Dynamics of a reactive falling film at large Péclet numbers. I. Long-wave approximation

Philip Trevelyan, Serafim Kalliadasis

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We study the dynamics of a vertically falling film in the presence of a first-order (exothermic or endothermic) chemical reaction. We extend the work by Trevelyan et al. [Phys. Fluids 14, 2402 (2002)] on the same problem to large heat/mass transport Péclet numbers and so we take into account the convective terms of the heat/mass transport equations. Our analysis is based on a long-wave expansion of the equations of motion and associated boundary conditions. Previous results by Trevelyan et al. are reviewed and compared with present results. Particular emphasis is given on permanent-form traveling solitary waves. We show that the inclusion of the heat/mass transport convective effects can have a dramatic effect on the evolution of the interface and in fact can make the solitary waves dispersive. The size of dispersion depends on the size of the Prandtl and Schmidt numbers while its sign can change from positive to negative leading to negative-hump solitary waves. We show that for large dispersion and for a sufficiently large region of Reynolds numbers, the liquid layer can be excited in the form of nondissipative solitary pulses which close to criticality assume the form of Korteweg–de Vries solitons
Original languageEnglish
Pages (from-to)3191-3208
Number of pages17
JournalPhysics of Fluids
Issue number8
Early online date7 Aug 2004
Publication statusE-pub ahead of print - 7 Aug 2004


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