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Bridging the gap between particle-scale forces and continuum modelling of size segregation: application to bedload transport

Published online by Cambridge University Press:  12 April 2021

Hugo Rousseau Open the ORCID record for Hugo Rousseau [Opens in a new window] ,
Remi Chassagne Open the ORCID record for Remi Chassagne [Opens in a new window] ,
Julien Chauchat Open the ORCID record for Julien Chauchat [Opens in a new window] ,
Raphael Maurin Open the ORCID record for Raphael Maurin [Opens in a new window]  and
Philippe Frey
Hugo Rousseau*
Affiliation:
Univ. Grenoble Alpes, INRAE, UR ETNA, 38000Grenoble, France
Remi Chassagne
Affiliation:
Univ. Grenoble Alpes, INRAE, UR ETNA, 38000Grenoble, France Univ. Grenoble Alpes, LEGI, CNRS, UMR 5519, Grenoble, France
Julien Chauchat
Affiliation:
Univ. Grenoble Alpes, LEGI, CNRS, UMR 5519, Grenoble, France
Raphael Maurin
Affiliation:
IMFT, Univ. Toulouse, CNRS, Toulouse, France
Philippe Frey
Affiliation:
Univ. Grenoble Alpes, INRAE, UR ETNA, 38000Grenoble, France
*
†Email address for correspondence: [email protected]
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Abstract

Gravity-driven size segregation is important in mountain streams where a wide range of grain sizes are transported as bedload. More particularly, vertical size segregation is a multi-scale process that originates in interactions at the scale of particles with important morphological consequences for the river bed. To address this issue, a volume-averaged multi-phase flow model for immersed bi-disperse granular flows was developed based on an interparticle segregation force (Guillard et al., J. Fluid Mech., vol. 807, 2016, R1) and a granular Stokesian drag force (Tripathi & Khakhar, J. Fluid Mech., vol. 717, 2013, pp. 643–669). An advection–diffusion model was derived from this model yielding parametrisations for the advection and diffusion coefficients based on the interparticle interactions. This approach makes it possible to bridge the gap between grain-scale physics and continuum modelling. Both models were successfully tested against existing discrete element model (DEM) simulations of size segregation in bedload transport (Chassagne et al., J. Fluid Mech., vol. 895, 2020, A30). Through a detailed investigation of the granular forces, it is demonstrated that the observed scaling of the advection and diffusion coefficients with the inertial number can be explained by the granular drag force dependency on the viscosity. The drag coefficient is shown to be linearly dependent on the small particle concentration. A new scaling relationship for the segregation force including the small particle concentration and the pressure is proposed. Lastly, adding a size-ratio dependency in the segregation force fairly reproduces the DEM results for a large range of small particle concentrations and size ratios.

JFM classification

Granular media: Granular media Geophysical and Geological Flows: Sediment transport Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A26
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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