Thin Film Dynamics

  • J. M. Chomaz
  • M. Costa
Part of the International Centre for Mechanical Sciences book series (CISM, volume 391)


Thin films1 possess two radically distinct typical scales associated with their transverse and their longitudinal dimensions. Two distinct dynamics are thus associated to these length scales: transverse or longitudinal dispersive waves linked to the film thickness, and longitudinal quasi-two-dimensional (2D) motion scaling on the film length. The physics of both waves and 2D motion are studied here. The response of a film to a localized impulse is computed, and the behaviour is interpreted in the light of group-velocity notions. When air is blown on the film, the waves turn into instability modes, as demonstrated by a simple pressure argument in the limit of small density ratios. The different behavior observed in the case of a water jet and in the case of air blowing on a film is explained by introducing the equivalent of group velocity for instability waves, which naturally leads to discriminate between the absolute and the convective type of instability. In the long-wave limit, waves become similar to the elastic waves propagating on a stretched membrane. In recent experiments, Couder [7] and Gharib [13] use soap films as a two-dimensional fluid. In the present paper, we show that the necessary condition for the film to comply to Navier-Stokes equations is that the typical flow velocity be small compared to the Marangoni elastic wave velocity.


Dispersion Relation Phase Velocity Weber Number Liquid Sheet Soap Film 
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Copyright information

© Springer-Verlag Wien 1998

Authors and Affiliations

  • J. M. Chomaz
    • 1
  • M. Costa
    • 2
  1. 1.Ecole PolytechniquePalaiseauFrance
  2. 2.University of Naples “Federico II”NaplesItaly

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