Coarsening of axial segregation patterns of slurries in a horizontally rotating drum Tilo Finger, 1 Andreas Voigt, 2 Jörg Stadler, 3 Heiko G. Niessen, 4 Lama Naji, 1 and Ralf Stannarius 1 1 Otto-von-Guericke-University, Institute of Experimental Physics, Universitätsplatz 2, D-39106 Magdeburg, Germany 2 Max-Planck-Institute for Dynamics of Complex Technical Systems, Sandtorstraße 1, D-39106 Magdeburg, Germany 3 Leibniz Institute for Neurobiology, Brenneckestraße 6, D-39118 Magdeburg, Germany 4 Center of Advanced Imaging (CAI) and Department of Neurology II, Otto-von-Guericke-University, Leipziger Straße 44, D-39120 Magdeburg, Germany Received 27 September 2005; revised manuscript received 30 January 2006; published 29 September 2006 Segregation structures of granular mixtures in rotating drums represent classical examples of pattern forma- tion in granular material. We investigate the coarsening of axial segregation patterns of slurries in a long horizontally rotating cylinder. The dynamics and the three-dimensional geometry of the segregation structures are analyzed with optical methods and nuclear magnetic resonance imaging. Previous studies have mainly considered global statistical features of the pattern dynamics. In order to get insight into driving mechanisms for the coarsening process, we focus on the details of the dissolution of individual bands. We treat the coarsening as a consequence of interactions of adjacent bands in the pattern, which are determined by their geometrical relations. In addition to initially homogeneous mixtures, which evolve to spontaneously formed patterns, we study the evolution of specially prepared simple initial states. The role of the three-dimensional geometry of the axial core in the dissolution process of segregation bands is demonstrated. Relations between geometry and dynamic processes are established, which may help to find the correct microscopic models for the coarsening mechanism. DOI: 10.1103/PhysRevE.74.031312 PACS numbers: 45.70.Mg, 45.70.Qj, 05.65.+b, 83.85.Fg I. INTRODUCTION Segregation processes in mixtures of granular materials represent a fascinating research topic, with many unresolved fundamental questions. Segregation phenomena in such ma- terials are ubiquitous in everyday life, in technological pro- cesses, as well as in very simple model systems 1–3. In particular, the dynamics of granular mixtures in horizontally rotating drums have attracted the interest of experimental and theoretical researchers. The system is particularly simple in its geometrical construction and its preparation, and the observation techniques are straightforward. Axial segregation has first been described more than 60 years ago 4 and it has been studied extensively during the last decade. Experiments have been performed under various geometrical conditions and with a wide variety of material compositions 4 –26. These experiments have pro- vided an abundance of experimental data. Different theoret- ical descriptions have been developed, including numerical simulations and analytical models 26–39. Nevertheless, the system dynamics are far from being fully understood. One of the reasons for that may be the large variety of influences that may have to be considered, but apart from that there is certainly a lack of fundamental understanding of granular dynamics in general. Many features of the segregation and coarsening processes are still not satisfactorily described. In the systems considered here “slowly” rotating drums, see below, the redistribution of grains in the granular bed is largely restricted to a shallow surface layer 40. The major- ity of investigations have focused on the segregation of bi- modal mixtures of spherical beads, but systems with ellipsoi- dally or irregularly shaped grains, e.g., Refs. 19,20, and polydisperse mixtures have been studied as well. Details of the dynamics of the segregation pattern depend crucially upon the conditions of the experiment. Traveling-wave-like patterns 19,20, “wavy” patterns 23, and stationary stripes e.g., Refs. 22,23 have been described, for example. The reversibility of the axial segregation processes has been dem- onstrated 13,14. The qualitative and quantitative character- istics of the segregation and coarsening dynamics is sensi- tively influenced by many parameters. Geometry and size distribution of the particles, densities, and masses, rotation speed of the drum i.e., energy supply per time, and the filling factor play a role, as well as the environment dry or wet surroundings. Most of the experiments have been per- formed in dry systems where the grains are immersed in air; only a few experiments deal with granulates 41,42 or granular mixtures 21–23 immersed in a liquid of lower density slurries. The segregation phenomena observed in a horizontally rotating long mixer, filled initially with a homogeneous mix- ture of different-sized granulate, can be roughly separated in three periods. Initially, during one or a few rotations, one observes a radial segregation of the material 43, where small-sized particles collect in an axial core of the granulate, while the large-sized component accumulates in the outer region. In a subsequent period of the order of a hundred rotations, axial segregation sets in. The core becomes modu- lated until the fine-grained material develops a band pattern 12,15,16. Axial segments are formed where the large-sized particles are more or less completely replaced by the small- sized components of the mixture. Such bands alternate with regions where only a narrow core of small particles is em- bedded in a surrounding shell of large particles. As the driv- ing factor for this axial structuring process, differences in the dynamic angles of repose of mixed and segregated granulate have been suggested 13. The following period is character- PHYSICAL REVIEW E 74, 031312 2006 1539-3755/2006/743/03131215 ©2006 The American Physical Society 031312-1