A new two-phase numerical model for species transfer in bubble flows: Comparison with the one-fluid method

Abstract

We present a robust, accurate, and computationally efficient numerical strategy for modeling species transfer across immiscible fluid interfaces on Cartesian meshes. The method provides an efficient alternative to the classical one-fluid approach while retaining its algorithmic simplicity and limited computational overhead. The proposed framework relies on a two-phase formulation in cut cells, combining dedicated phase reconstructions with a simple and robust mass-flux approximation to accurately enforce interfacial jump conditions.

The method is first assessed against analytical solutions for pure diffusion in both static and moving configurations. Compared with the standard one-fluid model, we demonstrate that appropriate phase reconstructions for the advection and the temporal scheme significantly improve the accuracy of the concentration field, including mean mass fluxes and interfacial concentrations.

The approach is then validated on fully coupled three-dimensional simulations of mass transfer on rising bubbles. The computed Sherwood numbers are compared with established numerical results from the literature. While the Sherwood number is shown to be an unreliable indicator of concentration-field accuracy, the proposed schemes provide accurate and robust mass transfer predictions over a wide range of grid resolutions. Overall, the method achieves a substantial gain in accuracy for interfacial mass transfer at a computational cost that is comparable to the classical one-fluid formulations.

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BibTeX RIS

BibTeX

@article{djaballah2026twophase,
  title = {{A new two-phase numerical model for species transfer in bubble flows: Comparison with the one-fluid method}},
  author = {N. Djaballah and B. Trouette and E. Chénier and C. Selçuk and S. Vincent},
  journal = {Computers and Fluids},
  year = {2026},
  month = sep,
  doi = {10.1016/j.compfluid.2026.107271},
  url = {https://hal.science/hal-05848555v1},
  note = {CC BY 4.0},
}

RIS

TY  - JOUR
TI  - A new two-phase numerical model for species transfer in bubble flows: Comparison with the one-fluid method
AU  - N. Djaballah
AU  - B. Trouette
AU  - E. Chénier
AU  - C. Selçuk
AU  - S. Vincent
PY  - 2026
DA  - 2026/09/07
JO  - Computers and Fluids
DO  - 10.1016/j.compfluid.2026.107271
UR  - https://hal.science/hal-05848555v1
AB  - We present a robust, accurate, and computationally efficient numerical strategy for modeling species transfer across immiscible fluid interfaces on Cartesian meshes. The method provides an efficient alternative to the classical one-fluid approach while retaining its algorithmic simplicity and limited computational overhead. The proposed framework relies on a two-phase formulation in cut cells, combining dedicated phase reconstructions with a simple and robust mass-flux approximation to accurately enforce interfacial jump conditions.  The method is first assessed against analytical solutions for pure diffusion in both static and moving configurations. Compared with the standard one-fluid model, we demonstrate that appropriate phase reconstructions for the advection and the temporal scheme significantly improve the accuracy of the concentration field, including mean mass fluxes and interfacial concentrations.  The approach is then validated on fully coupled three-dimensional simulations of mass transfer on rising bubbles. The computed Sherwood numbers are compared with established numerical results from the literature. While the Sherwood number is shown to be an unreliable indicator of concentration-field accuracy, the proposed schemes provide accurate and robust mass transfer predictions over a wide range of grid resolutions. Overall, the method achieves a substantial gain in accuracy for interfacial mass transfer at a computational cost that is comparable to the classical one-fluid formulations.
SN  - 0045-7930
SN  - 1879-0747
ER  -

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