Models and numerical methods for electrolyte flows
- Fuhrmann, Jürgen
- Guhlke, Clemens
- Linke, Alexander
- Merdon, Christian
- Müller, Rüdiger
2010 Mathematics Subject Classification
- 35Q35 35Q61 78A57 80A17
- Electro-thermodynamics, electroosmosis, ion transport, finite ion size, solvation
The most common mathematical models for electrolyte flows are based on the dilute solution assumption, leading to a coupled system of the Nernst--Planck--Poisson drift-diffusion equations for ion transport and the Stokes resp. Navier--Stokes equations for fluid flow. This contribution discusses historical and recent model developments beyond the dilute solution assumption and focuses on the effects of finite ion sizes and solvation. A novel numerical solution approach is presented and verified here which aims at preserving on the discrete level consistency with basic thermodynamic principles and structural properties like independence of flow velocities from gradient contributions to external forces.
- Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 183--209.