The pair of fluids exhibiting temperature-sensitive miscibility gap and phase separation behavior are termed binary fluids with miscibility gap. The dynamic nature of the thermophysical properties allows deployment of such fluids in crucial microfluidic applications, such as enhancement of liquid-liquid mass transfer and flow pattern tuning, to name a few. Therefore, a thorough understanding is necessary to achieve the desired flow feature control. In the present study, a modified phase-field method is proposed to model the continuous transition of binary fluids from immiscible state to a miscible state via partially miscible states. The model is employed to investigate the isothermal single-mode Rayleigh-Taylor (RT) instability for binary fluids as the system temperature is varied. Assuming potential flow and utilizing Boussinesq approximation, we derived the dispersion relation for gravity-capillary waves and the RT instability. For early-time stages, three zones with distinct qualitative behavior for the growth rate are identified as a function of Atwood number and Weber number. Subsequently, the Boussinesq approximation is relaxed to obtain coupled Cahn-Hilliard-Navier-Stokes equations to perform numerical simulations. The results from the numerical simulations corroborate the findings from the dispersion relation at early stages, thereby establishing the validity of the proposed phase-field model. The emanation of secondary instability in the form of Kelvin-Helmholtz rolls is observed. Finally, we present the effect of the slow nature of the diffusion process as compared to the growth rate of the instability as the system is driven toward the state of complete miscibility, starting from a purely immiscible state.

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• Binary fluids
• Liquid-liquid phase transition
• Rayleigh-Taylor instability
• Phase-field modeling