The dynamics of dry granular flows down a vertical glass pipe of small diameter have
been studied experimentally. Simultaneous measurements of pressure profiles, air and
grain flow rates and volume fractions of particles have been realized together with
spatio-temporal diagrams of the grain distribution down the tube. At large grain flow
rates, one observes a stationary flow characterized by high particle velocities, low
particle fractions and a downflow of air resulting in an underpressure in the upper
part of the pipe. A simple model assuming a free fall of the particles slowed down by
air friction and taking into account finite particle fraction effects through Richardson–Zaki's
law has been developed: it reproduces pressure and particle fraction variations
with distance and estimates friction forces with the wall. At lower flow rates, sequences
of high-density plugs separated by low-density bubbles moving down at a constant
velocity are observed. The pressure is larger than outside the tube and its gradient
reflects closely the weight of the grains. Writing mass and momentum conservation
equations for the air and for the grains allows one to estimate the wall friction, which
is less than 10% of the weight for grains with a clean smooth surface but up to
30% for grains with a rougher surface. At lower flow rates, oscillating-wave regimes
resulting in large pressure fluctuations are observed and their frequency is predicted.
Powder flow down a vertical pipe: the effect of air flow
