Slow and dense granular flows often exhibit narrow shear bands, making them
ill-suited for a continuum description. However, smooth granular flows have
been shown to occur in specific geometries such as linear shear in the absence
of gravity, slow inclined plane flows and, recently, flows in split-bottom
Couette geometries. The wide shear regions in these systems should be amenable
to a continuum description, and the theoretical challenge lies in finding
constitutive relations between the internal stresses and the flow field. We
propose a set of testable constitutive assumptions, including
rate-independence, and investigate the additional restrictions on the
constitutive relations imposed by the flow geometries. The wide shear layers in
the highly symmetric linear shear and inclined plane flows are consistent with
the simple constitutive assumption that, in analogy with solid friction, the
effective-friction coefficient (ratio between shear and normal stresses) is a
constant. However, this standard picture of granular flows is shown to be
inconsistent with flows in the less symmetric split-bottom geometry - here the
effective friction coefficient must vary throughout the shear zone, or else the
shear zone localizes. We suggest that a subtle dependence of the
effective-friction coefficient on the orientation of the sliding layers with
respect to the bulk force is crucial for the understanding of slow granular
flows.Comment: 11 pages, 7 figure