  Particles suspended in a Newtonian fluid raise the viscosity and also
generally give rise to a shear-rate dependent rheology. In particular,
pronounced shear thickening may be observed at large solid volume fractions. In
a recent article (R. Seto, R. Mari, J. F. Morris, and M. M. Denn., Phys. Rev.
Lett., 111:218301, 2013) we have considered the minimum set of components to
reproduce the experimentally observed shear thickening behavior, including
Discontinuous Shear Thickening (DST). We have found frictional contact forces
to be essential, and were able to reproduce the experimental behavior by a
simulation including this physical ingredient along with viscous lubrication.
In the present article, we thoroughly investigate the effect of friction and
express it in the framework of the jamming transition. The viscosity divergence
at the jamming transition has been a well known phenomenon in suspension
rheology, as reflected in many empirical laws for the viscosity. Friction can
affect this divergence, and in particular the jamming packing fraction is
reduced if particles are frictional. Within the physical description proposed
here, shear thickening is a direct consequence of this effect: as the shear
rate increases, friction is increasingly incorporated as more contacts form,
leading to a transition from a mostly frictionless to a mostly frictional
rheology. This result is significant because it shifts the emphasis from
lubrication hydrodynamics and detailed microscopic interactions to geometry and
steric constraints close to the jamming transition.
