  We consider extensional flows of a dense layer of spheres in a viscous fluid
and employ force and torque balances 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, and 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.
