A diffuse-interface analysis of two-phase thermo-convective instabilities

Abstract

Two-phase flows are ubiquitous in natural and industrial settings. In the present work, we have developed a general ‘one-fluid’ diffuse-interface model suitable for various two-phase flow problems. The specific two-phase problem considered in the current work involves a binary fluid system, which poses a unique property of being miscible in each other depending on the system’s temperature and is completely miscible above a particular temperature, called the upper critical solution temperature (UCST). Accordingly, we have developed a spectral collocation-based phase field model to study the onset characteristics of Rayleigh-Bénard convection in a two-layer binary fluid system. We have also considered the Marangoni effect (variation of surface tension) in addition to the pure buoyancy-driven instability to examine how the strength of surface tension gradient can alter the onset behavior of the system. We have observed that the strength of the Marangoni effect can expand or contract the oscillatory onset window observed in the case of pure buoyancy-driven convection. The solubility of the system acts in unison with the interfacial tension term and comes with its own dual role in making the onset of convection either oscillatory or stationary