A new differential (or multi-scale, mean field approach) model for the relative viscosity of bimodal suspensions is discussed in this paper. Solid spherical particles with a bimodal size distribution in a Newtonian solvent are considered. The problem of random close packing for a bidisperse system is studied. The bounds on volume fractions are given by o.639 < ${varphi}_{bm}$ < 0.869, where the random close packing volume fraction for a monodisperse system, ${varphi}_{rcp}$ = 0.639, is assumed. We propose that the bimodal suspension has a dominant large particle composition and that the small particles fill the empty spaces between the large particles. The model can therefore be based on the theory of monodisperse suspensions. The predictions of the relative viscosity for several bimodal suspensions given by the model are compared to experimental measurements. A reasonably good agreement is observed.