Rheology of surface granular flows

Surface granular flow, comprising granular material flowing on the surface of a heap of the same material, occurs in several industrial and natural systems. The rheology of such flow is investigated by means of measurements of velocity and number density profiles in a quasi-two-dimensional rotating cylinder, half-filled with a model granular material mono-size spherical stainless steel particles. The measurements are made at the center of the cylinder, where the flow is fully-developed, using streakline photography and image analysis . The stress profile is computed from the number density profile using a force balance which takes into account wall friction. Mean velocity and root mean square (r.m.s.) velocity profiles are reported for different particle sizes and cylinder rotation speeds. The profiles for the mean velocity superimpose when distance is scaled by the particle diameter (d) and the velocity by a characteristic shear rate (γ̇C = [g sin(βm − βs)/d cosβs] ) and the particle diameter where βm is the static angle of friction and βs is the sliding angle of friction. The scaling is also found to work for the r.m.s. velocity profiles. The mean velocity is found to decay exponentially with depth in the bed with a decay length of λ = 1.1d. The r.m.s. velocity shows similar behaviour but with λ = 1.7d. The r.m.s. velocity profile shows two regimes: near the free surface the r.m.s. velocity is nearly constant and below a transition point it decays linearly with depth. The shear rate, obtained by numerical differentiation of the velocity profile, is not constant anywhere in the layer and shows a maximum which occurs at the same depth as the transition in the r.m.s. velocity profile. Above the transition point the velocity distributions are Gaussian and below the transition point the velocity distributions gradually approach a Poisson distribution. The shear stress increases roughly linearly with depth. However, the variation of the apparent viscosity (η) with r.m.s. velocity (u) shows a relatively sharp transition at the shear rate maximum, and in the region below this point the apparent viscosity varies as η ∼ u. The measurements indicate that the flow comprises two layers: an upper low viscosity layer with a nearly constant r.m.s. velocity and a lower layer of increasing viscosity with a decreasing r.m.s. velocity. The thickness of the upper layer depends on the local flow rate and is independent of particle diameter while the reverse if found to hold for lower layer thickness. The experimental data is compared to predictions of three models for granular flow.