  We report here on experiments and simulations examining the effect of
changing wall friction on the gravity-driven flow of spherical particles in a
vertical hopper. In 2D experiments and simulations, we observe that the
exponent of the expected power-law scaling of mass flow rate with opening size
(known as Beverloo's law) decreases as the coefficient of friction between
particles and wall increases, whereas Beverloo scaling works as expected in 3D.
In our 2D experiments, we find that wall friction plays the biggest role in a
region near the outlet comparable in height to the largest opening size.
However, wall friction is not the only factor determining a constant rate of
flow, as we observe a near-constant mass outflow rate in the 2D simulations
even when wall friction is set to zero. We show in our simulations that an
increase in wall friction leaves packing fractions relatively unchanged, while
average particle velocities become independent of opening size as the
coefficient of friction increases. We track the spatial pattern of
time-averaged particle velocities and accelerations inside the hopper. We
observe that the hemisphere-like region above the opening where particles begin
to accelerate is largely independent of opening size at finite wall friction.
However, the magnitude of particle accelerations decreases significantly as
wall friction increases, which in turn results in mean sphere velocities that
no longer scale with opening size, consistent with our observations of mass
flow rate scaling. The case of zero wall friction is anomalous, in that most of
the acceleration takes place near the outlet.
