  We investigate the link between the geometric environment of particles, the
local deformations of the solvent, and the bulk effective viscosity in
non-Brownian suspensions. First, we discuss the caging of particles by their
neighbors,and especially the caging of small particles by large ones in
bidisperse suspensions.We develop a model that attributes an effective volume
to particles depending on their environment, and yields the local deformations
and effective viscosity. We compare this model to data from the literature, as
well as to our own experiments with suspensions of non-Brownian polystyrene
beads. Using dissolved polymers and their coil-stretch transition as strain
probes, we measure the local deformation of the liquid and the effect of caging
thereon. We obtain a linear relationship between the amplified local strain
rate and the particle volume fraction, in which the critical volume fraction
$\phi_\mathrm{c}$ appears as an effective volume of the particles; this
relationship is found valid up into the dense regime.
