A simple Python-based kinematic model of particle transport

We present results from a new particle-scale numerical model inspired by work completed by Christophe Ancey and colleagues who considered rarefied particle transport as a stochastic process. Key to the authors work is the hypothesis that in the absence of collective particle entrainment, the time varying activity N within a control area A above the bed surface is described by a Poisson probability mass function (pmf). An implication of their hypothesis is that particles are sporadically entrained from the bed surface at rate , when and where local flow conditions favor particle lift or dislodgement. In this context we developed a new kinematic particle-scale model Py_PK. The model domain measures some length nD of the particle diameter D, with a width of 1D (Figure 1). We tested the model with 30 simulations using a uniform particle diameter. Each simulation was run for 1 million iterations to explore the governing model parameters: SRe is the number of subregions; En is the particle entrainment rate per iteration, randomly sampled from a Poisson pmf; lt is the particle travel distance randomly sampled from a lognormal or truncated normal distribution; and Sh is the vertical particle stacking height ranging from 1-3D. The model produces a time varying signal of particle flux counted at the downstream domain, with a particle bed that changes through particle stacking and downstream motions of travel distance (Figure 1). An implication of particle stacking within the context of a stochastic model framework is a time varying signal of the average particle age, as well as the average particle age range, both metrics calculated at each iteration and across all subregions (results not shown). Last and most notably, all simulations show strong support for Ancey and colleagues hypothesis, with agreement between the particle flux probability mass distribtuion and the Poisson pmf (Figure 1). We find it remarkable that an essentially rules based model can produce transport behavior consistent with a rather complicated theoretical framework. This suggests that there is a unifying explanation that manifests within laboratory experiments and a simple rules based numerical model which captures the basic essence of rarefied particle transport.