Editing Granular convection

{{short description|Movement in granular material}}
{{unsolved|physics|What is the definitive explanation<ref name="AransonTsimring2006Review">{{Cite journal |last1=Aranson |first1=Igor S. |last2=Tsimring |first2=Lev S. |date=2006-06-01 |title=Patterns and collective behavior in granular media: Theoretical concepts |url=https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.78.641 |journal=Reviews of Modern Physics |volume=78 |issue=2 |pages=641–692 |doi=10.1103/RevModPhys.78.641 |quote=Yet despite major efforts by many groups, the theoretical description of granular systems remains largely a plethora of different, often contradictory concepts and approaches.|arxiv=cond-mat/0507419 |bibcode=2006RvMP...78..641A }}</ref> for why this phenomenon occurs?}}[[Image:Mixed nuts small white2.jpg|right|thumb|In a serving of [[mixed nuts]], the larger Brazil nuts will often end up on the surface]]
[[File:Brazil nut effect demonstration.webm|thumb|A demonstration of the Brazil nut effect using a glass jar, a cup of rice, and a stack of coins serving as the intruder initially located at the bottom.]]
'''Granular convection''' is a phenomenon where [[granular material]] subjected to shaking or vibration will exhibit circulation patterns similar to types of fluid [[convection]].<ref>{{cite journal | url=https://www.nature.com/articles/35104697 | doi=10.1038/35104697 | title=Size separation of granular particles | date=2001 | last1=Möbius | first1=Matthias E. | last2=Lauderdale | first2=Benjamin E. | last3=Nagel | first3=Sidney R. | last4=Jaeger | first4=Heinrich M. | journal=Nature | volume=414 | issue=6861 | page=270 | pmid=11713519 }}</ref> It is sometimes called the '''Brazil nut effect''',<ref>{{cite journal|title=Why the Brazil Nuts are on Top| doi=10.1103/physrevlett.58.1038|year=1987|last1=Rosato|first1=A.|last2=Strandburg|first2=K.J.|last3=Prinz|first3=F.|last4=Swendsen|first4=R.H.|journal=Physical Review Letters| volume=58| issue=10| pages=1038–41| pmid=10034316}}</ref> when the largest of irregularly shaped particles end up on the surface of a granular material containing a mixture of variously sized objects.<ref name=":0">{{Cite journal |last1=Gajjar |first1=Parmesh |last2=Johnson |first2=Chris G. |last3=Carr |first3=James |last4=Chrispeels |first4=Kevin |last5=Gray |first5=J. M. N. T. |last6=Withers |first6=Philip J. |date=2021-04-19 |title=Size segregation of irregular granular materials captured by time-resolved 3D imaging |journal=Scientific Reports |language=en |volume=11 |issue=1 |pages=8352 |doi=10.1038/s41598-021-87280-1 |issn=2045-2322 |pmc=8055975 |pmid=33875682}}</ref>  This name derives from the example of a typical container of [[mixed nuts]], in which the largest will be [[Brazil nut]]s. The phenomenon is also known as the '''muesli effect''' since it is seen in packets of [[breakfast cereal]] containing particles of different [[volume|sizes]] but similar [[density]], such as [[muesli]] mix.

Under experimental conditions, granular convection of variously sized particles has been observed forming [[convection cells]] similar to fluid motion.<ref>{{cite journal|doi=10.1103/PhysRevLett.100.078002|title=On the brink of jamming: Granular convection in densely filled containers|year=2008|last1=Rietz|first1=Frank|last2=Stannarius|first2=Ralf|s2cid=28054132|journal=[[Physical Review Letters]]|volume=100|issue=7|bibcode = 2008PhRvL.100g8002R|pmid=18352597|page=078002|arxiv=1706.04978}}</ref><ref>[https://web.archive.org/web/20091213070634/https://www.wired.com/wiredscience/2009/10/bead-cloud-mystery/#ixzz0xbmvgKP1 Baffling Patterns Form in Scientific Sandbox], Wired, Brandon Keim, October 28, 2009</ref>

==Explanation==
[[Image:Paranuss-Effekt_Brazil_Nut_Effect_Granular_Convection.webm|upright|thumb|A video demonstrating how shaking a bag of [[muesli]] causes the larger ingredients to rise to the surface]]
It may be [[counterintuitive]] to find that the largest and (presumably) heaviest particles rise to the top, but several explanations are possible:
* When the objects are irregularly shaped, random motion causes some oblong items to occasionally turn in a vertical orientation.  The vertical orientation allows smaller items to fall beneath the larger item.<ref name=":0" />  If subsequent motion causes the larger item to re-orient horizontally, then it will remain at the top of the mixture.<ref name=":0" />
* The [[center of mass]] of the whole system (containing the mixed nuts) in an arbitrary state is not optimally low; it has the tendency to be higher due to there being more empty space around the larger Brazil nuts than around smaller nuts.{{citation needed|date=December 2011}} When the nuts are shaken, the system has the tendency to move to a lower energy state, which means moving the center of mass down by moving the smaller nuts down and thereby the Brazil nuts up.{{citation needed|date=December 2011}}
* Including the effects of [[air]] in spaces between particles, larger particles may become [[buoyancy|buoyant]] or sink. Smaller particles can fall into the spaces underneath a larger particle after each shake. Over time, the larger particle rises in the mixture. (According to [[Heinrich Jaeger]], "[this] explanation for size separation might work in situations in which there is no granular convection, for example for containers with completely frictionless side walls or deep below the surface of tall containers (where convection is strongly suppressed). On the other hand, when friction with the side walls or other mechanisms set up a convection roll pattern inside the vibrated container, we found that the convective motion immediately takes over as the dominant mechanism for size separation."<ref>{{cite web|url=https://www.pbs.org/safarchive/3_ask/archive/qna/3294_sand.html |title=Sidney Nagel and Heinrich Jaeger Q&A |publisher=Pbs.org |accessdate=2010-09-27}}</ref>)
* The same explanation without buoyancy or center of mass arguments: As a larger particle moves upward, any motion of smaller particles into the spaces underneath blocks the larger particle from settling back in its previous position. Repetitive motion results in more smaller particles slipping beneath larger particles. A greater density of the larger particles has no effect on this process. Shaking is not necessary; any process which raises particles and then lets them settle would have this effect. The process of raising the particles imparts potential energy into the system. The result of all the particles settling in a different order may be an increase in the potential energy—a raising of the center of mass.{{cn|date=March 2025}}
* When shaken, the particles move in vibration-induced [[convection]] flow; individual particles move up through the middle, across the surface, and down the sides. If a large particle is involved, it will be moved up to the top by convection flow. Once at the top, the large particle will stay there because the convection currents are too narrow to sweep it down along the wall.
* The pore size distribution of a random packing of hard spheres with various sizes makes that smaller spheres have larger probability to move downwards by gravitation than larger spheres.<ref>W.Soppe, Computer simulation of random packings of hard spheres, Powder Technology, Volume 62, Issue 2, August 1990, Pages 189-197, https://doi.org/10.1016/0032-5910(90)80083-B</ref>

The phenomenon is related to [[Parrondo's paradox#The saw-tooth example|Parrondo's paradox]] in as much as the Brazil nuts move to the top of the mixed nuts against the gravitational gradient when subjected to random shaking.<ref>{{cite book |last=Abbott | first=Derek | authorlink=Derek Abbott |title=Applications of Nonlinear Dynamics |publisher=Springer |year=2009 |pages=307–321 |chapter=Developments in Parrondo's Paradox |isbn=978-3-540-85631-3}}</ref>

== Study techniques ==
Granular convection has been probed by the use of [[magnetic resonance imaging]] (MRI),<ref>{{cite journal|title=Granular Convection Observed by Magnetic Resonance Imaging |doi=10.1126/science.267.5204.1632|year=1995|last1=Ehrichs|first1=E. E.|last2=Jaeger|first2=H. M.|last3=Karczmar|first3=G. S.|last4=Knight|first4=J. B.|last5=Kuperman|first5=V. Yu.|last6=Nagel|first6=S. R.|s2cid=29865605|journal=Science|volume=267|issue=5204|pages=1632–4|pmid=17808181|bibcode = 1995Sci...267.1632E }}</ref> where [[convection rolls]] similar to those in fluids ([[Bénard cell]]s) can be visualized.

Other studies have used time-lapse [[CT scan|CT scans]], [[Refractive index matching|refractive index matched]] fluids, and [[Positron emission tomography tracer|positron emission tracing]].<ref name=":0" />  On the lower-tech end of the scale, researchers have also used thin, clear plastic boxes, so that the motion of some objects is directly visible.<ref name=":0" />

The effect has been observed in even tiny particles driven only by [[brownian motion]] with no external energy input.<ref>{{Cite web |last=Warsaw |first=University of |title=Defying gravity with the Brazil nut effect |url=https://phys.org/news/2023-04-defying-gravity-brazil-nut-effect.html |access-date=2023-04-21 |website=phys.org |language=en}}</ref>

==Applications==

===Manufacturing===
[[File:Raisin Bran Cereal in box (38390064056).jpg|alt=Raisins and bran flakes, inside a cereal box.  Multiple raisins are visible on top of the flakes|thumb|This phenomenon results in [[Raisin|raisins]] tending to rise to the top of a box of [[breakfast cereal]], so that the first servings of the cereal contain more raisins than usual, and only flakes are left at the bottom of the box.]]

The effect is of interest to food manufacturing and similar operations.<ref name=":0" /> Once a homogeneous mixture of granular materials has been produced, it is usually undesirable for the different particle types to segregate.  Several factors determine the severity of the Brazil nut effect, including the sizes and [[density|densities]] of the particles, the [[pressure]] of any [[gas]] between the particles, and the shape of the container. A rectangular box (such as a box of [[breakfast cereal]]) or [[cylinder (geometry)|cylinder]] (such as a can of nuts) works well to favour the effect,{{Citation needed|date=February 2008}} while a container with outwardly slanting walls (such as in a conical or spherical geometry) results in what is known as the '''reverse Brazil nut effect'''.<ref>{{Cite journal|last1=Knight|first1=James B.|last2=Jaeger|first2=H. M.|last3=Nagel|first3=Sidney R.|date=1993-06-14|title=Vibration-induced size separation in granular media: The convection connection|journal=Physical Review Letters|language=en|volume=70|issue=24|pages=3728–3731|doi=10.1103/PhysRevLett.70.3728|pmid=10053947|bibcode=1993PhRvL..70.3728K|issn=0031-9007}}</ref>

===Astronomy===
In [[astronomy]], it is common in low density, or [[rubble pile]] [[asteroid]]s, for example the asteroid [[25143 Itokawa]]<ref>{{Cite APOD |date=22 April 2007 |title=Smooth Sections of Asteroid Itokawa |access-date=}}</ref> and [[101955 Bennu]].<ref>{{cite journal|arxiv=2002.01468|doi=10.1016/j.icarus.2020.113963 |pmc=7571586|title=Ricochets on asteroids: Experimental study of low velocity grazing impacts into granular media|year=2020|last1=Wright|first1=Esteban|last2=Quillen|first2=Alice C.|last3=South|first3=Juliana|last4=Nelson|first4=Randal C.|last5=Sánchez|first5=Paul|last6=Siu|first6=John|last7=Askari|first7=Hesam|last8=Nakajima|first8=Miki|last9=Schwartz|first9=Stephen R.|s2cid=219965690|journal=Icarus|volume=351|page=113963|pmid=33087944 |bibcode=2020Icar..35113963W}}</ref>

===Geology===
In [[geology]], the effect is common in formerly glaciated areas such as [[New England]] and areas in regions of [[permafrost]] where the landscape is shaped into [[hummocks]] by [[frost heave]] — new stones appear in the fields every year from deeper underground. [[Horace Greeley]] noted "Picking stones is a never-ending labor on one of those New England farms. Pick as closely as you may, the next plowing turns up a fresh eruption of boulders and pebbles, from the size of a hickory nut to that of a tea-kettle."<ref>[http://www.osv.org/school/lesson_plans/ShowLessons.php?PageID=P&LessonID=34&DocID=96 excerpt from ''Recollections of a Busy Life''] {{webarchive|url=https://archive.today/20120910004003/http://www.osv.org/school/lesson_plans/ShowLessons.php?PageID=P&LessonID=34&DocID=96 |date=2012-09-10 }}, by Horace Greeley 1869</ref> A hint to the cause appears in his further description that "this work is mainly to be done in March or April, when the earth is saturated with ice-cold water". Underground water freezes, lifting all particles above it.  As the water starts to melt, smaller particles can settle into the opening spaces while larger particles are still raised.  By the time ice no longer supports the larger rocks, they are at least partially supported by the smaller particles that slipped below them.  Repeated freeze-thaw cycles in a single year speeds up the process.

This phenomenon is one of the causes of [[Graded bedding|inverse grading]] which can be observed in many situations including [[soil liquefaction]] during [[earthquake]]s or [[Mass wasting#Flows|mudslides]]. [[Liquefaction]] is a general phenomenon where a mixture of fluid and granular material subjected to vibration ultimately leads to circulation patterns similar to both fluid convection and granular convection. Indeed, liquefaction is fluid-granular convection with circulation patterns which are known as [[Sand boil|sand boils]] or sand volcanoes in the study of soil liquefaction.<ref>{{Cite journal |last=Taslimian |first=Rohollah |date=2024 |title=Turbulent-Fluid-Based Simulation of Dynamic Liquefaction Using Large Deformation Analysis of Solid Phase |url=https://thescipub.com/abstract/ajeassp.2024.51.55 |journal=American Journal of Engineering and Applied Sciences |language=en |volume=17 |issue=2 |pages=51–55 |doi= |issn=1941-7039}}</ref> Granular convection is also exemplified by [[debris flow]], which is a fast moving, liquefied landslide of unconsolidated, saturated debris that looks like flowing concrete. These flows can carry material ranging in size from clay to boulders, including woody debris such as logs and tree stumps. Flows can be triggered by intense rainfall, glacial melt, or a combination of the two.{{Cn|date=March 2025}}

==See also==
* [[Cheerios effect]]
* Popcorn effect on [[high-frequency vibrating screens]]

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==References==
{{reflist}}

==External links==
* {{YouTube|id = 4nnEGEjGWik|title = Beads in a Box}}
* [http://physicsweb.org/article/news/5/4/5 The Brazil Nut Effect] on [[Physicsweb|PhysicsWeb]]
* {{Cite journal
| doi = 10.1103/PhysRevLett.91.014302
| volume = 91
| issue = 1
| page = 014302
| last = Yan
| first = X.
|author2=Q. Shi |author3=M. Hou |author4=K. Lu |author5=C. K. Chan
 | title = Effects of Air on the Segregation of Particles in a Shaken Granular Bed
| journal = Physical Review Letters
| date = 2003-07-03
| pmid=12906541
| bibcode=2003PhRvL..91a4302Y
}}
* [http://mtrenouf.googlepages.com/simulationresults The Brazil Nut Effect: Numerical Simulation] Example of a numerical simulation of the Brazil Nut Effect.
* [http://news.bbc.co.uk/2/hi/science/nature/1655558.stm "Why brazils always end up on top"], [[BBC News]], 15 November 2001
* [http://www.sciam.com/article.cfm?id=why-does-shaking-a-can-of "Why does shaking a can of coffee cause the larger grains to move to the surface?"], ''[[Scientific American]]'', 9 May 2005
* [https://www.thestar.com/news/2008/01/13/of_airbags_avalungs_and_avalanche_safety.html "Of airbags, Avalungs and avalanche safety"], ''[[Toronto Star]]'', 13 January 2008
* {{cite web|last=Bowley|first=Roger|title=Γ – Ratio of Acceleration to Gravity (and the Brazil Nut effect)|url=http://www.sixtysymbols.com/videos/brazilnut.htm|work=Sixty Symbols|publisher=[[Brady Haran]] for the [[University of Nottingham]]|year=2009}}

{{DEFAULTSORT:Granular Convection}}
[[Category:Granularity of materials]]
[[Category:Convection]]