Shock transitions in Marangoni gravity-driven thin-film flow

Nonlinearity

Volumn 13, Issue 3, 2000, Pages 731-746

  Münch, Andreas ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034178761     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/13/3/312     Document Type: Article

References (15)

1. Bertozzi A L, Münch A. Fanton X and Cazabat A M 1998 Contact line stability and undercompressive shocks in driven thin film flow Phys. Rev. Lett. 81 5169-72
2. Bertozzi A L, Münch A and Shearer M 1999 Undercompressive shocks in thin film flow Physica D 134 431-64
3. Hayes B and Shearer M 1999 Undercompressive shocks and Riemann problems for scalar conservation laws with non-convex fluxes Proc. R. Soc. Edin. A 129 733-75
4. Shearer M. Schaeffer DG, Marchesin D and Paes-Leme P 1987 Solution of the Riemann problem for a prototype 2×2 system of non-strictly hyperbolic conservation laws Arch. Rat. Mech. Anal. 97 299-320
5. Carles P and Cazabat A M 1992 On the origin of the bump in the profile of surface-tension-gradient-driven spreading films Mat. Res. Soc. Symp. Proc. 248
6. Fanton X, Cazabat A M and Quéré D 1996 Thickness and shape of films driven by a Marangoni flow Langmuir 12 5875-80
7. Kataoka D E and Troian S M 1997 A theoretical study of instabilities at the advancing front of thermally driven coating films J. Colloid Interface Sci. 192 350-62
8. Dussan E B V and Davis S 1974 On the motion of a fluid-fluid interface along a solid surface J. Fluid Mech. 65 71-95
9. Huh C and Scriven L E 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line J. Colloid Interface Sci. 35 85-101
10. Troian S M, Herbolzheimer E, Safran S A and Joanny J F 1989 Fingering instabilities of driven spreading films Europhys. Lett. 10 25-30
11. Lax P D 1973 Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves (CBMS-NSF Regional Conf. Series in Applied Mathematics vol 11) (Philadelphia, PA: SIAM)
12. Bertozzi A L and Brenner M P 1997 Linear stability and transient growth in driven contact lines Phys. Fluids 9 530-9
13. Bertozzi A L and Shearer M 2000 Existence of undercompressive travelling waves in thin film equations SIAM J. Math. Anal to be published
14. Hindmarsh A C 1983 Odepack a systematized collection of ODE solvers Scientific Computing ed R S Stepleman et al (Amsterdam: North-Holland) pp 55-64
15. Guckenheimer J and Holmes P 1986 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields 2nd edn (Berlin: Springer)