Kinetic theory of jamming in hard-sphere startup flows

We consider the problem of hard spheres shearing from rest with hydrodynamic lubrication, but no Brownian forces. A theoretical model is presented, in terms of the aggregation of elongated clusters of particles, and predicts a jamming transition, where stress and average cluster size tend to infinity after a finite amount of strain. The model is compared with simulation data [Europhys. Lett. 32, 535 (1995)], and predicts a critical volume fraction above which jamming will occur in macroscopic systems.