granular particles and related system

Granular Particles Granular Particles and Related and Related

SystemSystemSparisoma Viridi

20160719Visit to Morikawa Lab, Osaka University, Japan 1

OutlineOutline• Granular world: A very short story• Some phenomena: Hopefully interesting • Recent works: Contactopy• Future collaboration: Some ideas • Let’s dream: CNT + self-assemble + swarm robot


Granular worldGranular worldA very short story


Granular materialGranular material• It is a conglomeration of discrete solid,

macroscopic particles with size typically more than 10-6 m, that is having dependency to thermal fluctuation, and looses its energy due to collision of the constituent particles1

• It is ubiquitous in nature and the second-most mani-pulated material in industry, while the first is water2

• It might be considered an additional state of matter in its own right, since it differs from solids, liquids, and gases3

[1] Wikipedia en:720595980; [2] Richard et al. Nat. Mater. 4 121 (2005); Jaeger et al. Phys. Today 49 32 (1996);


Granular particlesGranular particles• They construct granular materials and interact

mostly through short distance repulsion force, e.g. normal impact, oblique impact, and frictional contact4

• Long range interaction force can be addressed to gravitation and electrostatic force5

• Or, due to influence of surrounding particles long distance attraction force is similar to Casimir force6

• Their forms are 3-d (2-d), e.g. spherical (disk)7, ellipsoidal8, and irregular9(10)


[4] Schäfer et al. J. Phys. France 6 5 (1996); [5] Müller, Ph.D. thesis, University of Twente, 2007; [6] Cattuto et al. Phys. Rev. Lett. 96 278001 (2006); [7] Hong et al. Phys. Rev. Lett. 86 3423 (2001); [8] Vu-Quoc et al. Comput. Methods. Appl. Mech. Engrg. 187 483 (2000); [9] Azéma et al. Phys. Rev. E 87 062203 (2013); [10] Nouguier-Lehon et al. Int. J. Solids Struct. 42 6356 (2005);

Examples in natureExamples in nature


Example in Example in applicationsapplications


Example in artExample in art


Image sources


URL http://wholefoodcatalog.info/food_img/x-large/3006.jpg [20160716]URL http://vignette2.wikia.nocookie.net/uncyclopedia/images/a/a8/Sand_Dune.jpg/revision/latest?cb=20110301045549 [20160716]URL http://www.brauncewellquarries.co.uk/wp-content/uploads/2013/07/gravel_5-50mm_large.jpg [20160716]URL http://api.ning.com/files/b8ZVJ4Q*UlIjlhExFc*s9*a9YkzOCONYRlwRSiSKP-Fq5-2YI2wRohw6f*4dWjIfoj-dYoIvWyjkVROfugdqz9NTL79etD8L/ls3mar18india.jpg [20160716]URL http://www.nasa.gov/images/content/669779main_columbia_icebergs.jpg [20160716]URL http://profit.bg/uploads/userfiles/images/4(1174).jpg [20160716]URL https://images-na.ssl-images-amazon.com/images/I/41EDlvIX4uL.jpg [20160716]URL http://us.123rf.com/450wm/federicofoto/federicofoto1507/federicofoto150700959/42888665-machine-gun-with-ammunitions-over-the-sandbags-in-the-trench-war.jpg?ver=6 [20160716]URL http://transport.epfl.ch/files/content/sites/transport/files/projects/CFF_ballast/92453601.jpg [20160716]URL http://www.epicgardening.com/wp-content/uploads/2011/08/growstones-hydroponic-media.jpg [20160716]URL https://www.911metallurgist.com/blog/wp-content/uploads/2015/09/Ball-Mill.png [20160716]URL https://s-media-cache-ak0.pinimg.com/564x/b4/cc/ec/b4ccecd383bd057146ac39eb1630ba21.jpg [20160716]URL https://s-media-cache-ak0.pinimg.com/236x/59/24/9b/59249b700eb4225ed66745ef205e00fa.jpg [20160716]URL http://g03.a.alicdn.com/kf/HTB13rcsIVXXXXbDXXXXq6xXFXXX9/Diy-bahçe-malzemeleri-topraksız-kültür-dikim-seramik-karbon-top-topraksız-negatif-iyon-çiçek-dekorasyon-kapak-2mm.jpg [20160716]URL https://i.ytimg.com/vi/8t8a_k0362A/maxresdefault.jpg [20160716]

Some phenomenaSome phenomenaHopefully interesting


StratificationStratification• For non-percolating (dL/dS ≈ 2) granular flow it

depends on the fill rate of pouring process11

Stratified heap (slow feeding 7g/s) Well-mixed heap (fast feeding 800 g/s)• Angle of repose difference between smallest and largest

diameter is less than 1°, finer grains have brighter color


[11] Baxter et al. Nature 391 136 (1998);

Wet granular pileWet granular pile• Theory

θm: maximum angle, θd: dry angle, fp: packing fraction (0.64 for spherical grains), α0 = 1.2 ±0.05, r: particle radius, ρ: particle density, Γ: surface tension, g: acceleration due to gravity, L: length of the pile’s surface


[12] Nowak et al. Nature Phys. 1 50 (2005);

Avalanche typesAvalanche types


[13] Daerr & Douady Nature 399 241 (1999);

a

b c

flowing

stable without pertubation

μ: friction, h: layer thickness, h0 ≈ 2d,d: particle diameter ~ 240 μm,Δμ = μ(0) – μ(∞) (at the plane and in the pile)

stableafter flowing

Hourglass with Hourglass with obstacleobstacle


[14] Daerr & Douady Nature 399 241 (1999);

J: flow rate, D0 = 6.3d (for continuous flow in absence of obstacle),C = 1.4, c0 = 3.2, β: 3/2 (for 2-d), d: particle diameter

θθ

Beverloo relations (no obstacle)

Arching and jammingArching and jamming


[15] Garcimartín et al. Phys. Rev. E 82 031306 (2010);

Experiment in 2-d silo, R: D/d0, D: width of the orifice,d0: diameter of the spheres, d0 = 1 mm,η: number of particle forming the arch

Brazil-nut effect (BNE)Brazil-nut effect (BNE)


[16] Rosato et al. Phys. Rev. Lett. 58 1038 (1987);

Each shake ~ 3000 Monte Carlo steps: (a) 10 shakes, (b) 30 shakes, (c) 40 shakes, (f) 60 shakes

BNE rise timeBNE rise time


[17] Möbius et al. Nature 414 270 (2001);

nylon (intruder)

wood (intruder)

teflon (intruder)

steel (intruder)

ρm: bed particle density (glass),d: bed particle diameter,ρ: intruder density,D: intruder diameter,

Reverse BNE in 2-dReverse BNE in 2-d


[7] Hong et al. Phys. Rev. Lett. 86 3423 (2001);

crossover condition

RBNE

BNE

RBNE in 3-dRBNE in 3-d


[18] Breu et al. Phys. Rev. Lett. 90 014302 (2003);

crossover condition

RBNE: Influence of ΓRBNE: Influence of Γ


[19] Ciamarra et al. Phys. Rev. Lett. 96 058001 (2006);

crossover condition


[20] Godoy et al. Phys. Rev. E 78 031301 (2008);

BNE

Intruder clusteringIntruder clustering


[20a] Sanders et al. Phys. Rev. Lett. 93 208002 (2004);

floatρi/ρ = 0.6

sinkρi/ρ = 1.6

hoverρi/ρ = 1.0

Casimir force-likeCasimir force-like


[20b] Liétor-Santos and Burton arXiv:1604.05360v1 [cond-mat] 18 Apr 2016;

• Small pinned particles attractive force (environment packing dominant)• Large pinned particles repulsive force (Casimir force dominant)

Maxwell demonMaxwell demon• Asymmetry parameter


[21] Eggers Phys. Rev. Lett. 83 5322 (1999);

Directed clusteringDirected clustering


[22] Mikkelsen et al. Phys. Rev. Lett. 89 214301 (2002);

P1 = 300, r1 = 2.50 mm, m1 = 0.500 g,P2 = 600, r2 = 1.25 mm, m2 = 0.063 g,NA(t = 0) = (3P15, P2/3),NB(t = 0) = (2P15, 2P2/3),a = 2 mm, f = 60 Hz (moderate), 37.5 Hz (mild)

Granular oscillationGranular oscillation


[23] Viridi et al. Phys. Rev. E. 74 041301 (2006);

Granular ratchetGranular ratchet• Inspired by the Brownian ratchet or Feynman-

Smoluchowski ratchet, it wasa thought experiment


[24] Eshuis et al. Phys. Rev. Lett. 104 248001 (2010);ç

Control of 3-d gearsControl of 3-d gears• Imposing any slip-free

rotation states by onlycontrolling two spheres


[25] Stäger et al. Phys. Rev. Lett. 116 254301 (2016);

Recent worksRecent worksContactopy


Contactopy Contactopy maximationmaximation


[26] Viridi et al. AIP Conf. Proc. 1677 070001 (2015);

Contactopy Contactopy rise rise timetime

• There is a weak influence


[27] Kesuma et al. IOP Conf. Ser.: Earth Environ. Sci. 31 012001 (2016);

Asteroid in 2-dAsteroid in 2-d• The particles cluster due to gravitational force


[28] Viridi et al. International Symposium on Sun, Earth, and Life, Bandung, 3-4 June 2016 (in review);ç

C / N ~ 1.75

Future (collaboration)Future (collaboration)Some ideas


CNT rotational CNT rotational actuatoractuator


[29] Fenimore et al. Nature 424 408 (2003);

Cargo along CNTCargo along CNT• Cargoes are driven by thermal gradients along

CNT


[30] Barreiro et al. Science 320 775 (2008);

CNT electron CNT electron windmillswindmills

• Torque is generated by a flux of electrons passing through a chiral CNT


[31] Bailey et al. Phys. Rev. Lett. 100 256802 (2008);

nanomotor

nanodrill

Let’s dreamLet’s dreamCNT + self-assemble + swarm robot


Swarm of small robotSwarm of small robot

• https://www.youtube.com/watch?v=xK54Bu9HFRw


[32] URL https://www.youtube.com/watch?v=xK54Bu9HFRw [20160716];

Self-assemble small Self-assemble small cubescubes

• https://www.youtube.com/watch?v=6aZbJS6LZbs


[33] URL https://www.youtube.com/watch?v=6aZbJS6LZbs [20160716];;

Self-assemble objectsSelf-assemble objects

• https://www.youtube.com/watch?v=GIEhi_sAkU8


[34] https://www.youtube.com/watch?v=GIEhi_sAkU8 [20160716];

Origami self-motion Origami self-motion robotrobot

• https://www.youtube.com/watch?v=ZVYz7g-qLjs


[35] https://www.youtube.com/watch?v=ZVYz7g-qLjs [20160716];

??• CNT + self-assemble + swarm robot …


Thank youThank you
