Anomalous Diffusion in a Bench-Scale Pulsed Fluidized Bed

Abstract

We present our analysis on micro-rheology of a bench-scale pulsed fluidized bed, which represents a weakly confined system. Non-linear gas-particle and particle-particle interactions resulting from the pulsed flow are associated with harmonic and sub-harmonic modes. At the meso-scale, periodic bubbling pattern is produced, while particle-scale measurements reveal anomalous and non-ergodic diffusion possibly associated with a spatial and temporal dependence. The ensemble-averaged meansquared displacement is characterized by a non-unique exponent resulting from a combination of stochastic processes. There is an evident disparity with its time-averaged analogue indicating weak ergodicity breaking, which along with ageing represents the non-stationary nature of underlying dynamics. The spread of individual time-averaged displacements is non-Gaussian, asymmetric and has a finite trivial contribution accounting for immobile particles.

Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

“…[132][133][134][135] ) fractional BM (FBM) 42,[136][137][138][139][140][141][142][143][144] and of nonergodic heterogeneous diffusion processes (HDPs) 126,143,[146][147][148][149][150] as well as for a combination of FBM with varying Hurst exponent H 151,152 and HDPs with varying exponent of the power-law-like diffusivity γ 150 . Note that a "hybrid" process of SBM-HDP was also introduced 126 and recently applied to the experimental data 153 . The implications of resetting onto the MSD and PDF of FBM, HDPs, and HDP-FBM are also considered, being a secondary focus.…”