Kelvin–Helmholtz instability in binary fluids with miscibility gap

The isothermal spatiotemporal evolution of an interface between binary fluids, with temperature-sensitive miscibility gap, subjected to shear flow is investigated using direct numerical simulations. The thermophysical properties and the interfacial tension in such fluids exhibit a dynamic temperature dependence based on the degree of miscibility. These fluid pairs can therefore be deployed in crucial microfluidic applications involving enhancement of liquid–liquid mass transfer. In this study, a modified phase-field approach that allows modeling of partially miscible fluids and continuous transition from an initially immiscible state to a completely miscible state is employed to investigate the Kelvin–Helmholtz (KH) instability. The analysis entails two different configurations based on the thermodynamic state of the system. In the first configuration, the fluid pair is considered in equilibrium at different degrees of partially miscibility. The results reveal the effect of apparent surface tension in miscible fluids, shear flow profile, the degree of stratification, the density ratio, and the effect of mass redistribution across the interface. The shear instability in a fluid pair close to the consolute point is found to be independent of the extent of stratification. The second configuration, on the other hand, deals with fluid pair considered at a temperature above the upper critical solution temperature, thereby leading to non-equilibrium configuration. The study reveals the existence of the diffusion-dominated regime and the advection-dominated regime in the process of the development of the KH instability. The prevalence of these regimes is found to be governed by the combination of the initial degree of partial miscibility and the corresponding initial surface tension of the binary fluid pair.