A polydisperse suspension with a particle size distribution from submicrometer to hundreds of micrometers is treated as bimodal, wherein it is made up of a colloidal fine fraction and a noncolloidal coarse fraction. According to the bimodal model, the fine fraction imparts to the suspension its non-Newtonian characteristics and behaves independently of the coarse fraction, whereas the coarse particles only raise the apparent viscosity through hydrodynamic interactions. It is shown that when the particle microstructure is random, the contribution to the viscosity of the coarse fraction, which is generally polymodal, is characterized by lubrication concepts with the maximum packing fraction phi(m) as the scaling parameter. It is found that phi(m) is equal to the dry random packing fraction divided by a filler dilatancy factor of 1.19. The bimodal model and lubrication concepts have also been successfully applied to bidisperse suspensions with a very large particle size ratio. An inverse procedure is described that makes use of the results from viscosity and dry random packing measurements to divide a continuous size distribution into a colloidal and a noncolloidal fraction.