  We study the rheological behaviour of bidisperse suspensions in three
dimensions under a non-uniform shear flow, made by the superimposition of a
linear shear and a sinusoidal disturbance. Our results show that i) only a
streamwise disturbance in the shear-plane alters the suspension dynamics by
substantially reducing the relative viscosity, ii) with the amplitude of the
disturbance determining a threshold value for the effect to kick-in and its
wavenumber controlling the amount of reduction and which of the two phases is
affected. We show that, iii) the rheological changes are caused by the
effective separation of the two phases, with the large or small particles
layering in separate regions. We provide a physical explanation of the phase
separation process and of the conditions necessary to trigger it. We test the
results in the whole flow curve, and we show that the mechanism remains
substantially unaltered, with the only difference being the nature of the
interactions between particles modified by the phase separation.
