Heat and Mass Transfer

, Volume 54, Issue 3, pp 697–713 | Cite as

Validation of a numerical method for interface-resolving simulation of multicomponent gas-liquid mass transfer and evaluation of multicomponent diffusion models

  • Mino Woo
  • Martin WörnerEmail author
  • Steffen Tischer
  • Olaf Deutschmann


The multicomponent model and the effective diffusivity model are well established diffusion models for numerical simulation of single-phase flows consisting of several components but are seldom used for two-phase flows so far. In this paper, a specific numerical model for interfacial mass transfer by means of a continuous single-field concentration formulation is combined with the multicomponent model and effective diffusivity model and is validated for multicomponent mass transfer. For this purpose, several test cases for one-dimensional physical or reactive mass transfer of ternary mixtures are considered. The numerical results are compared with analytical or numerical solutions of the Maxell-Stefan equations and/or experimental data. The composition-dependent elements of the diffusivity matrix of the multicomponent and effective diffusivity model are found to substantially differ for non-dilute conditions. The species mole fraction or concentration profiles computed with both diffusion models are, however, for all test cases very similar and in good agreement with the analytical/numerical solutions or measurements. For practical computations, the effective diffusivity model is recommended due to its simplicity and lower computational costs.

List of symbols


Molar concentration of species i (mol m−3)


Reference concentration (mol m−3)


Total molar concentration of mixture (mol m−3)


Concentration normalized by c ref (−)

Di , j

Fick diffusion coefficient in the GFL diffusivity matrix (m2 s−1)

Ði , j

Maxwell-Stefan diffusion coefficient for species pair i and j (m2 s−1)

Di , eff

Effective diffusivity of species i (m2 s−1)


Volume fraction of liquid phase (−)


Henry number of species i (−)


Length of computational domain (m)

ji ,  ji

Diffusive molar flux relative to molar-average velocity (mol m−2 s−1)

\( {j}_i^{\mathrm{V}},\kern0.5em {\mathbf{j}}_i^{\mathrm{V}} \)

Diffusive molar flux relative to volume-average velocity (mol m−2 s−1)


Species vector of diffusive molar fluxes, J = (j 1, j 2, …, j n − 1)T (mol m−2 s−1)


Reaction constant (m s−1)


Time step index (−)


Molecular weight of species i (g mol−1)


Number of species (−)


Molar flux (mol m−2 s−1)

Pei , j

Binary Péclet number (−)


Reference Péclet number (−)


Reactive source term of species i in Eq. (5) (mol m−3 s−1)

\( {r}_i^{\mathrm{V}} \)

Reactive source term of species i in Eq. (6) (mol m−3 s−1)

\( {\dot{s}}_i \)

Reaction rate (mol m−2 s−1)

\( {\dot{S}}_i \)

Non-dimensional reaction rate (−)


Time (s)


Partial velocity of species i (m s−1)

u ,  u

Molar-average velocity (m s−1)

uV ,  uV

Volume-average velocity (m s−1)

uM ,  uM

Mass-average velocity (m s−1)

\( {\overline{V}}_i \)

Partial molar volume of species i (m3 mol−1)

\( {\overline{V}}_{\mathrm{t}} \)

Total molar volume of mixture, \( {\overline{V}}_{\mathrm{t}}=1/{c}_{\mathrm{t}} \) (m3 mol−1)


Mole fraction of species i (−)


Coordinate of one-dimensional problem (m)


Non-dimensional coordinate, Z = z/L ref (−)

Greek symbols


Degree of dilution (−)


Stoichiometric coefficient (−)


Partial mass density of species i (kg m−3)


Total mass density (kg m−3)


Non-dimensional time (−)


Mass fraction of species i (−)





Species index




Gas phase


Liquid phase


Two-phase mixture quantity






Initial value





Mass average


Volume average



Continuous concentration diffusivity model


Effective diffusivity model


Generalized Fick law


Multicomponent model




Non-equilibrium stage model



We gratefully acknowledge the funding of this project by Helmholtz Energy Alliance “Energy Efficient Chemical Multiphase Processes” (HA-E-0004) and thank the Steinbeis GmbH & Co. KG für Technologietransfer (STZ 240 Reaktive Strömung) for a cost-free academic license of DETCHEM™.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institute of Catalysis Research and TechnologyKarlsruhe Institute of Technology (KIT)KarlsruheGermany
  2. 2.Institute for Chemical Technology and Polymer ChemistryKarlsruhe Institute of Technology (KIT)KarlsruheGermany

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