Rayleigh-Taylor instability in binary fluids with miscibility gap

TL;DR

This paper introduces a new phase field model to study the Rayleigh-Taylor instability in binary fluids with temperature-dependent miscibility, combining theoretical analysis and numerical simulations to explore early and late-stage dynamics.

Contribution

A novel phase field method is developed to model the transition from immiscible to miscible states in binary fluids and applied to analyze RT instability across different regimes.

Findings

Identified three growth rate zones based on Atwood and Weber numbers.

Numerical simulations confirm early-stage dispersion relation predictions.

Observed Kelvin-Helmholtz rolls and their dependence on temperature.

Abstract

A novel phase field method is proposed to model the continuous transition of binary fluids exhibiting temperature sensitive miscibility gap, from immiscible state to 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. The study reveals the early-stage growth characteristics of the interfacial perturbation. Three zones with distinct qualitative behaviour for the growth rate are identified as a function of Atwood number and Weber Number. Subsequently, 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. Further investigation of the late-time dynamics for viscous fluid pair reveal the tortuous topology presumed by the interface. The emanation of secondary instability in form of Kelvin-Helmholtz rolls is observed. The formation of Kelvin-Helmholtz rolls is found to be dependent on the system temperature. Finally, we present the effect of the slow nature of diffusion process.