Physical Chemistry

A thermalized electrokinetics model including stochastic reactions suitable for multiscale simulations of reaction-advection-diffusion systems

Authors

Abstract

We introduce a scheme to simulate the spatial and temporal evolution of the densities of charged species, taking into account diffusion, thermal fluctuations, coupling to a carrier fluid, and chemical reactions. To this end, the diffusive fluxes in the electrokinetic model by Capuani et al. [1] are supplemented with thermal fluctuations. Chemical reactions are included via an additional source term in the mass balance equation. The diffusion-reaction model is then coupled to a solver for fluctuating hydrodynamics based on the lattice Boltzmann method. We describe our implementations, one based on the automatic code generation tools using pystencils and lbmpy, and another one contained as in the molecular dynamics package ESPResSo which allows the coupling of particles to the density fields. We validate our implementations by demonstrating that the expected influence of density fluctuations on the reaction rate for chemical reactions of order > 1 is reproduced. Our novel algorithm will be applicable to coarse-grained catalysis problems as well as to many other multi-scale problems that require the coupling of explicit-particle simulations with flow fields, diffusion, and reaction problems in arbitrary geometries.

Content

Thumbnail image of A thermalized electrokinetics model including stochastic reactions suitable for multiscale simulations of reaction-advection-diffusion systems.pdf

Supplementary material

Thumbnail image of fluctuating_reactive_ek.ipynb
fluctuating_reactive_ek.ipynb
Jupyter notebook to demonstrate the themalized reaction-advection-diffusion algorithm which is being implemented using pystencils. To fully run this script the other 3 files ('poisson.py', 'ideal_gas_md_hist.dat' and 'coulomb_gas_md_hist.dat') are required.
Thumbnail image of poisson.py
poisson.py
A script to solve the poisson equation using pystencils. This script is being imported in the 'fluctuating_reactive_ek.ipynb' notebook.
Thumbnail image of ideal_gas_md_hist.dat
ideal_gas_md_hist.dat
Density probability histogram data of an ideal gas MD simulation. This data is being compared to the data obtained by the 'fluctuating_reactive_ek.ipynb' notebook.
Thumbnail image of coulomb_gas_md_hist.dat
coulomb_gas_md_hist.dat
Density probability histogram data of an coulomb gas MD simulation. This data is being compared to the data obtained by the 'fluctuating_reactive_ek.ipynb' notebook.