Density profiles of a colloidal liquid at a wall under shear flow

Using a dynamical density functional theory we analyse the density profile of a colloidal liquid near a wall under shear flow. Due to the symmetries of the system considered, the naive application of dynamical density functional theory does not lead to a shear induced modification of the equilibrium density profile, which would be expected on physical grounds. By introducing a physically motivated dynamic mean field correction we incorporate the missing shear induced interparticle forces into the theory. We find that the shear flow tends to enhance the oscillations in the density profile of hard spheres at a hard wall and, at sufficiently high shear rates, induces a non-equilibrium transition to a steady state characterized by planes of particles parallel to the wall. Under gravity, we find that the centre of mass of the density distribution increases with shear rate, i.e. shear increases the potential energy of the particles.