Ordering transition of non-Brownian suspensions in confined steady shear flow

We report on ordering transitions of concentrated non-Brownian suspensions confined by two parallel walls under steady shear. At a volume fraction as low as phi=0.48, particles near the wall assemble into strings which are organized as a simple hexagonal array by hydrodynamic interactions. The suspension exhibits a complex phase behavior depending on the ratio of the channel height to the particle radius, H-y/a. In a strongly confined system H-y/a < 12, the order state and rheology depend on the commensurability between particle layers and the channel height. At phi=0.60, the order structure in the horizontal plane changes between hexagonal and rectangular structures depending on H-y/a. It is shown that the relative viscosity is a function of both the volume fraction and the ordered state.