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

Area of Science:

• Fluid Dynamics
• Chemical Physics
• Non-equilibrium Thermodynamics

Background:

• Ternary mixtures exhibit complex dynamics due to coupled diffusion and convection.
• The Soret effect, a thermodiffusion phenomenon, significantly influences mixture behavior under thermal gradients.
• Understanding these dynamics is crucial for applications involving multi-component systems.

Purpose of the Study:

• To experimentally and numerically investigate dynamic regimes in a toluene-methanol-cyclohexane mixture.
• To analyze the role of the Soret effect and cross-diffusion in pattern formation and instability.
• To elucidate the conditions leading to oscillatory instability in a thermogravitational column.

Main Methods:

• Experimental study using a thermogravitational column setup.
• Three-dimensional numerical simulations of the ternary mixture dynamics.
• Analysis of Soret coefficients, thermodiffusion, cross-diffusion, and convection.

Main Results:

• Observed primary long-wave instability manifesting as a standing wave.
• Identified secondary instability emerging as a swinging pattern.
• Demonstrated that oscillatory instability is contingent on a specific range of the cross-diffusion coefficient (D12).

Conclusions:

• Opposite signs of Soret and thermodiffusion coefficients for toluene trigger oscillatory instability.
• Cross-diffusion plays a critical role in the emergence and stability of oscillatory patterns.
• Instability transitions to stationary patterns (Turing-like or monotonic) outside the critical D12 range.