On the Squire's transformation for stratified two-phase flows in inclined channels

I. Barmak*, A. Yu Gelfgat, A. Ullmann, N. Brauner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The applicability of the Squire's transformation for stability analysis of stratified two-phase flow in horizontal and inclined channels is examined. It is shown that for the considered flow such a transformation requires some additional constraints on the change of the inclination angle and flow rates of each of the phases. While the Squire's theorem (on the two-dimensionality of the critical disturbances) rigorously holds for the horizontal two-phase flow, for the inclined flow an exact mathematical theorem cannot be formulated. Nevertheless, it has been proven that 2D perturbations are the critical ones also for the case of inclined channel, since the transformation of a 3D stability problem to its 2D analog is associated with a stabilizing effect of reducing the system inclination, in addition to the reduction of the phases flow rates as in the case of horizontal flows.

Original languageEnglish
Pages (from-to)142-151
Number of pages10
JournalInternational Journal of Multiphase Flow
StatePublished - 1 Jan 2017


  • 3D perturbations
  • Inclined channel
  • Squire's transformation
  • Stability
  • Stratified two-phase flow


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