Dense suspensions of solid particles immersed in a liquid are ubiquitous in industry and these suspensions exhibit rich, fascinating flow behaviour. Experiments and simulations have been conducted to understand the rheology of dense suspensions. Numerous theories and models have been developed based on these studies to explain and predict the flow behaviour of dense suspension systems. The discontinuous shear thickening behaviour  in dense suspensions can be explained as transitions from frictionless contacts between particles to frictional contacts , which indicates that the jamming volume fraction of a suspension interpolates between the frictional and frictionless jamming volume fractions with the proportionality being the fraction of frictional contacts. By simulating binary systems containing different proportions of frictional and frictionless particles, we find a non-linear interpolation between the "mixed" jamming volume fraction and the fraction of frictional contacts.
Recent results show that this non-linear correlation depends on the friction coefficient for interaction between pairs of frictional and frictionless particles, which indicates that additional parameters such as the spatial distribution of frictional contacts should be taken into consideration for predicting the viscosity of dense suspensions.
R. Seto, R. Mari, J. F. Morris, and M. M. Denn. Discontinuous shear thickening of frictional hard-sphere suspensions. Phys. Rev. Lett., 111:218301, 2013.
M. Wyart and M. E. Cates. Discontinuous shear thickening without inertia in dense nonbrownian suspensions. Phys. Rev. Lett., 112:098302, 2014.