Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems pp 109-129 | Cite as

# Nonlinear Convection in Binary Mixtures

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## Abstract

The experimental observation of travelling wave convection^{1} has stimulated much of the recent work, both experimental and theoretical, on convection in binary fluids. Two systems have been extensively studied experimentally: ^{3}He-^{4}He mixtures above the λ-point^{2}, and water-ethanol mixtures^{3,4}. 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 patterns^{5}, 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 pattern^{6}.

## Keywords

Rayleigh Number Hopf Bifurcation Bifurcation Diagram Global Bifurcation Oscillatory Convection## Preview

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