Diffusion and mixing in gravity-driven dense granular flows
Jaehyuk Choi, Arshad Kudrolli, R. Ruben Rosales, Martin Z. Bazant
Status: published, Phys. Rev. Lett. 92, 174301 (2004).
Abstract: We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from superdiffusion to normal diffusion, as a function of the distance fallen, independent of the flow speed. In the superdiffusive (but sub-ballistic) regime, which occurs before a particle falls through its diameter, the displacements have fat-tailed and anisotropic distributions. In the diffusive regime, we observe very slow cage breaking and Péclet numbers of order 100, contrary to the only previous microscopic model (based on diffusing voids). Overall, our experiments show that diffusion and mixing are dominated by geometry, consistent with long-lasting contacts but not thermal collisions, as in normal fluids.
Non-technical summary: In normal fluids, microscopic fluctuations are associated with an internal temperature, unrelated to the mean flow. According to Boltzmann’s kinetic theory, collisions cause molecular positions to switch from ballistic (linear) to diffusive (square root) scaling in time. Kinetic theories have also been proposed for dilute granular flows, taking into account inelastic collisions via a modified “granular temperature”. The new experiments of Choi et al., however, reveal a radically different, non-thermal picture of dense granular flows. By tracking grains with high resolution in a draining silo at different flow rates, the authors find a universal transition from (sub-ballistic) superdiffusion to diffusion, as a function of distance dropped, not time. In other words, the system seems to go through the same configurations, only more slowly, with decreasing flow rate. The cage breaking distance is also shown to be very long, comparable to the system size, showing that grains tend to remain stuck with their neighbors. These observations call for new statistical theory based on cooperative rearrangements, not collisions.