In this paper, a simple shear flow of a dense suspension is studied. We propose a new constitutive relationship based on the second grade fluid model for the suspension, capable of exhibiting non-linear effects, where the normal stress coefficients are assumed to depend on the volume fraction of the particles and the shear viscosity depends on the shear rate and the volume fraction. After non-dimensionalizing the equations, we perform a parametric study looking at the effects of the normal stress coefficients and the variable viscosity. The numerical results show that for a certain range of parameters, the particles tend to form a region of high and uniform volume fraction, near the lower half of the flow.
