A two-sided subgrid-scale model for mass transfer across fluid interfaces

Abstract

The occurrence of extremely thin concentration boundary layers at fluid interfaces for high local P\'eclet numbers is a severe obstacle for efficient and accurate numerical simulation of mass transfer processes in two-phase fluid systems. Especially challenging are liquid-liquid systems, in which thin concentration boundary layers can appear on both sides of the fluid interface under convection-dominated conditions. In those cases, the one-sided species concentrations at the interface are a-priori not even known approximately, but are determined by a conjugate mass transfer problem governed by interfacial jump conditions. To the best of the authors' knowledge we for the first time introduce a two-sided Subgrid-Scale (SGS) boundary layer model for conjugate mass transfer at fluid interfaces. It accurately computes the local mass transfer rates on moderate or coarse mesh resolutions even when very high concentration gradients in interface vicinity occur. For this purpose, SGS modeling is applied on both sides of an interface transmissive to passive scalars, such as the interface in a two-phase fluid system, enabling the accurate capture of conjugate mass transfer across thin boundary layer on one or on both sides of the interface. We implement our approach in the unstructured Finite-Volume Arbitrary Lagrangian / Eulerian Interface-Tracking (ALE-IT) OpenFOAM module twoPhaseInterTrackFoam. We have made twoPhaseInterTrackFoam publicly available in our previous publication (Schwarzmeier et al., 2025).