Original Papers

Acta Mechanica

, Volume 156, Issue 1, pp 79-91

First online:

Effect of nonuniform wall heating on the three-dimensional secondary instability of falling films

  • S. MiladinovaAffiliated withInstitute of Mechanics, Bulgarian Academy of Sciences
  • , D. StaykovaAffiliated withInstitute of Mechanics, Bulgarian Academy of Sciences
  • , G. LebonAffiliated withInstitute of Physics, University of Liege
  • , B. ScheidAffiliated withMicrogravity Research Center, Universite Libre de Bruxelles

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Secondary three-dimensional instabilities of nearly sinusoidal waves on vertically falling and nonuniformly heated films are studied by using a long-wave evolution equation. Two-dimensional waves are unstable with respect to transverse modulations with sufficiently long spanwise wavelength. Two distinct three-dimensional modes of instability are examined: a synchronous mode which does not alter the wave number of the basic two-dimensional waves and a subharmonic mode with one-half of the streamwise wave number. According to a Floquet analysis, the subharmonic instability is most likely to be dominant for streamwise wavenumbers close to the neutral curve. The three-dimensional instability mechanism depends on film heating. The secondary growth rate increases (decreases) with increasing (decreasing) film heating downstream, but the contribution of thermocapillarity to synchronous and subharmonic instabilities is different.