Pattern selection in steady binary-fluid convection

Mary Silber*, Edgar Knobloch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

Three-dimensional convection in a binary-fluid mixture is studied near the onset of the steady-state instability using symmetric bifurcation theory. Idealized boundary conditions are assumed in which the temperature and solute concentration are fixed at top and bottom, with stress-free boundary conditions on the velocity field. The effects of sidewalls are neglected. The problem is formulated as a bifurcation problem on a doubly periodic lattice, with two cases considered in detail: the square lattice and the hexagonal lattice. Symmetry considerations determine the form of the ordinary differential equations governing the dynamics of the neutrally stable modes. The relevant coefficients of these equations are calculated from the governing binary-fluid equations. The bifurcation diagrams are given for all physical values of the separation ratio, the Lewis number, and the Prandtl number. It is found that supercritical rolls are stable to all perturbations lying on the square and hexagonal lattices. Squares, hexagons, and triangles are never stable for the physically accessible regions of parameter space.

Original languageEnglish (US)
Pages (from-to)1468-1477
Number of pages10
JournalPhysical Review A
Volume38
Issue number3
DOIs
StatePublished - 1988

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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