Scheid On the instability of a falling film due to localized heating J. Fluid Mech. 475 2003 1 19
21. L.Y. Yeo, R.V. Craster, O.K. Matar, Marangoni instability of a thin liquid film resting on a locally heated horizontal wall, Phys. Rev. E 67 (5) (2003) 6315:1-14.
22. C.M. Gramlich, S. Kalliadasis, G.M. Homsy, and C. Messer Optimal leveling of flow over one-dimensional topography by Marangoni stresses Phys. Fluids 14 6 2002 1841 1850
23. A.L. Bertozzi, A. Münch, and M. Shearer Undercompressive shocks in thin film flows Physica D 134 1999 431 464
24. J. Sur, T.P. Witelski, R.P. Behringer, Steady-profile fingering flows in Marangoni driven thin films, preprint, 2004.
25. R. Levy, M. Shearer, Kinetics and nucleation for driven thin film flow, submitted for publication.
26. J. Sur, A.L. Bertozzi, R.P. Behringer, Reverse undercompressive shocks structures in thin film flow. Phys. Rev. Lett. 90 (12) (2003) 6105:1-4.
27. A. Münch, Pinch-off transition in Marangoni-driven thin films. Phys. Rev. Lett. 91 (1) (2003) 6105:1-4.
28. A. Münch Shock transitions in Marangoni gravity-driven thin-film flow Nonlinearity 13 3 2000 731 746
29. A. Kar, and J. Mazumder Mathematical modeling of key-hole laser welding J. Appl. Phys. 78 11 1995 6353 6360
30. L. Trefethen, Surface tension in fluid mechanics, in: National Committee for Fluid Mechanics Films (Ed.), Fluid Mechanics Films, Encyclopedia Britanica Educational Co., 1969.
31. S. Kalliadasis, C. Bielarz, and G.M. Homsy Steady free-surface thin film flows over topography Phys. Fluids 12 8 2000 1889 1898
32. R.P. Haskett, T.P. Witelski, Perturbation analysis of driven thin films with localized forcing, in preparation.
33. A. Münch, P.L. Evans, Marangoni-driven liquid films rising out of a meniscus onto a nearly horizontal substrate, preprint, WIAS technical report 941, 2004.
34. A. Münch, The role of the meniscus in the formation of non-classical shocks in thin Marangoni-gravity driven films, Ph.D. thesis, Technical University of Munich, 2001.
35. T.P. Witelski, and M. Bowen ADI schemes for higher-order nonlinear diffusion equations Appl. Numer. Math. 45 2-3 2003 331 351
36. M. Bowen, J. Sur, A.L. Bertozzi, R.P. Behringer, Nonlinear dynamics of two-dimensional undercompressive shocks, submitted for publication.