Scaling relations for granular flow in quasi-two-dimensional rotating cylinders - art. no. 031302

An experimental study of the flow of different materials (steel balls, glas s beads, and sand) in quasi-two-dimensional rotating cylinders is carried o ut using flow visualization. The flow in the rotating cylinder comprises of a thin-flowing surface layer with the remaining particles rotating as a fi xed bed. Experimental results indicate that the scaled layer thickness incr eases with increasing Froude number (Fr= omega (2) R/g, where omega is the angular speed, R is the cylinder radius, and g the acceleration due to grav ity) and with increase in size ratio (s=d/R, where d is the particle diamet er). The free surface profile. is nearly flat at low Fr and becomes increas ingly S shaped with increasing Fr. The layer thickness profiles, which are symmetric at low Fr become skewed at high values of Fr and small s. The dyn amic angles of repose for all the materials studied show a near-linear incr ease with rotational speed (omega). Scaling analysis of the experimental da ta shows that the shape of the scaled surface profiles and the scaled layer thickness profiles are nearly identical when Froude number and size ratio are held constant, for each material. The surface profiles and layer thickn ess profiles are also found to be nearly independent of the material used. The dynamic angle of repose (beta). however, does not scale with Fr and s a nd depends on the particle properties. The experimental results are compare d to continuum models for flow in the layer, The models of Elperin and Vikh ansky [Europhys. Lett. 42, 619 (1998)] and Makse [Phys. Rev. Lett. 83, 3186 (1999)] show good agreement at low Fr while that of Khakhar et al. [Phys. Fluids, 9, 31 (1997)] gives good predictions over the entire range of param eters considered. An analysis of the data indicate that the velocity gradie nt (gamma) is nearly constant along the layer at low Fr, and the value calc ulated at the layer midpoint varies as gamma (proportional to)(0)[g sin(bet a (0)-beta (s))/d cos beta (s)](1/2) for all the experimental data, where b eta (s) is the static angle of repose and beta (0) is the interface angle a t the layer midpoint. An extension of "heap" models (BCRE, BRdG) is used to predict the interface angle profiles, which are in reasonable agreement wi th experimental measurements.