Onset of thermo-convective instabilities in two-layer binary fluid systems

The current work analyses the onset characteristics of buoyancy and thermocapillary-driven instabilities in two-layer binary fluid systems near their upper critical solution temperature (UCST). To account for the non-trivial thickness of the fluids’ interface and the temperature-dependent solubility in such regimes, the present analysis utilises the phase-field approach with a modified free-energy expression. The spatial discretisation of the field variables is carried out here using the spectral collocation approach with a suitable grid mapping strategy to accurately evaluate the field gradients around the diffuse-interface region. The results reveal that in the case of pure buoyancy-driven (Rayleigh–Bénard) convection, the parametric range for oscillatory onset is found to shrink when the system approaches the UCST, as the increased solubility results in less favourable conditions for oscillatory onset. The marginal stability curves of different fluid combinations considered here exhibit unique drift patterns based on their thermo-physical and transport properties. For systems with added thermocapillarity effects (Rayleigh–Bénard–Marangoni convection), the changing solubilities and the interfacial thickness, like the interfacial tension, exhibit a dual role that results in system-specific expansion/shrinkage of the parametric space for oscillatory flow onset.