Hauptseminar Multiscale Simulations SS 2016/An electrokinetic LB based model for ion transport and macromolecular electrophoresis
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- An electrokinetic LB based model for ion transport and macromolecular electrophoresis
- Michael Kuron
In this topic, a continuum method for the treatment of hydrodynamics and diffusion, advection and migration of salt ions will be discussed. 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.
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. Third, the Standard Electrokinetic Model by O'Brien and White is introduced and it is explained how this perturbation theory approach can be used to solve the case of a spherical particle. The Capuani method, on the other hand, is much more generic and applicable to arbitrary complex geometries. Finally, coupling of colloids and polymers to the water and salt system is discussed. Such particles can either be treated via force coupling or as boundary conditions.