Shear dispersion in dense granular flows

Christov, Ivan; Stone, Howard A.

doi:10.1007/s10035-014-0498-0

Cited by 18 publications

(14 citation statements)

References 42 publications

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“…Taylor dispersion models have proved indispensable and are used to great effect across the hydrologic sciences and beyond [e.g. 20,21,4,33,23,13,58,9,53].…”

Section: Introductionmentioning

confidence: 99%

Upscaling of dilution and mixing using a trajectory based Spatial Markov random walk model in a periodic flow domain

Sund

Porta

Bolster

2017

Advances in Water Resources

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The Spatial Markov Model (SMM) is an upscaled model that has been used successfully to predict effective mean transport across a broad range of hydrologic settings. Here we propose a novel variant of the SMM, applicable to spatially periodic systems. This SMM is built using particle trajectories, rather than travel times. By applying the proposed SMM to a simple benchmark problem we demonstrate that it can predict mean effective transport, when compared to data from fully resolved direct numerical simulations. Next we propose a methodology for using this SMM framework to predict measures of mixing and dilution, that do not just depend on mean concentrations, but are strongly impacted by pore-scale concentration fluctuations. We use information from trajectories of particles to downscale and reconstruct pore-scale approximate concentration fields from which mixing and dilution measures are then calculated. The comparison between measurements from fully resolved simulations and predictions with the SMM agree very favorably

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“…Taylor dispersion models have proved indispensable and are used to great effect across the hydrologic sciences and beyond [e.g. 20,21,4,33,23,13,58,9,53].…”

Section: Introductionmentioning

confidence: 99%

Upscaling of dilution and mixing using a trajectory based Spatial Markov random walk model in a periodic flow domain

Sund

Porta

Bolster

2017

Advances in Water Resources

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“…Moreover, the asymptotic value of the longitudinal dispersion coefficient at the large time can be estimated by the triple integral formula (Aris, ; Christov & Stone, ; Fischer et al, ) as

D_{L} = - P e^{2} \int_{0}^{1} U false(y^{''} false) \int_{0}^{y^{''}} \frac{1}{D_{y} false(y^{'} false)} \int_{0}^{y^{'}} U false(y false) normald y normald y^{'} normald y^{''} .

…”

Section: Methods and Solutionsmentioning

confidence: 99%

Transient Solute Dispersion in Wetland Flows With Submerged Vegetation: An Analytical Study in Terms of Time‐Dependent Properties

Guo

Jiang

Chen

2020

Water Resources Research

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Predicting the concentration distribution of solute transport in vegetated flows is significant for associated environmental applications in water resources. While a semianalytical study has been made for the steady dispersion with a continuous release (Rubol et al., 2016, https://doi.org/10.1002/2016WR018907), an in‐depth analytical investigation has yet to be performed for the more complicated case of transient dispersion due to an instantaneous release. In regard to the pioneering benchmark observation (Murphy et al., 2007, https://doi.org/10.1029/2006WR005229) of transient solute dispersion in a submerged vegetated flow for an instantaneous source release at the top of the canopy, an extensive analytical effort is paid in this work to derive the time‐dependent basic properties and to investigate the temporal evolution of concentration distribution. Obtained large‐time asymptotic dispersivities agree well with available experimental results (Murphy et al., 2007, https://doi.org/10.1029/2006WR005229), with higher significance ( R2=0.87, n=24) for correlation between analytical results and experimental data. Analytical solutions covering effects of dispersivity, skewness, and kurtosis of detailed concentration distribution are compared satisfactorily with numerical results obtained by the random displacement method. The findings illuminate the applicability of this analytical approach in environmental risk assessment and water quality management.

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“…They further assume a no-slip condition between the bottom layer of particles and the slope, so a half parabolic velocity profile emerges and from this the shear rate could be calculated. Christov and Stone (2014) suggest to investigate the influence of variation in the volume fraction of solids and to provide experimental verification of the theory.…”

Section: Theory Of Axial Dispersionmentioning

confidence: 98%