1. Symposyium du Département de Chimie Analytique, Minérale et Appliquée Davide Alemani – University of Geneva Lattice Boltzmann (LB) and time splitting method for reaction-diffusion modelling 1.Reaction-diffusion in the environment. 2.The LB approach: why and how 3.The time splitting method: why and how 4.Some numerical results 5.Work in progress: grid refinement

2. The environmental problem

3. Schematic representation of various chemical species of a given element (M)

4. Schematic representation of the physicochemical problem under investigation Metal concentration: 10 -7 mol/m 3 - 10 -3 mol/m 3 Diffusion coefficient: 10 -12 m 2 /s - 10 -9 m 2 /s Kinetic rate constants: 10 -6 s -1 - 10 9 s -1

5. M L ML LB approach: Why and how Macroscopic Model Mesoscopic Model (LB)

6. The LBGK model (1D) LBGK Evolution Equations Flux Computation Schematic Representation (1D)

7. Time splitting method: Why and How Important when physical and chemical processes occur simultaneously and rate constants vary over many order of magnitudes Enables to split a complex problem into two or more sub-problems more simply handled NS RD

8. M L ML A detailed example of Time Splitting (RD) coupled with LBGK approach

9. Flux at the electrode for a semilabile complex Labile flux: Inert flux: Numerical flux:

10. Comparison between RD and NS with an exact solution Red circle values are taken from: De Jong et al., JEC 1987, 234, 1

11. Flux at the electrode for two complexes ML (1) and ML (2) with very different time scale reaction rates Labile flux: Inert flux: Numerical flux: M+L (1)  ML (1) labile – M+L (2)  ML (2) inert

12. Concentration profiles close to the electrode Strong variation close to the electrode surface M+L (1)  ML (1) labile – M+L (2)  ML (2) inert

13. Error vs grid size and the equilibrium constant

15. Work in progress M + L (n)  ML (n) Problem to solve A grid refinement approach for solving LBGK scheme

16. Conservation of mass and flux at the grid interface Work in progress A grid refinement approach for solving LBGK scheme

17. That’s all. Thanks to come Hoping to have been clear Have a nice day