  Off-diagonal (transverse) effects in micro-patterned geometries are predicted
and analyzed within the general frame of linear response theory, relating
applied presure gradient and electric field to flow and electric current. These
effects could contribute to the design of pumps, mixers or flow detectors.
Shape and charge density modulations are proposed as a means to obtain sizeable
transverse effects, as demonstrated by focusing on simple geometries and using
the lubrication approximation.
