Predictions of microstructure and stress in two-dimensional pure shearing of a dense viscous suspension.

We consider pure shearing of a dense layer of spheres in a viscous fluid and employ force and moment equilibrium to determine the trajectory of particle pairs that contribute to the stress. In doing this, we use Stokesian Dynamics simulations to guide the choice of the near-contacting pairs that follow such a trajectory. We specify the boundary conditions on the representative trajectory, determine the distribution of particles along it, and how the stress depends on the microstructure and strain-rate. We test the resulting predictions using the numerical simulations. Also, we show that the relation between the tensors of stress and strain rate involves the second and fourth moments of the particle distribution function.