Granular clustering (Maxwell's demon in a granular gas)

This project focuses upon the clustering of vertically shaken granular matter in an array of connected compartments. This type of clustering is found in transport bands around the world (food processing, mining, pharmaceutical industries), causing huge losses in terms of money and efficiency. 

Clustering, its tendency to spontaneously separate into dense and dilute regions, is the key feature of a granular gas. This clustering effect, which makes granular gases fundamentally different from any ordinary molecular gas, stems from the fact that the collisions between the particles are inelastic: Some energy is dissipated in every collision, which means that a relatively dense region dissipates more energy, and thus becomes even denser. Vice versa, a relatively dilute region becomes more dilute.


Figure 1: Clustering beads in a row of five vertically shaken compartments.

The clustering shows up very clearly in the compartmentalized system depicted above. Starting with 195 steel beads distributed equally over 5 boxes, it takes about a minute before they have clustered into a single compartment. The beads do not go into one box directly, but first form a transient state in which two of the boxes are competing for dominance. In this particular experiment the cluster ends up in the middle box, but it could have gone into any of the compartments.

The pictures below show the break-up of the cluster: Surprisingly, the cluster persists for no less than 42 seconds, and then suddenly (within 1 second) vanishes. This is what we call the "sudden death" of a granular cluster. The collapse of a cluster is strikingly different from the cluster formation in reverse time order.


Figure 2: Sudden collapse of a granular cluster.

We have shown that the clustering effect is a coarsening process in which small local clusters merge into larger ones at increasingly long timescales, and that the effect can be used to create directed transport along the chain of compartments ("granular ratchet"). In bi-disperse mixtures of large and small particles we found that the clustering can be directed (either towards the larger particles, or to the smaller ones) by tuning the shaking strength.

Info: Devaraj van der Meer

Researchers: René Mikkelsen, Detlef Lohse, Ko van der Weele, Devaraj van der Meer, Michel Versluis.
Master students: Marcel KloostermanArthur van BilsenPeter EshuisRemco Rauhé.
Collaborators: Hans Kuipers (U Twente), Peter Reimann (University of Bielefeld), Werenfried Spit (Consulting Engineering Company Witteveen + Bos)
Embedding: JMBC
Sponsors: FOM

Publications

Transient granular shock waves and upstream motion on a staircase
J.P. van der Weele, G. Kanellopoulos, C. Tsiavos, and D. van der Meer
Phys. Rev. E 80, 011305 (2009)BibTeΧ
Compartmentalized granular gases: flux model results
D. van der Meer, J.P. van der Weele, P. Reimann, and D. Lohse
J. Stat. Mech. Theor. Exp. 2007, P07021 (2007)BibTeΧ
Granular fountains: Convection cascade in a compartmentalized granular gas
D. van der Meer, J.P. van der Weele, and P. Reimann
Phys. Rev. E 73, 061304 (2006)BibTeΧ
Small-number statistics near the clustering transition in a compartmentalized granular gas
R. Mikkelsen, J.P. van der Weele, D. van der Meer, M. van Hecke, and D. Lohse
Phys. Rev. E 71, 041302 (2005)BibTeΧ
Spontaneous Ratchet Effect in a Granular Gas[arΧiv]
D. van der Meer, P. Reimann, J.P. van der Weele, and D. Lohse
Phys. Rev. Lett. 92, 184301 (2004)BibTeΧ
Competitive clustering in a bidisperse granular gas: Experiment molecular dynamics, and flux model ,
R. Mikkelsen, D. van der Meer, J.P. van der Weele, and D. Lohse
Phys. Rev. E 70, 061307 (2004)BibTeΧ
Coarsening dynamics in a vibrofluidized compartmentalized granular gas
D. van der Meer, J.P. van der Weele, and D. Lohse
J. Stat. Mech. Theor. Exp. 2004, P04004 (2004)BibTeΧ
Competitive clustering in a Granular Gas
R. Mikkelsen, J.P. van der Weele, D. van der Meer, M. Versluis, and D. Lohse
Phys. Fluids 15, s8 (2003)BibTeΧ
Birth and sudden death of a granular cluster
J.P. van der Weele, D. van der Meer, and D. Lohse
Granular Gas dynamics, 335–346 (2003)
Sudden Collapse of a Granular Cluster[arΧiv]
D. van der Meer, J.P. van der Weele, and D. Lohse
Phys. Rev. Lett. 88, 174302 (2002)BibTeΧ
Competitive Clustering in a Bidisperse Granular Gas[arΧiv]
R. Mikkelsen, D. van der Meer, J.P. van der Weele, and D. Lohse
Phys. Rev. Lett. 89, 214301 (2002)BibTeΧ
Clustering in een granulair gas: Maxwell's duivel op de korrel genomen
J.P. van der Weele, D. van der Meer, and D. Lohse
Nederlands Tijdschrift voor Natuurkunde 68, 22–25 (2002)BibTeΧ
Maxwells duivel staat naast je in de file
M. Sandtke and J.P. van der Weele
Natuur en Techniek, 28–33 (2002)
Bifurcation diagram for compartmentalized granular gases[arΧiv]
D. van der Meer, J.P. van der Weele, and D. Lohse
Phys. Rev. E 63, 061304 (2001)BibTeΧ
Hysteretic clustering in granular gas[arΧiv]
J.P. van der Weele, D. van der Meer, M. Versluis, and D. Lohse
Europhys. Lett. 53, 328 (2000)BibTeΧ

 

Max Planck Gesellschaft

MCEC

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