Analysis of Marangoni Effects on the Non-isothermal Immiscible Rayleigh-Taylor Instability

Abstract

• Hydrodynamics and heat transfer of immiscible Rayleigh-Taylor Instability (RTI) with thermocapillary effect are studied. • A critical range of Marangoni numbers that result in the suppression of the RTI is found. • The dependence of the critical range of Marangoni numbers on the density of the fluids has been explained. • The contribution of the forces was found to vary non-monotonically with the Marangoni number. • All the above-mentioned nonmonotonicities are explained in terms of the vorticity and enstrophy of the system. Non-isothermal Rayleigh-Taylor Instability (RTI) has been investigated for incompressible, Newtonian, immiscible flows. Thermal gradients were triggered by imposing a cold and a hot temperature at the top and the bottom side of the domain, respectively. The effects of thermocapillary stresses resulting from temperature-induced interfacial tension gradients were investigated. The governing equations together with a conservative phase-field equation to track the interface, were solved numerically using the Lattice Boltzmann Method. The investigation focused on analyzing the effects of the Marangoni number and fluids density ratio and comparison of the flows of the isothermal and the non-isothermal cases when Marangoni effects are neglected. The results revealed that thermocapillary effects can change the instability characteristics by slowing down the usual downward flow or even inducing and sustaining an upward flow. This reversed flow phenomenon was found to occur only within an interval of the Marangoni numbers, outside of which the typical downward flow is observed again. The effects of the density ratio on this reversed flow phenomenon were analyzed. The phenomenon was characterized, and the underlying physics were explained by analyzing the flow dynamics and examining the relative contribution of the forces acting on the interface. In particular, the competing effects of the temperature gradients on the components of the interfacial tension along and normal to the interface, were found to play a major role. This study offers a new perspective for the control and orientation of the interface deformation and motion via thermocapillary stresses.