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Traditional models of electrokinetic transport in porous media are based onhomogenized material properties, which neglect any macroscopic effects ofmicroscopic fluctuations. This perspective is taken not only for convenience,but also motivated by the expectation of irrotational electro-osmotic flow,proportional to the electric field, for uniformly charged surfaces (or constantzeta potential) in the limit of thin double layers. Here, we show that theinherent heterogeneity of porous media generally leads to macroscopic vortexpatterns, which have important implications for convective transport andmixing. These vortical flows originate due to competition betweenpressure-driven and electro-osmotic flows, and their size are characterized bythe correlation length of heterogeneity in permeability or surface charge. Theappearance of vortices is controlled by a single dimensionless controlparameter, defined as the ratio of a typical electro-osmotic velocity to thetotal mean velocity.

Vortices of Electro-osmotic Flow in Heterogeneous Porous Media