  The steady flow of spherical particles in a rectangular bin is studied using
the Discrete Element Method (DEM) for different flow rates of the particles
from the bin, in the slow flow regime. The flow has two non-zero velocity
components and is more complex than the widely studied unidirectional shear
flows. The objective of the study is to characterize, in detail, the local
rheology of the flowing material. The flow is shown to be nearly constant
density, with a symmetric stress tensor and the principal directions of the
stress and rate of strain tensors nearly colinear. The local rheology is
analyzed using a coordinate transformation which enables direct computation of
the viscosity and components of the pressure assuming the granular material to
be a generalized Newtonian fluid. The scaled viscosity, fluctuation velocity
and volume fraction are shown to follow power law relations with the inertial
number, a scaled shear rate, and data for different flow rates collapse to a
single curve in each case. Results for flow of the particles on an inclined
surface, presented for comparison, are similar to those for the bin flow, but
with a lower viscosity and a higher solid fraction due to layering of the
particles. The in plane normal stresses are nearly equal and slightly larger
than the third component. All three normal stresses correlate well with the
corresponding fluctuation velocity components. Based on the empirical
correlations obtained, a continuum model is presented for computation of
granular flows.
