Modelling the wall friction coefficient for a simple shear granular flow in view of the degradation mechanism

A steady granular flow experiment was performed in a confined annular shear cell to examine how the wall friction coefficient mu(w) degrades from the intrinsic sliding friction coefficient f between the grains and the container wall. Two existing models are invoked to examine the decay trend of mu(w)/f in view of the ratio of shear velocity to the square root of granular temperature chi (Artoni & Richard, Phys. Rev. Lett., vol. 115, 2015, 158001) and the ratio of grain angular and slip velocities Omega (Yang & Huang, Granul. Matt., vol. 18, issue 4, 2016, p. 77), respectively. As both models correlate mu(w)/f to different flow properties, a hidden relation is speculated between chi and Omega, or equivalently, between the granular temperature and the grain rotation speed. We used experiment data to confirm and reveal this hidden relation. From there, a unified mu(w)/f - chi model is proposed with physical meanings for the model coefficients and to show general agreement with the measured trend. Hence we may conclude that both the fluctuations in grain translations and their mean rotation are the crucial yet equivalent mechanisms to degrade mu(w)/f.