  We present a numerical study of nonlinear electrokinetic transport in porous
media, focusing on the role of heterogeneity in a porous microstructure on ion
concentration polarization and over-limiting current. For simplicity, the
porous medium is modeled as a network of long, thin charged cylindrical pores,
each governed by one-dimensional effective transport equations. For weak
surface conduction, when sufficiently large potential is applied, we
demonstrate that electrokinetic transport in a porous network can be dominated
by electroconvection via internally induced flow loops, which is not properly
captured by existing homogenized models. We systematically vary the topology
and "accessivity" of the pore network and compare with simulations of
traditional homogenized parallel-pore (capillary-bundle) models, in order to
reveal the effects of regular and hierarchical connectivity. Our computational
framework sheds light on the complex physics of nonlinear electrokinetic
phenomena in microstructures and may be used to design porous media for
applications, such as water desalination and purification by shock
electrodialysis.
