EGU General Assembly 2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

Thermo-chemo-mechanical coupling in Maxwell-Stefan multi-component diffusion

Lyudmila Khakimova1,2,3, Evangelos Moulas4, Ivan Utkin2,5, and Yury Podladchikov1,2
Lyudmila Khakimova et al.
  • 1Institute of Earth Sciences, University of Lausanne, Lausanne, Switzerland (
  • 2Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
  • 3Center for Hydrocarbon Recovery, Skolkovo Institute of Science and Technology, Moscow, Russia
  • 4Institute of Geosciences, Johannes Gutenberg University Mainz, Mainz, Germany
  • 5Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETH Zürich, Zürich, Switzerland

Classical Fickian linear diffusion of inert or trace-like elements is restricted to ideal solution models of components with equal molar mass. Simultaneous diffusion of multiple concentrations is well-treated by the classical Maxwell-Stefan model. Quantitative predictions of concentrations evolution in real mixtures require careful replacement of concentration gradients by gradients of chemical potentials. Coupling of multi component diffusion to mechanics result in pressure gradients that contribute to Gibbs-Duhem relationship. We aim at developing of thermodynamically admissible multicomponent thermo-chemo-mechanical (TMC) model with ensured non-negative entropy production. We also ensure correct equilibrium limit with zero gradients of chemical potentials of individual components and satisfaction of classical Gibbs-Duhem and Maxwell relationships under pressure gradients. Following recent Tajčmanová et al. (2021) we consider both molar and mass formulations. We present optimal pseudo-transient numerical scheme for multi-diffusional fluxes coupled to visco-elastic bulk deformation.

Tajčmanová, L., Podladchikov, Y., Moulas, E. and L. Khakimova. The choice of a thermodynamic formulation dramatically affects modelled chemical zoning in minerals. Sci Rep 11, 18740 (2021).

How to cite: Khakimova, L., Moulas, E., Utkin, I., and Podladchikov, Y.: Thermo-chemo-mechanical coupling in Maxwell-Stefan multi-component diffusion, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-11836,, 2022.