Hauptseminar Soft Matter SS 2019/Modelling and simulation of catalytically driven particles
- Modelling and simulation of catalytically-driven particles
- Jan Finkbeiner
- Michael Kuron
In this talk, a continuum method for the treatment of electrokinetics will be introduced. When combined with a simple scheme for chemical reactions, this allows for the treatment of chemically-propelled swimmers. Electrokinetics refers to the coupled occurence of hydrodynamics and diffusion, advection and migration of dissolved chemical species. Thanks to a separation of time scales, many systems do not need explicit treatment neither of water nor of solutes and computational efficiency can therefore be gained by discretizing the continuum equations on a lattice.
For hydrodynamics, the lattice-Boltzmann method, discussed in a previous topic, can be used. For diffusion-advection-migration, the lattice electrokinetics method by Capuani et al. is the method of choice. By adding a simple scheme based on the stoichiometric coefficients and rate constant of a chemical reaction, the propulsion can be described as a flux boundary condition for the diffusion-advection-migration scheme.
First, the underlying system of continuum equations, often referred to as Poisson-Nernst-Planck, is introduced. This includes Fick's diffusion equation and Poisson's equation for electrostatics. Second, the discretization by Capuani et al. is constructed and it is shown that applicable in the same limit as Poisson-Boltzmann. Finally, the application to the study of individual and multiple swimmers is sketched out and some results are summarized.