  We propose a method to parameterize a coarse grained model for the
hydrodynamic friction between nearly touching rough spheres in suspension
flows. The frictional resistance due to surface roughness primarily alters the
sliding and rolling modes of motion of rough particles. Stokesian dynamics
simulations incorporating a near-field pairwise resistance model accounting for
these enhanced frictional modes were employed to compute particle trajectories
in shear flow. In this model, the resistance to sliding and rolling modes of
motion are augmented from a weakly diverging log$(1/h)$ form for smooth spheres
to a strongly diverging $1/h$ form for rough spheres to account for the
additional resistance due to squeezing flows between surface asperities, where
$h$ is the mean surface separation between particles. We determine new bounds
on the relative magnitude of the augmentations to the resistance to different
modes of motion using inequality constraints reflecting the positive
definiteness of the Stokes resistance tensor for a pair of rough particles.
Using the simulations of a particle pair in a shear flow, a simple model for
angular rotation rate of the pair centerline is computed as a function of its
orientation in the shear flow and the free parameters of the hydrodynamic
resistance model: the friction coupling strength, $\alpha$, and friction
coupling range, $h_0$. Values of $\alpha$ and $h_0$ for real-world rough
particles can then be inferred by matching the pair rotation rate in the model
to experimental observations when a dilute rough particle suspension is
subjected to a linear shear flow. The same model is used to calculate the
hydrodynamic contribution to the high frequency viscosity of rough particle
suspensions. For different $\alpha$ and $h_0$, we observe that the viscosity
diverges differently depending on $h_0$.
