Granular physics

322 Pages·2007·4.195 MB·English

by  Anita Mehta

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GRANULAR PHYSICS
Thefieldofgranularphysicshasburgeonedsinceitsdevelopmentinthelate1980s,
when physicists first began to use statistical mechanics to study granular media.
They are prototypical of complex systems, manifesting metastability, hysteresis,
bistabilityandarangeofotherfascinatingphenomena.
Thisbookprovidesawide-rangingaccountofdevelopmentsingranularphysics,
and lays out the foundations of the statics and dynamics of granular physics. It
covers a wide range of subfields, ranging from fluidisation to jamming, and these
are modelled through a range of computer simulation and theoretical approaches.
Written with an eye to pedagogy and completeness, this book will be a valuable
assetforanyresearcherinthisfield.
In addition to Professor Mehta’s detailed exposition of granular dynamics,
the book contains contributions from Professor Sir Sam Edwards, jointly with
DrRaphaelBlumenfeld,onthethermodynamicsofgranularmatter;fromProfes-
sorIsaacGoldhirschongranularmatterinthefluidisedstate;andProfessorPhilippe
Claudinongranularstatics.
Anita Mehta, a former Rhodes scholar, is currently a Radcliffe Fellow at
Harvard University. She is well known for being one of the pioneers in granular
physics,andiscreditedwiththeintroductionofmanynewconceptsinthisfield,in
particulartodowiththecompetitionofslowandfastmodesingranulardynamics.

GRANULAR PHYSICS
ANITA MEHTA
HarvardUniversity
Withcontributionsfrom
SIR SAM EDWARDS AND RAPHAEL BLUMENFELD
ISAAC GOLDHIRSCH
PHILIPPE CLAUDIN
CAMBRIDGEUNIVERSITYPRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge CB28RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521660785
© A. Mehta 2007
This publication is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
First published in print format 2007
ISBN-13 978-0-511-29669-7 eBook (NetLibrary)
ISBN-10 0-511-29669-X eBook (NetLibrary)
ISBN-13 978-0-521-66078-5 hardback
ISBN-10 0-521-66078-5 hardback
Cambridge University Press has no responsibility for the persistence or accuracy of urls
for external or third-party internet websites referred to in this publication, and does not
guarantee that any content on such websites is, or will remain, accurate or appropriate.
Sables
Iln’estpasdede´sertsivaste
Quenepuissetraverser
Celuiquiportelamusiquedese´toiles.
PoemontheParisUnderground,
attributedtoMichelLeSaint
Sands
Thereisnodesertsovast
thatitcannotbetraversed
byonewhocarriesthemusic
ofthestars.
Mytranslation

Contents
Preface pagex
1 Introduction 1
1.1 Statisticalmechanicsframework,packingandtheroleoffriction 2
1.2 Granularflowthroughwedges,channelsandapertures 4
1.3 Instabilities,convectionandpatternformationinvibrated
granularbeds 5
1.4 Sizesegregationinvibratedpowders 8
1.5 Self-organisedcriticality–theoreticalsandpiles? 11
1.6 Cellularautomatonmodelsofsandpiles 13
1.7 Theoreticalstudiesofsandpilesurfaces 15
2 Computersimulationapproaches–anoverview 18
2.1 Granularstructures–MonteCarloapproaches 18
2.2 Granularflow–moleculardynamicsapproaches 22
2.3 Simulationsofshakensand–somegeneralremarks 24
3 Structureofvibratedpowders–numericalresults 27
3.1 Detailsofsimulationalgorithm 27
3.2 Thestructureofshakensand–somesimulationresults 29
3.3 Vibratedpowders:transientresponse 40
3.4 Istherespontaneouscrystallisationingranularmedia? 44
3.5 Someresultsonshaking-inducedsizesegregation 46
4 Collectivestructuresinsand–thephenomenonofbridging 52
4.1 Introduction 52
4.2 Onbridgesinsandpiles–anoverarchingscenario 52
4.3 Sometechnicaldetails 54
4.4 Bridgesizesanddiameters:whendoesabridgespanahole? 55
4.5 Turningoveratthetop;howlinearbridgesformdomes 58
4.6 Discussion 61
vii
viii Contents
5 Onanglesofrepose:bistabilityandcollapse 63
5.1 Couplednonlinearequations:dilatancyvstheangleofrepose 63
5.2 Bistabilitywithinδθ :howdilatancy‘fattens’theangleofrepose 65
B
5.3 Whensandpilescollapse:rareevents,activatedprocesses
andthetopologyofroughlandscapes 67
5.4 Discussion 69
5.5 Anothertakeonbistability 69
6 Compactionofdisorderedgrainsinthejamminglimit:sandon
randomgraphs 79
6.1 Thethree-spinmodel:frustration,metastabilityandslowdynamics 81
6.2 Howtotapthespins?–dilationandquenchphases 82
6.3 ResultsI:thecompactioncurve 84
6.4 ResultsII:realisticamplitudecycling–howgranular
mediajamatdensitieslowerthanclose-packed 90
6.5 Discussion 93
7 ShakingaboxofsandI–asimplelatticemodel 94
7.1 Introduction 94
7.2 Definitionofthemodel 94
7.3 ResultsI:onthepackingfraction 96
7.4 ResultsII:onannealedcooling,andtheonsetofjamming 97
7.5 ResultsIII:whenthesandboxisfrozen 100
7.6 ResultsIV:twononequilibriumregimes 102
7.7 Discussion 103
8 ShakingaboxofsandII–atthejamminglimit,whenshapematters! 104
8.1 Definitionofthemodel 105
8.2 Zero-temperaturedynamics:(ir)retrievabilityofground
states,densityfluctuationsandanticorrelations 106
8.3 Ruggedentropiclandscapes:Edwards’ornot? 108
8.4 Low-temperaturedynamicsalongthecolumn:intermittency 113
8.5 Discussion 114
9 Avalancheswithreorganisinggrains 115
9.1 AvalanchestypeI–SOC 115
9.2 AvalanchestypeII–granularavalanches 118
9.3 Discussionandconclusions 131
10 Fromearthquakestosandpiles–stick–slipmotion 132
10.1 Avalanchesinarotatingcylinder 132
10.2 Themodel 133
10.3 Results 135
10.4 Discussion 146