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The shear rheology of dense colloidal and granular suspensions is stronglynonlinear, as these materials exhibit shear-thinning and shear-thickening,depending on multiple physical parameters. We numerically study the rheology ofa simple model of soft repulsive particles at large densities, and show thatnonlinear flow curves reminiscent of experiments on real suspensions can beobtained. By using dimensional analysis and basic elements of kinetic theory,we rationalize these multiple rheological regimes and disentangle the relativeimpact of thermal fluctuations, glass and jamming transitions, inertia andparticle softness on the flow curves. We characterize more specifically theshear-thickening regime and show that both particle softness and the emergenceof a yield stress at the jamming transition compete with the inertial effectsresponsible for the observed thickening behaviour. This allows us to constructa dynamic state diagram, which can be used to analyze experiments.

Thinning or thickening? Multiple rheological regimes in dense suspensions of soft particles