AMaSiS 2018 Workshop: Abstracts

Poster Models and numerical methods for electroosmotic flow with finite ion effects

Jürgen Fuhrmann, Clemens Guhlke, Alexander Linke, Christian Merdon, and Rüdiger Müller

Weierstrass Institute for Applied Analysis and Stochastics

We present a recently developed geometrically flexible approach to simulate electroosmotic flows, based on quality preserving finite element and finite volume discretization methods.

This approach combines a pressure robust, divergence free mixed finite element method on unstructured meshes [1, 2] with a thermodynamically consistend finite volume method for the discretization of ion drift and diffusion in a self-consistent electric field based on a generalized Nernst-Planck-Poisson system which takes into account finite ion size and solvation effects [3, 4]. We provide recent results of numerical simulations of elecroosmotic flows in nanopores confirming the validity and the advantages of the discretization approach [5].

Acknowledgments: German Federal Ministry of Education and Research Grant 03EK3027D (Network “Perspectives for Rechargeable Magnesium-Air batteries”), Einstein Center of Mathematics, Berlin, project CH11 “Sensing with Nanopores”.

References

  • 1 A. Linke. On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime. Computer methods in applied mechanics and engineering, 268:782–800, 2014.
  • 2 V. John, A. Linke, C. Merdon, M. Neilan, and L. G. Rebholz. On the divergence constraint in mixed finite element methods for incompressible flows. SIAM Review, 59(3):492–544, 2017.
  • 3 W. Dreyer, C. Guhlke, and R. Müller. Overcoming the shortcomings of the Nernst–Planck model. PCCP, 15(19):7075–7086, 2013.
  • 4 J. Fuhrmann. A numerical strategy for Nernst-Planck systems with solvation effect. Fuel cells, 16(6):704–714, 2016.
  • 5 J. Fuhrmann, C. Guhlke, A. Linke, Ch. Merdon, and R. Müller. Models and numerical methods for electrolyte flows. Preprint 2525, WIAS Berlin, 2018.