Hauptseminar Multiscale Simulations SS 2016/An electrokinetic LB based model for ion transport and macromolecular electrophoresis

More information will become available soon.

"{{{number}}}" is not a number.

Date

tba"tba" contains an extrinsic dash or other characters that are invalid for a date interpretation.

Topic

An electrokinetic LB based model for ion transport and macromolecular electrophoresis

Speaker

tba

Tutor

Michael Kuron

Contents

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.

Literature

• R. W. O'Brien, L. R. White.
  Electrophoretic Mobility of a spherical colloidal Particle.
  Journal of the Chemical Society, Faraday Transactions 2: Molecular and Chemical Physics 74(2):1607, 1978.
  [PDF] (3.2 MB) [DOI]
• Brian J. Kirby.
  Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices.
  Cambridge University Press, 2010. ISBN: 9781139489836.
  [DOI] [URL]
• Fabrizio Capuani, Ignacio Pagonabarraga, Daan Frenkel.
  Discrete solution of the electrokinetic equations.
  The Journal of Chemical Physics 121:973–986, 2004.
  [PDF] (592 KB) [DOI]
• U. D. Schiller.
  Thermal fluctuations and boundary conditions in the lattice Boltzmann method.
  PhD thesis, Johannes Gutenberg-Universität Mainz, 2008.
  [PDF] (938 KB) [DOI]
• Michael Kuron.
  Efficient Lattice Boltzmann Algorithms for Colloids Undergoing Electrophoresis.
  Master's thesis, University of Stuttgart, 2015.
  
• Giovanni Giupponi, Ignacio Pagonabarraga.
  Colloid Electrophoresis for Strong and Weak Ion Diffusivity.
  Physical Review Letters 106(24):248304, 2011.
  [PDF] (130 KB) [DOI] [URL]

- https://arxiv.org/abs/1604.02054