We show that when particles are suspended in an electrolyte confined between
corrugated charged surfaces, electrokinetic flows lead to a new set of
phenomena such as particle separation, mixing for low-Reynolds micro- and
nano-metric devices and negative mobility. Our analysis shows that such
phenomena arise, for incompressible fluids, due to the interplay between the
electrostatic double layer and the corrugated geometrical confinement and that
they are magnified when the width of the channel is comparable to the Debye
length. Our characterization allows us to understand the physical origin of
such phenomena therefore shading light on their possible relevance in a wide
variety of situations, ranging from nano- and micro-fluidic devices to
biological systems