Zeina S. Khan

Subdiffusive axial transport of granular materials in a long drum mixer.

Granular mixtures segregate radially by size when tumbled in a partially filled horizontal drum. The smaller component moves toward the axis of rotation and forms a buried core, which then splits into axial bands. Models have generally assumed that the axial segregation is opposed by diffusion. Using narrow pulses of the smaller component as initial conditions, we have characterized axial transport in the core. We find that the axial advance of the segregated core is well described by a self-similar concentration profile whose width scales as talpha, with alpha approximately 0.3<1/2. Thus, the process is subdiffusive rather than diffusive as previously assumed. We compare our results to two one-dimensional model equations which contain self-similarity and subdiffusion: a linear fractional diffusion model and the nonlinear porous medium equation.

High-speed measurements of axial grain transport in a rotating drum

Granular mixtures segregate radially by size when tumbled in a partially filled horizontal drum on short timescales. The smaller component moves towards the axis of rotation and forms a buried core, which then forms undulations that grow into axial bands. Experimental and simulational studies have provided differing accounts of the type of transport taking place in radially segregated and self-diffusing grains. We investigate the bulk axial transport of small quantities of tracer particles travelling amongst glass spheres using non-invasive high-speed synchrotron x-ray particle tracking, which allows us to access timescales not explored previously. The mixtures used have varying propensity to axially segregate based on the glass sphere sizes when the tracers are present in larger proportions; we found that the single-particle dynamics of these mixtures when the tracer concentration is low do not appreciably depend on the relative particle sizes, implying that the potential for a mixture to axially segregate cannot be inferred from the microscopic dynamics of individual small particles. From the single-particle dynamics, we also found that while the standard measure of diffusive behaviour, the slope of the mean-squared displacement, is close to that expected from diffusive transport, more detailed analyses indicate anomalous transport.

Wet granular walkers and climbers

Mechanisms of locomotion in microscopic systems are of great interest not only for technological applications but also for the sake of understanding, and potentially harnessing, processes far from thermal equilibrium. Downscaling is a particular challenge and has led to a number of interesting concepts, including thermal ratchet systems and asymmetric swimmers. Here we present a granular ratchet system employing a particularly robust mechanism that can be implemented in various settings. The system consists of wetted spheres of different sizes that adhere to each other, and are subject to a symmetric oscillating, zero average external force field. An inherent asymmetry in the mutual force network leads to force rectification and hence to locomotion. We present a simple model that accounts for the observed behaviour, underscores its robustness and suggests a potential scalability of the concept.