Geodesic
Dynamics of a Reactive Thin Film
P.M.J. Trevelyan1, 2 ; A. Pereira1 ; S. Kalliadasis1
1 Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
2 Division of Mathematics & Statistics, University of Glamorgan, Pontypridd, CF37 1DL, Wales
Mathematical modelling of natural phenomena, Tome 7 (2012) no. 4, pp. 99-145.

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Consider the dynamics of a thin film flowing down an inclined plane under the action of gravity and in the presence of a first-order exothermic chemical reaction. The heat released by the reaction induces a thermocapillary Marangoni instability on the film surface while the film evolution affects the reaction by influencing heat/mass transport through convection. The main parameter characterizing the reaction-diffusion process is the Damköhler number. We investigate the complete range of Damköhler numbers. We analyze the steady state, its linear stability and nonlinear regime. In the latter case, long-wave models are compared with integral-boundary-layer ones and bifurcation diagrams for permanent solitary wave solutions of the different models are constructed. Time-dependent computations with the integral-boundary-layer models show that the system approaches a train of coherent structures that resemble the solitary pulses obtained in the bifurcation diagrams.
DOI : 10.1051/mmnp/20127408

P.M.J. Trevelyan 1, 2 ; A. Pereira 1 ; S. Kalliadasis 1

1 Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
2 Division of Mathematics & Statistics, University of Glamorgan, Pontypridd, CF37 1DL, Wales 
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P.M.J. Trevelyan; A. Pereira; S. Kalliadasis. Dynamics of a Reactive Thin Film. Mathematical modelling of natural phenomena, Tome 7 (2012) no. 4, pp. 99-145. doi : 10.1051/mmnp/20127408. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20127408/

[1] A. Oron, S. H. Davis, S. G. Bankoff Rev. Mod. Phys. 1997 931 980

[2] S. Kalliadasis, U. Thiele (Ed) Thin Films of Soft Matter. Springer-Wien, New York, 2007.

[3] R. V. Craster, O. K. Matar Rev. Mod. Phys. 2009 1131 1198

[4] P. L. Kapitza Zh. Eksp. Tear. Fiz. 1948 3 18

[5] P. L. Kapitza Zh. Eksp. Teor. Fiz. 1948 19 28

[6] P. L. Kapitza, S. P. Kapitza Zh. Eksp. Teor. Fiz. 1949 105 120

[7] H.-C. Chang Ann. Rev. Fluid Mech. 1994 103 136

[8] H.-C. Chang, E. A. Demekhin. Complex Wave Dynamics on Thin Films. Elsevier, 2002.

[9] Z. Dagan, L. M. Pismen J. Colloid Interface Sci. 1984 215 225

[10] A. Pereira, P. M. J. Trevelyan, U. Thiele, S. Kalliadasis J. Eng. Math. 2007 207 220

[11] A. Pereira, P. M. J. Trevelyan, U. Thiele, S. Kalliadasis Phys. Fluids 2007 112102

[12] A. Pereira, P. M. J. Trevelyan, U. Thiele, S. Kalliadasis Eur. Phys. J. Special Topics 2009 121 125

[13] A. Y. Rednikov, Y. S. Ryazantsev, M. G. Velarde Phys. Fluids 1994 451 468

[14] L. M. Pismen Phys. Rev. E 2010 026307

[15] E. R. Gilliland, R. F. Baddour, P. L. T. Brian Am. Inst. Chem. Eng. J. 1958 223

[16] P. M. J. Trevelyan, S. Kalliadasis Phys. Fluids 2004 3191 3208

[17] P. M. J. Trevelyan, S. Kalliadasis Phys. Fluids 2004 3209 3226

[18] A. A. Nepomnyashchy, M. G. Velarde, P. Colinet. Interfacial Phenomena and Convection. Chapman Hall, London, 2002.

[19] R. C. Weast, M. J. Astle. Handbook of Chemistry and Physics. CRC Press, Boca Raton, FL, 1979.

[20] C. E. Wylock, P. Colinet, T. Cartage, B. Haut Int. J. Chem. React. Engng. 2008 A4

[21] S. Kalliadasis, E. A. Demekhin, C. Ruyer-Quil, M. G. Velarde J. Fluid Mech. 2003 303 338

[22] P. Trevelyan, S. Kalliadasis J. Eng. Math. 2004 177 208

[23] C. Ruyer-Quil, B. Scheid, S. Kalliadasis, M. G. Velarde, R. Kh. Zeytounian J. Fluid Mech. 2005 199 222

[24] P. M. J. Trevelyan, B. Scheid, C. Ruyer-Quil, S. Kalliadasis J. Fluid Mech. 2007 295 334

[25] T. B. Benjamin J. Fluid Mech. 1957 554 574

[26] C. S. Yih Phys. Fluids 1963 321 334

[27] D. J. Benney J. Math. Phys. 1966 150 155

[28] B. Scheid, C. Ruyer-Quil, S. Kalliadasis, M. G. Velarde, R. Kh. Zeytounian J. Fluid Mech. 2005 223 244

[29] C. Ruyer-Quil, P. Trevelyan, F. Giorgiutti-Dauphiné, C. Duprat, S. Kalliadasis J. Fluid Mech. 2008 431 462

[30] A. Pumir, P. Manneville, Y. Pomeau J. Fluid Mech. 1983 27 50

[31] C. Nakaya Phys. Fluids 1989 1143 1154

[32] A. Oron, O. Gottlieb Phys. Fluids 2002 2622 2636

[33] B. Scheid, C. Ruyer-Quil, U. Thiele, O.A. Kabov, J.C. Legros, P. Colinet J. Fluid Mech. 2004 303 335

[34] V. Ya. Shkadov Izv. Akad. Nauk SSSR, Mekh. Zhidk Gaza 1967 43 50

[35] C. Ruyer-Quil, P. Manneville Eur. Phys. J. B 1998 277 292

[36] C. Ruyer-Quil, P. Manneville Eur. Phys. J. B 2000 357 369

[37] C. Ruyer-Quil, P. Manneville Phys. Fluids 2002 170 183

[38] S. Kalliadasis, A. Kiyashko, E. A. Demekhin J. Fluid Mech. 2003 377 408

[39] I. L. Kliakhandler, S. H. Davis, S. G. Bankoff J. Fluid Mech. 2001 381 390

[40] C. Duprat, C. Ruyer-Quil, S. Kalliadasis, F. Giorgiutti-Dauphiné Phys. Rev. Lett. 2007 244502

[41] N. A. Malamataris, M. Vlachogiannis, V. Bontozoglou Phys. Fluids 2002 1082 1094

[42] B. Scheid, C. Ruyer-Quil, P. Manneville J. Fluid Mech. 2006 183 222

[43] E. Doedel, A. Champneys, T. Fairfrieve, Y. Kuznetsov, B. Sandstede, X. Wang. AUTO97 : Continuation and bifurcation software for ordinary differential equations. Concordia University, Montreal, 1997.

[44] P. Huerre, P. A. Monkewitz Annu. Rev. Fluid. Mech. 1990 473 537

[45] P. Huerre, M. Rossi. Hydrodynamic and Nonlinear Instabilities. In : Hydrodynamic Instabilities in Open Flows (Ed. C. Godréche, P. Manneville), Cambridge University Press, 1998, 81-294.

[46] H.-C. Chang, E. A. Demekhin, D. I. Kopelevich Phys. Rev. Lett. 1995 1747 1750

[47] E. A. Demekhin, E. N. Kalaidin, S. Kalliadasis, S. Yu. Vlaskin Phys. Fluids 2007 114104

[48] A. A. Golovin, A. A. Nepomnyashchy, L. M. Pismen Phys. Fluids 1994 34 48

[49] U. Thiele, E. Knobloch Physica D 2004 213 248

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