(310a) Anomalous Diffusion On Segregating Mono-Layers of Granular Materials: Experimental, Computational and Theoretical Observations

Despite recent efforts to better understand the so called “Four State of Matter”, there is still no complete comprehension of the phenomena that surrounds this kind of materials. For example, segregation of granular materials due to size or density differences under shear or externally energized conditions is a very well known phenomenon but poorly understood. Such a lag in understanding makes mixing of granular materials notoriously difficult.  Here we present an experimental, computational and theoretical work on segregation/mixing dynamics in a very simple system such as a bi-dimensional diffusion cell one particle deep for a wide range of filling fractions. The system considered in this work comprises a set of mono-layer round particles of low-density polyethylene of approximately 6 mm in diameter which are put under thermal agitation and the dynamics of mono-dispersed and bi-dispersed mixtures in the system are followed in time. Experimentally a piezoelectric and a wave magnitude amplifier were used in order to generate the agitation needed; a square wave with constant amplitude and frequency was implemented. A digital camera was used to record the motion of the particles and the trajectories of such particles where analyzed statistically. Granular Brownian motion, caging dynamics and other relevant behaviors and parameters are obtained from the experimental observations.  A computational implementation using DEM that mimics the experimental setup is also considered. Values for mean square displacement (MSD) show the deviation from the Fick's law of diffusion as the filling fraction increases. The well-known caging effect also arises in both, experimental and computational results. Finally a theoretical model for the anomalous diffusion in such a dissipative systems is considered and the three approximations are compared.