The classical Nernst-Planck model suffers from its inability to accurately resolve boundary layers where locally large ion concentrations and pronounced voltage differences occur. In nanofluidic applications like nanopores with charged pore walls,
one spatial dimension is in the order of the Debye length which corresponds to the boundary layer width.
Improved models, in particular models that take the finite size of the ions into account, can give a more realistic description of the ion flow in the boundary layers.
Since typically the aspect ratio of the pore geometry is large the numerical discretization of the nanopore problem needs very fine meshes to resolve the layers, leading to extremely large algebraic systems to be solved.
By asymptotic analysis we derive a dimension reduced system 1D PDE system for averaged quantities plus a small algebraic system in each discretization point.
We compare our reduced 1D model to the full 2D model over a large range of bulk ion concentrations and boundary charges.
We demonstrate that improved material models lead to considerable deviations from solutions of the Nernst-Planck model.
Joint work with: J. Fuhrmann (WIAS), C. Guhlke (WIAS), B. Matejczyk (U Warwick)