Statistics of particle diffusion subject to oscillatory flow in a porous bed

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An experimental study was conducted of particle diffusion within a porous bed when exposed to oscillatory flow. The particle oscillates up and down within the porous bed in response to the oscillatory flow, but also becomes intermittently stuck for time intervals of varying duration. The combination of oscillating flow and random hindering of the particle motion by the porous bed leads to a diffusive process called oscillatory diffusion. A variety of statistical measures are used to characterize the particle diffusion under the oscillatory flow. These measures show that the experimental data exhibit characteristics of both classical diffusive processes as well as oscillatory processes. The particle hold-up time duration was found to be well fit by a log-normal distribution for all experimental cases examined. A simple stochastic model that captures the key features of the oscillatory diffusion process is shown to yield statistical measures that compare well with experimental data.