A rigid-plastic Cosserat model for slow frictional flow of granular materials, proposed
by us in an earlier paper, has been used to analyse plane and cylindrical Couette flow.
In this model, the hydrodynamic fields of a classical continuum are supplemented
by the couple stress and the intrinsic angular velocity fields. The balance of angular
momentum, which is satisfied implicitly in a classical continuum, must be enforced
in a Cosserat continuum. As a result, the stress tensor could be asymmetric, and
the angular velocity of a material point may differ from half the local vorticity. An
important consequence of treating the granular medium as a Cosserat continuum is
that it incorporates a material length scale in the model, which is absent in frictional
models based on a classical continuum. Further, the Cosserat model allows determination
of the velocity fields uniquely in viscometric flows, in contrast to classical
frictional models. Experiments on viscometric flows of dense, slowly deforming granular
materials indicate that shear is confined to a narrow region, usually a few grain
diameters thick, while the remaining material is largely undeformed. This feature
is captured by the present model, and the velocity profile predicted for cylindrical
Couette flow is in good agreement with reported data. When the walls of the Couette
cell are smoother than the granular material, the model predicts that the shear layer
thickness is independent of the Couette gap H when the latter is large compared to
the grain diameter dp. When the walls are of the same roughness as the granular
material, the model predicts that the shear layer thickness varies as
(H/dp)1/3 (in the
limit H/dp [Gt ] 1) for plane shear under gravity and cylindrical Couette flow.
Stability analysis for cylindrical Couette flow of compressible fluids
