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.  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. This combination is particularly useful for soft matter simulations, due to the ability to couple particles to the lattice-Boltzmann fluid. These could, e.g., be charged colloids or polymers, which then interact with an ion distribution. We describe one implementations based on the automatic code generation tools pystencils and lbmpy, and another one that is contained in the molecular dynamics package ESPResSo and that allows for an easy coupling of particles to the density fields. We validate our implementations by comparing to several known analytic results. Our method can be applied to coarse-grained catalysis problems as well as to many other multi-scale problems that require the coupling of explicit-particle simulations to flow fields, diffusion, and reaction problems in arbitrary geometries.
Better description of the used LB. Explained the solving of the Poisson equation via Fourier transformation. Added numerical works showing the grid independence. Added numerical works towards the reaction-diffusion-advection channel.