Heated falling films

Journal of Fluid Mechanics

Volumn 592, Issue , 2007, Pages 295-334

  Trevelyan, P M J ^a,b   Scheid, B ^b,d   Ruyer Quil, C ^c   Kalliadasis, S ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^c Centre National de la Recherche Scientifique   (France)

^d HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; GALERKIN METHODS; HEAT FLUX; MATHEMATICAL MODELS; PECLET NUMBER; POLYNOMIALS; THERMODYNAMICS;

ENERGY EQUATION; HEATED WALL; HIGH-ORDER GALERKIN PROJECTION; INTERFACIAL TEMPERATURE; THERMAL BOUNDARY LAYER;

FLUID MECHANICS;

BOUNDARY CONDITIONS; FLUID MECHANICS; GALERKIN METHODS; HEAT FLUX; MATHEMATICAL MODELS; PECLET NUMBER; POLYNOMIALS; THERMODYNAMICS;

BOUNDARY CONDITION; FLUID MECHANICS; GALERKIN METHOD; HEAT FLUX; HEAT TRANSFER; NUMERICAL MODEL;

EID: 36348969329     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112007008476     Document Type: Article

References (37)

1. BENJAMIN, T. B. 1957 Wave formation in laminar flow down an inclined plane. J. Fluid Mech. 2, 554-574.
2. BENNEY, D. J. 1966 Long waves on liquid films. J. Math. Phys. 45, 150-155.
3. CHANG, H.-C. & DEMEKHIN, E. A. 2002 Complex Wave Dynamics on Thin Films. Elsevier.
4. DEMEKHIN, E. A., KAPLAN, M. A. & SHKADOV, V. YA. 1987 Mathematical models of the theory of viscous liquid films. Izv. Akad. Nauk SSSR, Mekh. Zhidk i Gaza 6, 9-16.
5. DOEDEL, E., CHAMPNEYS, A., FAIRFRIEVE, T., KUZNETSOV, Y., SANDSTEDE, B. & WANG, X. 1997 Auto 97 Continuation and Bifurcation Software for Ordinary Differential Equations. Montreal Concordia University.
6. GOODWIN, R. & HOMSY, G. M. 1991 Viscous flow down a slope in the vicinity of a contact line. Phys. Fluids 3, 515-528.
7. GOTTLIEB, D. & ORSZAG, S. A. 1977 Numerical Analysis of Spectral Methods: Theory and Applications. SIAM.
8. Goussls, D. A. & KELLY, R. E. 1991 Surface waves and thermocapillary instabilities in a liquid film flow. J. Fluid Mech. 223, 24-45.
9. JOO, S. W., DAVIS, S. H. & BANKOFF, S. G. 1991 Long-wave instabilities of heated falling films: Two-dimensional theory of uniform layers. J. Fluid Mech. 230, 117-146.
10. KABOV, O. A. 1998 Formation of regular structures in a falling liquid film upon local heating. Thermophys. Aeromech. 5, 547-551.
11. KABOV, O. A., LEGROS, J. K., MARCHUK, I. V. & SCHEID, B. 2000 Deformation of the free surface in a moving locally-heated thin liquid layer. Izv. Akad. Nauk SSSR, Mekh. Zhidk Gaza 3, 200-208.
12. KALLIADASIS, S., KIYASHKO, A. & DEMEKHIN, E. A. 2003a Marangoni instability of a thin liquid film heated from below by a local heat source. J. Fluid Mech. 475, 377-408.
13. KALLIADASIS, S., DEMEKHIN, E. A., RUYER-QUIL, C. & VELARDE, M. G. 2003b Thermocapillary instability and wave formation on a film falling down a uniformly heated plane. J. Fluid Mech. 492, 303-338.
14. KAPITZA, P. L. 1948 Wave flow of thin layers of a viscous fluid. Sov. Phys. J. Exp. Theor. Phys. 18, 3-28.
15. KAPITZA, P. L. & KAPITZA, S. P. 1949 Wave flow of thin layers of a viscous fluid: III. Experimental study of undulatory flow conditions. Sov. Phys. J. Exp. Theor. Phys. 19, 105-120.
16. KAWAHARA, T. 1983 Formation of saturated solitons in a nonlinear dispersive system with instability and dissipation. Phys. Rev. Lett. 51, 381-383.
17. NAKAYA, C. 1989 Waves on a viscous fluid film down a vertical wall. Phys. Fluids A 1 (7), 1143-1154.
18. ORON, A., DAVIS, S. H. & BANKOFF, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931-980.
19. PUMIR, A., MANNEVILLE, P. & POMEAU, Y. 1983 On solitary waves running down an inclined plane. J. Fluid Mech. 135, 27-50.
20. RAMASWAMY, B., CHIPPADA, S. & Joo, S. W. 1996 A full-scale numerical study of interfacial instabilities in thin film flows. J. Fluid Mech. 325, 163-194.
21. RUYER-QUIL, C. & MANNEVlLLE, P. 2000 Improved modeling of flows down inclined planes. Eur. Phys. J. B 15, 357-369.
22. RUYER-QUIL, C. & MANNEVlLLE, P. 2002 Further accuracy and convergence results of the modeling of flows down inclined planes by weighted residual approximations. Phys. Fluids 14, 170-183.
23. RUYER-QUIL, C., SCHEID, B., KALLIADASIS, S., VELARDE, M. G. & ZEYTOUNIAN, R. KH. 2005 Thermocapillary long waves in a liquid film flow. Part 1. Low-dimensional formulation. J. Fluid Mech. 538 199-222.
24. SALAMON, T. R., ARMSTRONG, R. C. & BROWN, R. A. 1994 Travelling waves on vertical films: Numerical analysis using the finite element method. Phys. Fluids 6 (6), 2202-2220.
25. SCHEID, B. 2004 Evolution and stability of falling liquid films with thermocapillary effects. PhD thesis, Université Libre de Bruxelles.
26. SCHEID, B., ORON, A., COLINET, P., THIELE, U. & LEGROS, J. C. 2002 Nonlinear evolution of nonuniformly heated falling liquid films. Phys. Fluids 14 (12), 4130-4151.
27. SCHEID, B., RUYER-QUIL, C., THIELE U., KABOV, O. A., LEGROS, J. C. & COLINET, P. 2004 Validity domain of the Benney equation including Marangoni effect for closed and open flows. J. Fluid Mech. 527 303-335.
28. SCHEID, B., RUYER-QUIL, C., KALLIADASIS, S., VELARDE, M. G. & ZEYTOUNIAN, R. KH. 2005 Thermocapillary long waves in a liquid film flow. Part 2. Linear stability and nonlinear waves. J. Fluid Mech. 538, 223-244.
29. SHKADOV, V. YA. 1967 Wave models in the flow of a thin layer of a viscous liquid under the action of gravity. Izv. Akad. Nauk SSSR, Mekh. Zhidki Gaza 1, 43-50.
30. SHKADOV, V. YA. 1968 Theory of wave flow of a thin layer of a viscous liquid. Izv. Akad. Nauk SSSR, Mekh. Zhidki Gaza 2, 20-25.
31. SHKADOV, V. YA. 1977 Solitary waves in a layer of viscous liquid. Izv. Akad. Nauk SSSR, Mekh. Zhidki Gaza 12, 63-66.
32. SHRAIMAN, B. 1987 Diffusive transport in a Rayleigh-Bénard convection cell. Phys. Rev. A 36, 261-267.
33. SMITH, K. A. 1966 On convective instability induced by surface-tension gradients. J. Fluid Mech. 14, 401-414.
34. STRELITZ, S. 1977 On the Routh-Hurwitz problem. Am. Math. Mon. 84, 542-544.
35. TREVELYAN, P. M. J. & KALLIADASIS, S. 2004 Dynamics of a reactive falling film at large Péclet numbers. I. Long-wave approximation. Phys. Fluids 16 (8), 3191-3208.
36. TREVELYAN, P. M. J., KALLIADASIS, S., MERKIN, J. H. & SCOTT, S. K. 2002 Mass transport enhancement in regions bounded by rigid walls. J. Engng Maths 42, 45-64.
37. YIH, C.-S. 1963 Stability of liquid flow down an inclined plane. Phys. Fluids 6 (3), 321-334.