  In low-permeability rock, fluid and mineral transport occur in pores and
fracture apertures at the scale of micrometers and below. At this scale, the
presence of surface charge, and a resultant electrical double layer, may
considerably alter transport properties. However, due to the inherent
non-linearity of the governing equations, numerical and theoretical studies of
the coupling between electric double layers and flow have mostly been limited
to two-dimensional or axisymmetric geometries. Here, we present comprehensive
three-dimensional simulations of electrohydrodynamic flow in an idealized
fracture geometry consisting of a sinusoidally undulated bottom surface and a
flat top surface. We investigate the effects of varying the amplitude and the
Debye length (relative to the fracture aperture) and quantify their impact on
flow channeling. The results indicate that channeling can be significantly
increased in the plane of flow. Local flow in the narrow regions can be slowed
down by up to $5 \%$ compared to the same geometry without charge, for the
highest amplitude considered. This indicates that electrohydrodynamics may have
consequences for transport phenomena and surface growth in geophysical systems.
