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

TL;DR

The paper tackles the numerical challenge of simulating mass transfer across fluid interfaces when extremely thin boundary layers exist on both sides under convection-dominated conditions. It extends subgrid-scale (SGS) modeling to handle conjugate transfer with two-sided, interface-transmissive boundary conditions, including cases with unknown far-field concentrations $c_ty$, within an ALE-IT/OpenFOAM framework. Key contributions are a linear Dirichlet-Dirichlet coupling for conjugate transfer, robustness enhancements for tiny boundary-layer parameters, a novel two-sided SGS algorithm (TOS-F-SGS) with nested iterations, and a comprehensive validation suite comprising a one-sided flat plate, a two-sided planar interface, and a moving droplet. The results demonstrate high accuracy, mesh-independence of local fluxes and boundary layers, and practical applicability to complex multiphase mass-transfer problems in engineering systems.

Abstract

The occurrence of extremely thin concentration boundary layers at fluid interfaces for high local Péclet 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).

Figures (21)

• Figure 1: Definition of the solution domain for the ALE-IT method
• Figure 2: Concentrations at the interface for resolved simulations
• Figure 3: Surfactant interface concentration at $t=5e-5s$
• Figure 4: Minimum boundary layer thickness $\overline{\delta}$
• Figure 5: Effect of the minimum boundary layer thickness