Rheology of surface granular flows

TL;DR

This study investigates the rheology of surface granular flows in a rotating cylinder, revealing velocity profiles, stress distributions, and viscosity behavior, and compares experimental results with existing models.

Contribution

It provides detailed measurements of velocity, density, and stress profiles in granular flows, and evaluates the applicability of different rheological models.

Findings

Velocity decays exponentially with depth, with a decay length of 1.1 times the particle diameter.

RMS velocity remains constant near the surface and decays linearly below a transition point.

Apparent viscosity exhibits a sharp transition and scales as u^{-1.5} below the shear rate maximum.

Abstract

The rheology of surface granular flows is investigated by means of measurements of velocity and number density profiles in a quasi-two-dimensional rotating cylinder, half-filled with mono-disperse steel balls. 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 taking into account wall friction. The profiles for the mean velocity superimpose when distance is scaled by the particle diameter and the velocity by a characteristic shear rate and the particle diameter. The mean velocity is found to decay exponentially with depth in the bed with a decay length of $\lambda=1.1d$. The r.m.s. velocity is nearly constant near the free surface and below a transition point it decays linearly with depth. The shear rate, obtained by numerical differentiation of the velocity profile, shows a maximum which occurs at the same depth as the transition in the r.m.s. velocity profile. The velocity distribution is Maxwellian above the transition point and a Poisson velocity distribution is obtained deep in the layer. The variation of the apparent viscosity ($\eta$) 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 $\eta\sim u^{-1.5}$. The experimental data is compared to predictions of three models for granular flow.