Simple model for granular friction

Friction of a slider on a granular layer: nonmonotonic thickness dependence and effect of boundary conditions

We investigate the effective friction encountered by a mass sliding on a granular layer as a function of bed thickness and boundary roughness conditions. The observed friction has minima for a small number of layers before it increases and saturates to a value that depends on the roughness of the sliding surface. We use an index-matched interstitial liquid to probe the internal motion of the grains with fluorescence imaging in a regime where the liquid has no significant effect on the measured friction. The shear profiles obtained as a function of depth show a decrease in slip near the sliding surface as the layer thickness is increased. We propose that the friction depends on the degree of grain confinement relative to the sliding surfaces.

Stick-slip dynamics of a granular layer under shear

Stick-slip regime of shear granular flows is studied theoretically and numerically. Numerical experiments are carried out for a thin Couette cell using soft-particle molecular dynamics code in two dimensions. We apply order parameter theory of partially fluidized granular flows and find a good agreement with simulations and experiments by Nasuno et al.

Continuum theory of partially fluidized granular flows

A continuum theory of partially fluidized granular flows is developed. The theory is based on a combination of the equations for the flow velocity and shear stresses coupled with the order-parameter equation which describes the transition between the flowing and static components of the granular system. We apply this theory to several important granular problems: avalanche flow in deep and shallow inclined layers, rotating drums, and shear granular flows between two plates. We carry out quantitative comparisons between the theory and experiment.

Slow viscous flows in micropolar fluids

A systematic calculation of micropolar fluid flows around a sphere and a cylinder is presented. The explicit velocity fields and the drag forces exerted by the fluid flow in both two and three dimensions are obtained. The solution of a steady micropolar fluid flow inside the cylinder is also obtained and is identical to the form observed in an experiment on granular vibrating beds.