Our purpose is to estimate numerically the influence of particles on the global viscosity of fluid–particle mixtures. Particles are supposed to rigid, and the surrounding fluid is newtonian. The motion of the mixture is computed directly, i.e. all the particle motions are computed explicitly. Apparent viscosity, based on the force exerted by the fluid on the sliding walls, is computed at each time step of the simulation.In order to perform long–time simulations and still control the solid fraction, we assume periodicity of the flow in the shear direction.Direct simulations are based on the so–called Arbitrary Lagrangian Eulerian approach, which we adapted to make it suitable to periodic domains.As a first step toward modelling of interacting red cells in the blood, we propose a simple model of circular particles submitted to an attractive force which tends to form aggregates.