Cross diffusion governs an oscillatory instability in a ternary mixture with the Soret effect

Abstract

In a ternary mixture with the Soret effect, the interplay between cross-diffusion, thermodiffusion, and convection can lead to rich and complex dynamics including spatial patterns and oscillations. We present an experimental and three-dimensional numerical study of dynamic regimes in the toluene–methanol–cyclohexane ternary mixture with the Soret effect in the geometry of a thermogravitational column. An important feature of the system is that for the first component, toluene, the Soret and thermodiffusion coefficients have opposite signs, which triggers the oscillatory instability. Our experiments and numerical analysis show that the primary long-wave instability manifests itself in the form of a standing wave, and the secondary one emerges in the form of a swinging pattern. The computational model provides insight into the role of cross-diffusion coefficient D₁₂ in the emergence and development of oscillatory instability. This study demonstrates that the long-wave oscillatory instability in transverse direction occurs only within a limited range of the D₁₂ values and outside of this range it decays to a stationary pattern of either Turing-like or monotonic instability.