Abstract: The present application relates to an apparatus for inducing motion of particles of one or more substances and to methods of designing the same. The apparatus has a chamber (15) and utilises a supply means (A) and a removal means (B, C) to cyclically supply and remove one or more substances from the chamber. The supply and removal means are configured so as to tend to maximise the degree of transversality in the crossing of streamlines of first and second flow patterns within a working region of the chamber. They are also configured so as to tend to maximise the area over which the velocity function of said first and second flow patterns varies monotonically within the working region.