Transport of electrolytes in rock–formations, where the fluid paths are on the scale of micrometersdown to nanometers, are common in geology. If the rock–electrolyte interface is charged, the effecton flow–permeability can be rather dramatic on such a small scale due to the electric double layer.Good theoretical and numerical studies of such effects have been rather limited because of strongnon-linearities of the governing equations, which are even difficult to handle in simple geometries.However, in this work we present a numerical study of geometrical effects on electrohydrodynamicflow in a model fracture, a channel with sinusoidal varying depths. The simulations suggest thatelectrohydrodynamics leads to increased channeling of the flow which might be of importance in rockprecipitation and dissolution.Furthermore, electrolytes can also play a key role in two-phase flow as it can change the wettingproperties on a macroscopic scale, leading to vastly different transport properties. Such electrowettingeffects are present near charged rock–fluid–interfaces and play a vital role in settings where twoimmiscible fluids coexist in a porous media. To study such phenomena in pore–like geometries wehave performed a numerical study of two–phase electrohydrodynamics. In these simulations we haveseen clear evidence that the release of an electric–inert fluid from a charged pore can be driven byelectric–interactions between the pore-wall and the ions of electrolyte