Analog of discontinuous shear thickening flows under confining pressure

We use two-dimensional numerical simulations to study dense suspensions of non-Brownian hard particles using the Critical Load Model (CLM) under constant confining pressures. At constant packing fraction this simple model shows shear thickening as the tangential forces get activated upon increased shear stresses. By parameterizing a simple binary system of frictional and nonfrictional particles of different proportions we show that the jamming packing fraction, at which the viscosity diverges, is controlled by the fraction of frictional contacts. The viscosity of dense suspensions can thereby be expressed as a function of the fraction of frictional contacts as well as the packing fraction of solid particles. In addition, we show that there exists a simple relationship between the fraction of frictional contacts and the two control parameters (under confining pressure): the viscous number J and the ratio between the repulsive barrier force and confining pressure. Under confining pressures the viscosity curves are found to depend on the shear protocol, with the possibility of yielding negative dynamic compressibility, an analog to the discontinous shear thickening found at high but constant packing fractions for the same system.