Axial and radial segregation of granular mixtures in a rotating spherical container.

We report the formation of axial segregation patterns of bidisperse granular mixtures of glass beads in a spherical container which is rotated about a central axis. When the rotation axis is horizontal, three distinct segregation bands are formed for a broad range of geometrical and dynamical parameters. We find two distinct regimes: at low fill levels the small size beads of the mixture are collected at the poles and the large size beads in a central band. At high fill levels the pole regions are occupied by large beads, while the small beads form the central band. The critical fill level for this structural transition decreases with increasing container size. For a container with 37 mm inner diameter, containing a mixture of 0.5 and 1.5 mm beads, the transition occurs between 40% and 50% fill level. When the rotation axis is tilted, the band positions are shifted and two-band structures are formed with the smaller particles at the lower pole. In our experiments the granulate is submersed in water; this allows NMR imaging of the complete three-dimensional band structures. We compare the observed segregation structures to those in cylindrical mixers and propose a model for the qualitative explanation of the pattern formation process.

Coarsening of axial segregation patterns of slurries in a horizontally rotating drum.

Segregation structures of granular mixtures in rotating drums represent classical examples of pattern formation 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.

Evaluation of cartilage composition and degradation by high-resolution magic-angle spinning nuclear magnetic resonance.

Rheumatic diseases are accompanied by a progressive destruction of the cartilage layers of the joints. Although the number of patients suffering from rheumatic diseases is steadily increasing, degradation mechanisms of cartilage are not yet understood, and methods for early diagnosis are not available. Although some information on pathogenesis could be obtained from the nuclear magnetic resonance (NMR) spectra of degradation products in the supernatants of cartilage specimens incubated with degradation-causing agents, the most direct information on degradation processes would come from the native cartilage as such. To obtain highly resolved NMR spectra of cartilage, application of the recently developed high-resolution magic-angle spinning (HR-MAS) NMR technique is advisable to obtain small line-widths of individual cartilage resonances. This technique is nowadays commercially available for most NMR spectrometers and has the considerable advantage that the same pulse sequences as in high-resolution NMR can be applied. Except for a MAS spinning equipment, no solid-state NMR hardware is required. Therefore, this method can be easily implemented. Here, we describe the most important requirements that are necessary to record HR-MAS NMR spectra. The capabilities of the HR-MAS technique are discussed for the 1H and 13C NMR spectra of cartilage.

Pulsed-field gradient-nuclear magnetic resonance (PFG NMR) to measure the diffusion of ions and polymers in cartilage: applications in joint diseases.

Since cartilage contains neither blood nor lymph vessels, diffusion is the most important transport process for the supply of cartilage with nutrients and for the removal of metabolic waste products. Therefore, diffusion measurements are of high interest in cartilage research. Different techniques of diffusion measurements exist. Here we describe methods based on pulsed-field gradient nuclear magnetic resonance (PFG NMR). This technique offers the considerable advantage that neither concentration gradients nor labeling of the diffusing species are required. In addition to the description of the fundamentals and the applicability of PFG NMR studies in cartilage research, emphasis is on the influence of the observation time, Delta, on the diffusion coefficient, D: at short times, diffusion is primarily determined by the water content of the sample, and great care is needed to keep this parameter constant. However, by varying the diffusion time, data on the internal structure of cartilage, e.g., the distance of the collagen fibrils, can also be obtained. In addition to classical water diffusion, the diffusion behavior of selected ions and polymers in cartilage is described. The capabilities, the limitations, and the clinical relevance of diffusion measurements for the assessment of joint diseases are discussed.

Self-diffusion of polymers in cartilage as studied by pulsed field gradient NMR.

Pulsed field gradient (PFG) nuclear magnetic resonance (NMR) was used to investigate the self-diffusion behaviour of polymers in cartilage. Polyethylene glycol and dextran with different molecular weights and in different concentrations were used as model compounds to mimic the diffusion behaviour of metabolites of cartilage. The polymer self-diffusion depends extremely on the observation time: The short-time self-diffusion coefficients (diffusion time Delta approximately 15 ms) are subjected to a rather non-specific obstruction effect that depends mainly on the molecular weights of the applied polymers as well as on the water content of the cartilage. The observed self-diffusion coefficients decrease with increasing molecular weights of the polymers and with a decreasing water content of the cartilage. In contrast, the long-time self-diffusion coefficients of the polymers in cartilage (diffusion time Delta approximately 600 ms) reflect the structural properties of the tissue. Measurements at different water contents, different molecular weights of the polymers and varying observation times suggest that primarily the collagenous network of cartilage but also the entanglements of the polymer chains themselves are responsible for the observed restricted diffusion. Additionally, anomalous restricted diffusion was shown to occur already in concentrated polymer solutions.