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We consider extensional flows of a dense layer of spheres in a viscous fluidand employ force and torque balances to determine the trajectory of particlepairs that contribute to the stress. In doing this, we use Stokesian dynamicssimulations to guide the choice of the near-contacting pairs that follow such atrajectory. We specify the boundary conditions on the representativetrajectory, and determine the distribution of particles along it and how thestress depends on the microstructure and strain rate. We test the resultingpredictions using the numerical simulations. Also, we show that the relationbetween the tensors of stress and strain rate involves the second and fourthmoments of the particle distribution function.

Predictions of microstructure and stress in planar extensional flows of a dense viscous suspension