ABSTRACT
Nonequilibrium systems often organize into interesting spatiotemporal structures or patterns. Examples include the patterns in pure fluid flow systems, such as Rayleigh-Be´nard convection in a vertical temperature gradient, the Taylor-Couette flow between two concentric rotating cylinders, and those concerning particulate flow systems in a partially or fully filled horizontal rotating cylinder, such as well-defined periodic clusters, normal to the axis of rotation. Particulate flows exhibiting axial clusters along the horizontal axis in a partially filled horizontal rotating cylinder were observed in [1-3], which are in part attributed to the presence of the free surface caused by the partial filling of the cylinder. Similar cluster and other pattern formations were also found for a settling suspension of uniform non-Brownian particles in a fully filled horizontal rotating cylinder [4-7]. In [4] Lipson used a horizontal rotating cylinder filled with oversaturated solution to grow crystal without any interaction with a substrate, and found that crystals accumulate in welldefined periodic clusters, normal to the axis of rotation. Lipson and Seiden have suggested that it could be caused by the interaction between particles and the flow in the tube [5]. A variety of patterns and structures were encountered for a settling suspension of uniform non-Brownian particles in a fully filled horizontal rotating cylinder [7], in which Matson et al. explained that those patterns and dynamics result from the interplay between the viscous drag and the gravitational and centrifugal forces.
