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

03 September 2021, Version 1
This content is a preprint and has not undergone peer review at the time of posting.

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.

Keywords

Reaction-Advection-Diffusion

Supplementary materials

Title
Description
Actions
Title
fluctuating_reactive_ek.ipynb
Description
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.
Actions
Title
poisson.py
Description
A script to solve the poisson equation using pystencils. This script is being imported in the 'fluctuating_reactive_ek.ipynb' notebook.
Actions
Title
ideal_gas_md_hist.dat
Description
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.
Actions
Title
coulomb_gas_md_hist.dat
Description
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.
Actions

Comments

Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.