Hauptseminar Active Matter SS 2017/Lattice Boltzmann Modeling of Chemical Swimmers

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Date

2017-05-17

Time

canceled

Topic

Lattice Boltzmann Modeling of Chemical Swimmers

Speaker

Matthias Bayerbach

Tutor

Michael Kuron

Contents

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.

Literature

• 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]
• Georg Rempfer, Gary B. Davies, Christian Holm, Joost de Graaf.
  Reducing spurious flow in simulations of electrokinetic phenomena.
  The Journal of Chemical Physics 145(4):044901, 2016.
  [PDF] (3.1 MB) [DOI]
• Michael Kuron.
  Efficient Lattice Boltzmann Algorithms for Colloids Undergoing Electrophoresis.
  Master's thesis, University of Stuttgart, 2015.
  
• Michael Kuron, Georg Rempfer, Florian Schornbaum, Martin Bauer, Christian Godenschwager, Christian Holm, Joost de Graaf.
  Moving charged particles in lattice Boltzmann-based electrokinetics.
  The Journal of Chemical Physics 145(21):214102, 2016.
  [PDF] (718 KB) [DOI]