Nonlinear Convection in Binary Mixtures
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The experimental observation of travelling wave convection1 has stimulated much of the recent work, both experimental and theoretical, on convection in binary fluids. Two systems have been extensively studied experimentally: 3He-4He mixtures above the λ-point2, and water-ethanol mixtures3,4. Of these the former cannot be visualized, and the dynamics has to be inferred from point measurements. The experiments reveal the existence of both time-independent patterns5, and a variety of time-dependent travelling waves 3,4. The latter are small amplitude states that come into existence near the Hopf bifurcation from the pure conduction state. This bifurcation occurs in binary fluid mixtures characterized by a sufficiently negative separation ratio S. This ratio provides a measure of the stabilizing concentration gradient set up in response to a destabilizing temperature gradient by the (negative) Soret effect. With increasing Rayleigh number the conduction state loses stability to growing oscillations provided the restoring force due to the concentration gradient is sufficiently strong to overcome viscous dissipation. The instability occurs because heat diffuses faster than concentration, setting up a phase difference between the concentration and temperature fields, which persists into the nonlinear regime, regardless of whether the instability evolves into a travelling or standing pattern6.
KeywordsRayleigh Number Hopf Bifurcation Bifurcation Diagram Global Bifurcation Oscillatory Convection
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