A computational model for interfacial heat and mass transfer in two-phase flows using a phase field method

Abstract

Two-phase flows involving heat/mass transfer are widespread in industrial and environmental applications such as chemical reactors, bubbly flows, combustion, boiling, carbon sequestration, and ocean-atmosphere exchanges. It is therefore important to accurately predict the rate of heat/mass transfer across capillary interfaces via numerical simulations. Due to the absence of a well-defined interface, modeling interfacial transfer between two phases is particularly challenging for phase field (diffuse interface) models. In the context of second-order conservative phase field models, by assuming a microstructure that is consistent with the interfacial profile, we use perturbation theory and asymptotic analysis to derive interfacial heat/mass exchange terms that are consistent extensions of the underlying phase field equations. The developed two-scalar model is conservative, preserves positivity of total scalar concentration, and correctly predicts the transient and equilibrium solutions in all limits of diffusivity ratio. Additionally, we demonstrate that by assuming thermodynamic equilibrium in the microstructure, a more reduced model in the form of a one-scalar equation is derived. Several canonical and realistic simulations are presented to assess the consistency, accuracy, and convergence of the models. Crucially, while the one-scalar and two-scalar models both perform well when the two phases have comparable diffusivities, the two-scalar model is found to be much more accurate for realistic problems with large diffusivity ratios as it prevents unphysical leakage of heat/mass.