Shear-induced order in suspensions

A suspension of particles in a liquid is considered. Each particle is affected by forces due to the other particles, a drag force proportional to the velocity of the particles relative to the local velocity of the liquid and a fluctuating random noise. The effect of the particles on the velocity field of the liquid is neglected. The problem is mapped onto a quantum mechanical many-boson non-Hermitian system. It is shown within the random-phase approximation (RPA) that, for constant rate shear flow, the system of particles may become unstable against one-dimensional ordering (in parallel planes). The line of instability and the interplane distance are obtained for the hard sphere system.