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

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.

Measurements of molecular and thermal diffusion coefficients in ternary mixtures.

Thermal diffusion coefficients in three ternary mixtures are measured in a thermogravitational column. One of the mixtures consists of one normal alkane and two aromatics (dodecane-isobutylbenzene-tetrahydronaphthalene), and the other two consist of two normal alkanes and one aromatic (octane-decane-1-methylnaphthalene). This is the first report of measured thermal diffusion coefficients (for all species) of a ternary nonelectrolyte mixture in literature. The results in ternary mixtures of octane-decane-1-methylnaphthalene show a sign change of the thermal diffusion coefficient for decane as the composition changes, despite the fact that the two normal alkanes are similar. In addition to thermal diffusion coefficients, molecular diffusion coefficients are also measured for three binaries and one of the ternary mixtures. The open-end capillary-tube method was used in the measurement of molecular diffusion coefficients. The molecular and thermal diffusion coefficients allow the estimation of thermal diffusion factors in binary and ternary mixtures. However, in the ternaries one also has to calculate phenomenological coefficients from the molecular diffusion coefficients. A comparison of the binary and ternary thermal diffusion factors for the mixtures comprised of octane-decane-1-methylnaphthalene reveals a remarkable difference in the thermal diffusion behavior in binary and ternary mixtures.