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Interaction dynamics of solitary waves on a falling film

Published online by Cambridge University Press:  26 April 2006

H.-C. Chang ,
E. Demekhin  and
E. Kalaidin
H.-C. Chang
Affiliation:
Department of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
E. Demekhin
Affiliation:
Department of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA Permanent Address: Department of Applied Mathematics, Kuban State Technological University, Krasnodar, 3500072, Russia.
E. Kalaidin
Affiliation:
Department of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA Permanent Address: Department of Applied Mathematics, Kuban State Technological University, Krasnodar, 3500072, Russia.
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Abstract

Beyond a short transition region near the inlet, waves on a falling film evolve into distinct pulse-like solitary waves that dominate all subsequent interfacial dynamics. Numerical and physical experiments indicate that these localized structures can attract and repel each other. Attractive interaction through the capillary ripples of the pulses causes two pulses to coalesce into a bigger pulse which accelerates and precipitates further coalescence. This binary interaction between an ‘excited’ pulse after coalescence and its smaller front neighbour is the key mechanism that drives the observed wave dynamics. From symmetry arguments, two dominant modes for a solitary pulse are obtained and used to develop an inelastic coherent structure theory for binary interaction between an excited pulse and its front neighbour. The theory offers a simple dynamical system that quantitatively describes the binary interaction and promises to elucidate the complex wave dynamics on a falling film.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 294 , 10 July 1995 , pp. 123 - 154
Copyright
© 1995 Cambridge University Press

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