Modified description of wave motion in a falling film

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Abstract
The presence of gravity‐capillary waves at the surface of a viscous falling film has been studied theoretically by a more rigorous linear treatment than presently available.The present analysis is based on the assumption of steady state periodic solutions of the complete Navier‐Stokes equations. It provides methods of prediction, to a first order of approximation, for the wavelength, celerity, and wave number, in terms of the Weber number which emerges as the governing dimensionless group. This treatment includes as special cases the low Weber number analyses of Yih, Benjamin, Hanratty and Hershman, and Kapitza, as well as the high Weber number theory of Ishihara, Iwagaki, and Iwasa. Agreement with experimental observation is improved over that obtained from previous analyses.The stream function of the system has been derived and the instantaneous streamlines have been constructed for application to heat and mass transfer.

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