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The effect of liquids on radial segregation of granular mixtures in rotating drums

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Abstract

The presence of liquids can significantly affect the dynamics of granular flow. This paper investigates the effect of liquids on radial segregation of granular mixture in a rotating drum using the discrete element method. The wet granular mixture, due to differences in particle size and density, segregates in a similar way to that of dry particles: lighter/larger particles move to the periphery of the bed while heavier/smaller particles stay in the centre. An index based on the variance of local concentration of one type of particles was proposed to measure the degree of segregation. While the liquid induced capillary force slows down the segregation process, its effect on the final state is more complicated: small cohesion shows no or even positive effect on segregation while high cohesion significantly reduces particle segregation. The effect can be explained by the change of flow regimes and the competing effects of mixing and segregation (un-mixing) in particle flow which are both reduced by the interparticle cohesion. A diagram is generated to describe the combined effect of particle size and density on segregation of wet particles. A theory is adopted to predict the segregation of particles under different density/size ratios.

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Abbreviations

\(d\) :

Interparticle gap, m

\(d_\mathrm{{min}}\) :

Minimum gap for capillary/viscous force, m

\(d_\mathrm{{rup}}\) :

Liquid bridge rupture distance, m

\(d_{S}\) :

Size of small particles, mm

\(d_{L}\) :

Size of large particles, mm

\(f\) :

Filling level

\(\mathbf{F}_{ij}^n\) :

Normal contact force, N

\(\mathbf{F}_{ij}^s\) :

Tangential contact force, N

\(\mathbf{F}_{ij}^{cap}\) :

Capillary force, N

\(\mathbf{F}_{ij}^{vis,n}\) :

Normal viscous force, N

\(\mathbf{F}_{ij}^{vis,s}\) :

Tangential viscous force, N

Fr:

Froude number

g :

Gravitational acceleration, \(\text{ m}/ \text{ s}^{-2}\)

\(I_{i}\) :

Moment of inertia of particle \(i\),

\(k\) :

Rate constant of segregation, \(s^{-1}\)

\(m_{i}\) :

Mass of particle \(i\), kg

\(P\) :

Segregation parameter

\(R_{i}\) :

Radius of particle \(i\), m

\(S\) :

Segregation index

\(S_{\infty }\) :

Equilibrium segregation index

\(S_{T}\) :

Predicted equilibrium segregation index

\(V_{f}\) :

Volumetric water content

\(\mathbf{v}_{i}\) :

Velocity of particle \(i\), m/s

\(v_{n}\) :

Normal relative velocity, m/s

\(v_{t}\) :

Tangential relative velocity, m/s

\(Y\) :

Elastic modulus, Pa

\(\alpha \) :

Size ratio

\(\beta \) :

Density ratio

\(\gamma \) :

Liquid surface tension, N/m

\(\gamma _{n}\) :

The normal damping coefficient, s

\(\varepsilon \) :

Bed porosity

\(\theta _{c}\) :

Contact angle, rad

\(\upmu \) :

Liquid viscosity, Pa\(\cdot \)s

\(\upmu _\mathrm{{r}}\) :

Rolling friction coefficient

\(\upmu _\mathrm{{s,pp}}\) :

Particle- particle sliding friction coefficient

\(\upmu _\mathrm{{s,pwc}}\) :

Particle-curved wall sliding friction coefficient

\(\upmu _\mathrm{{s,pwe}}\) :

Particle-end wall sliding friction coefficient

\(v\) :

Bed volume fraction

\(\xi _{n}\) :

Particle overlap, m

\(\xi _{s}\) :

Total tangential displacements, m

\(\xi _{s,max}\) :

Maximum tangential displacements, m

\(\rho _{S}\) :

Density of small particles, \(\text{ kg}/\text{ m}^{3}\)

\(\rho _{L}\) :

Density of large particles, \(\text{ kg}/\text{ m}^{3}\)

\(\varphi \) :

Liquid bridge half-filling angle, rad

\(\tilde{\sigma }\) :

Poisson’s ratio

\({\varvec{\upomega }}_{i}\) :

Angular velocity of particle \(i\), rad/s

\(\Omega \) :

Drum rotation speed

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Acknowledgments

The authors are grateful to the Australia Research Council (ARC) for the financial support for this work. In addition, this work was supported by the National Computational Infrastructure (NCI) National Facility.

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  1. Laboratory for Simulation and Modelling of Particulate Systems, School of Materials Science and Engineering, The University of New South Wales, Sydney, NSW, 2052, Australia

    P. Y. Liu, R. Y. Yang & A. B. Yu

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  1. P. Y. Liu
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Correspondence to R. Y. Yang.

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Liu, P.Y., Yang, R.Y. & Yu, A.B. The effect of liquids on radial segregation of granular mixtures in rotating drums. Granular Matter 15, 427–436 (2013). https://doi.org/10.1007/s10035-013-0392-1

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