Three-dimensional instability of a two-layer Dean flow

A. Yu Gelfgat, Alexander Yarin, P. Z. Bar-Yoseph

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Stability of a two-layer Dean flow in a cylindrical annulus with respect to three-dimensional perturbations is studied by a global Galerkin method. It is shown that for large inner radius of the annulus (i) the instability becomes three-dimensional if one of the fluid layers is thin, (ii) its onset is not affected by possible small deformations of the interface, and (iii) multiple three-dimensional flow states are expected in a slightly supercritical flow regime. Stability diagrams and patterns of the three-dimensional perturbations are reported. It is concluded that even when the axisymmetric perturbation is the most dangerous, the resulting supercritical flow is expected to be three-dimensional. Possible multiplicity of supercritical three-dimensional states is predicted. The basis functions of the global Galerkin method are constructed so as to satisfy analytically the boundary conditions on no-slip walls and at the liquid-liquid interface. A modification of the numerical approach, accounting for small deformations of the interface which is subject to the action of the capillary force, is proposed. The results are of potential importance for development of novel bioseparators employing Dean vortices for enhancement of mass transfer of a passive scalar (say, a protein) through the interface. The developed numerical approach can be used for stability analysis in other two-fluid systems.

Original languageEnglish
Pages (from-to)3185-3195
Number of pages11
JournalPhysics of Fluids
Volume13
Issue number11
DOIs
Publication statusPublished - 2001 Nov 1
Externally publishedYes

Fingerprint

supercritical flow
Galerkin method
annuli
Galerkin methods
perturbation
liquid-liquid interfaces
three dimensional flow
Fluids
fluids
Liquids
mass transfer
Vortex flow
slip
Mass transfer
diagrams
Boundary conditions
vortices
boundary conditions
scalars
proteins

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Physics and Astronomy(all)
  • Fluid Flow and Transfer Processes
  • Condensed Matter Physics

Cite this

Gelfgat, A. Y., Yarin, A., & Bar-Yoseph, P. Z. (2001). Three-dimensional instability of a two-layer Dean flow. Physics of Fluids, 13(11), 3185-3195. https://doi.org/10.1063/1.1409967

Three-dimensional instability of a two-layer Dean flow. / Gelfgat, A. Yu; Yarin, Alexander; Bar-Yoseph, P. Z.

In: Physics of Fluids, Vol. 13, No. 11, 01.11.2001, p. 3185-3195.

Research output: Contribution to journalArticle

Gelfgat, AY, Yarin, A & Bar-Yoseph, PZ 2001, 'Three-dimensional instability of a two-layer Dean flow', Physics of Fluids, vol. 13, no. 11, pp. 3185-3195. https://doi.org/10.1063/1.1409967
Gelfgat, A. Yu ; Yarin, Alexander ; Bar-Yoseph, P. Z. / Three-dimensional instability of a two-layer Dean flow. In: Physics of Fluids. 2001 ; Vol. 13, No. 11. pp. 3185-3195.
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