  We study effective shear viscosity $\mu^\star$ and effective extensional
viscosity $\lambda^\star$ of concentrated non-colloidal suspensions of rigid
spherical particles. The focus is on the spatially disordered arrays. We use
recently developed discrete network approximation techniques to obtain
asymptotic formulas for the viscosities as the typical inter-particle distance
$\delta$ tends to zero. For disordered arrays, the volume fraction alone does
not determine the effective viscosity. Use of the network approximation allows
us to study the dependence of the effective viscosities on variable distances
between neighboring particles. Our analysis can be characterized as global
because it goes beyond the local analysis of the flow between two particles.
The principal conclusion in the paper is that, in general, asymptotic formulas
obtained by global analysis are different from the formulas obtained from local
analysis. In particular, the leading term in the asymptotics of $\mu^\star$ is
of lower order than suggested by the local analysis (weak blow up), while the
order of the leading term in the asymptotics of $\lambda^\star$ depends on the
geometry of the particle array (either weak or strong blow up). We obtain
geometric conditions on a random particle array that lead to the strong blow up
of $\lambda^\star$, and show that these conditions are generic. We also provide
an example of a closely packed particle array for which the leading term in the
asymptotics of $\lambda^\star$ degenerates (weak blow up).
