  Slowly sheared particulate media like sand and suspensions flow
heterogeneously as they yield via narrow shear bands where most of the strain
is accumulated. Understanding shear band localization from microscopics is
still a major challenge. One class of so-called non-local theories identified
that the width of the shearing zone should depend on the stress field. We
explicitly test this picture by using a uniquely stress-sensitive suspension
while probing its flow behavior in a classic geometry in which shear bands can
be well-tuned: the Split-Bottom Shear Cell (SBSC). The stress-sensitive
suspension is composed of mildly polydisperse soft, slippery hydrogel spheres
submersed in water. We measure their flow profiles and rheology while
controlling the confinement stress via hydrostatic effects and compression. We
determine the average angular velocity profiles in the quasi-static flow regime
using Magnetic Resonance Imaging based particle image velocimetry (MRI-PIV) and
discrete element method (DEM) simulations. We explicitly match a
pressure-sensitive non-local granular fluidity (NGF) model to observed flow
behavior. We find that shear bands for this type of suspension become extremely
broad under the low confining stresses from the almost density-matched fluid
particle mixture, while collapsing to a narrow shear zone under finite,
externally imposed compression levels. The DEM and NGF results match the
observations quantitatively, confirming the conjectured pressure sensitivity
for suspensions and its role in NGF. Our results indicate that pressure
sensitivity should be part of non-local flow rules to describe slow flows of
granular media.
