Cayley's theorem: Difference between revisions

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{{About|the scientific device|the Christian camp|Centrifuge (camps)|spin direction in quantum mechanics|Spin (physics)#Spin direction}}
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{{refimprove|date=January 2009}}
 
[[File:Tabletop centrifuge.jpg|thumb|200px|A laboratory tabletop centrifuge. The rotating unit, called the rotor, has fixed holes drilled at an angle (to the vertical). Test tubes are placed in these slots and the motor is spun.  As the centrifugal force is in the horizontal plane and the tubes are fixed at an angle, the particles have to travel only a little distance before they hit the wall and drop down to the bottom. These angle rotors are very popular in the lab for routine use.]]
A '''centrifuge''' is a piece of equipment, generally driven by an electric motor (or, in some older models, by hand), that puts an object in [[rotation around a fixed axis]], applying a force perpendicular to the axis. A centrifuge is also used to separate the components of blood in blood banks. The centrifuge works using the [[Sedimentation|sedimentation principle]], where the [[centripetal acceleration]] causes denser substances to separate out along the radial direction (the bottom of the tube).  By the same token lighter objects will tend to move to the top (of the tube; in the rotating picture, move to the centre).
 
== Theory ==
 
Protocols for centrifugation typically specify the amount of [[acceleration]] to be applied to the sample, rather than specifying a [[rotational speed]] such as [[revolutions per minute]]. This distinction is important because two rotors with different diameters running at the same rotational speed will subject samples to different accelerations. During [[circular motion]] the acceleration is the product of the [[radius]] and the square of the [[angular velocity]] <math>\omega</math>, and the acceleration relative to "''g''" is traditionally named "relative centrifugal force" (RCF). The acceleration is measured in multiples of "''g''" (or &times;&nbsp;"''g''"), the standard acceleration due to [[gravity]] at the Earth's surface,  a [[dimensionless quantity]] given by the expression:[[File:19thCentrifuge.JPG|right|thumb|200px|A 19th-century hand cranked laboratory centrifuge.]]
 
: <math> \text{RCF} =  \frac{r \omega^2}{g}</math>
 
where
:<math>\textstyle g </math> is earth's [[Standard gravity|gravitational acceleration]],
:<math>\textstyle r </math> is the rotational radius,
:<math>\omega</math> is the [[angular velocity]] in radians per unit time
 
This relationship may be written as
 
: <math> \text{RCF} = 1.11824396\, \times 10^{-5}\, r_\text{cm} \, N_\text{RPM}^2</math>
 
where
:<math>\textstyle r_\text{cm} </math> is the rotational radius measured in centimetres (cm), and
:<math>\textstyle N_\text{RPM} </math> is [[rotational speed]] measured in [[revolutions per minute]] (RPM).
 
== History and predecessors ==
 
[[File:Alfa Laval separator reklam.jpg|right|thumb|200px|Early 20th-century advertising poster for a [[separator (milk)|milk separator]].]]
 
English military engineer [[Benjamin Robins]] (1707&ndash;1751) invented a whirling arm apparatus to determine [[Drag (physics)|drag]]. In 1864, [[Antonin Prandtl]] invented the first dairy centrifuge in order to separate cream from milk. In
first continuous centrifugal separator, making its commercial application feasible.
 
== Types ==
 
There are multiple types of centrifuge, which can be classified by intended use or by rotor design:
 
Types by rotor design: <ref name=ColeParmer>{{cite web|title=Basics of Centrifugation|url=http://www.coleparmer.com/TechLibraryArticle/30|publisher=Cole-Parmer|accessdate=11 March 2012}}</ref><ref>[http://www.thermo.com/eThermo/CMA/PDFs/Various/File_6810.pdf "Plasmid DNA Separation: Fixed-Angle and Vertical Rotors in the Thermo Scientific Sorvall Discovery™ M120 & M150 Microultracentrifuges" (Thermo Fischer  publication)]</ref><ref name=UQU.edu/><ref name=Heidcamp>{{cite web|last=Heidcamp|first=Dr. William H.|title=Appendix F|url=http://homepages.gac.edu/~cellab/appds/appd-f.html|work=Cell Biology Laboratory Manual|publisher=Gustavus Adolphus College,|accessdate=11 March 2012}}</ref>
* Fixed-angle centrifuges are designed to hold the sample containers at a constant angle relative to the central axis.
* Swinging head (or swinging bucket) centrifuges, in contrast to fixed-angle centrifuges, have a hinge where the sample containers are attached to the central rotor.  This allows the samples to swing outwards as the centrifuge is spun.
* Continuous tubular centrifuges don't have individual sample vessels and are used for high volume applications.
 
Types by intended use:
* [[Ultracentrifuge]]s  are optimized for spinning a rotor at very high speeds and are popular in the fields of molecular biology, biochemistry and polymer science.  This type may include preparative or analytical, fixed-angle or swing head varieties.<ref name=UQU.edu>http://uqu.edu.sa/files2/tiny_mce/plugins/filemanager/files/4250119/lectures/1._instr.pdf</ref>  
* [[Haematocrit]] centrifuges are used to measure  the percentage of red blood cells in whole blood.
* [[Gas centrifuge]]s, including [[Zippe-type centrifuge]]s
 
Industrial centrifuges may otherwise be classified according to the type of separation of the high density fraction from the low density one:
*Screen centrifuges, where the centrifugal acceleration allows the liquid to pass through a [[Sieve|screen]] of some sort, through which the solids cannot go (due to [[granulometry]] larger than the screen gap or due to agglomeration). Common types are:
**[[Screen scroll centrifuge|Screen/scroll centrifuges]]
**[[Pusher centrifuge]]s
**[[Peeler centrifuge]]s
**[[Decanter centrifuge]]s, in which there is no physical separation between the solid and liquid phase, rather an accelerated [[settling]] due to centrifugal acceleration.
**Continuous liquid; common types are:
***[[Solid bowl centrifuge]]s
***[[Conical plate centrifuge]]s
 
== Uses ==
=== Isolating suspensions ===
{{main|Laboratory centrifuge}}
Simple centrifuges are used in chemistry, biology, and biochemistry for isolating and separating suspensions. They vary widely in speed and capacity. They usually comprise a rotor containing two, four, six, or many more numbered wells within which the samples, contained in centrifuge tubes, may be placed.
 
=== Isotope separation ===
{{main|Gas centrifuge}}
Other centrifuges, the first being the [[Zippe-type centrifuge]],  separate [[isotope]]s, and these kinds of centrifuges are in use in [[nuclear power]] and [[nuclear weapon]] programs.
 
[[Gas centrifuge]]s are used in [[uranium enrichment]]. The heavier [[isotope]] of uranium ([[uranium-238]]) in the [[uranium hexafluoride]] gas tends to concentrate at the walls of the centrifuge as it spins, while the desired [[uranium-235]] isotope is extracted and concentrated with a scoop selectively placed inside the centrifuge.{{citation needed|date=February 2012}} It takes many thousands of centrifugations to enrich uranium enough for use in a [[nuclear reactor]] (around 3.5% enrichment),{{citation needed|date=February 2012}} and many thousands more to enrich it to [[weapons-grade]] (above 90% enrichment) for use in [[nuclear weapons]].{{citation needed|date=February 2012}}
 
=== Aeronautics and astronautics ===
{{main|High-G training}}[[File:20G centrifuge.jpg|thumb|300px|left|The 20 G centrifuge at the [[NASA Ames Research Center]]]]
'''Human centrifuges''' are exceptionally large centrifuges that test the reactions and tolerance of [[aviator|pilots]] and [[astronaut]]s to acceleration above those experienced in the Earth's [[gravity]].
 
The US Air Force at [[Holloman Air Force Base]], New Mexico operates a human centrifuge.  The centrifuge at Holloman AFB is operated by the [[aerospace physiology]] department for the purpose of training and evaluating prospective fighter pilots for high-''g'' flight in Air Force fighter aircraft.<ref name=Hypergravity>{{cite web|title=The Pull of HyperGravity - A NASA researcher is studying the strange effects of artificial gravity on humans.|url=http://science.nasa.gov/science-news/science-at-nasa/2003/07feb_stronggravity/|publisher=NASA|accessdate=11 March 2012}}</ref>
 
The use of large centrifuges to simulate a feeling of [[gravity]] has been proposed for future long-duration space missions. Exposure to this simulated gravity would prevent or reduce the [[bone decalcification]] and [[muscle atrophy]] that affect individuals exposed to long periods of freefall. <ref name=Hypergravity /> <ref name=Space>{{cite web|last=Hsu|first=Jeremy|title=New Artificial Gravity Tests in Space Could Help Astronauts|url=http://www.space.com/8384-artificial-gravity-tests-space-astronauts.html|publisher=Space.com|accessdate=11 March 2012}}</ref>
 
The first centrifuges used for human research were used by Erasmus Darwin, the grandfather of Charles Darwin.  The first largescale human centrifuge designed for Aeronautical training was created in Germany in 1933.<ref>http://www.dtic.mil/dtic/tr/fulltext/u2/a236267.pdf</ref>
 
===Geotechnical centrifuge modeling===
[[Geotechnical centrifuge modeling]] is used for physical testing of models involving soils. Centrifuge acceleration is applied to scale models to scale the gravitational acceleration and enable prototype scale stresses to be obtained in scale models. Problems such as building and bridge foundations, earth dams, tunnels, and slope stability, including effects such as blast loading and earthquake shaking.<ref name=KOWACO>{{cite book |title=Physical Modelling in Geotechnics: proceedings of the Sixth International Conference on Physical Modelling in Geotechnics |author=C. W. W. Ng, Y. H. Wang, L. M. Zhang |page=135 |url=http://books.google.com/books?id=mzQlFBqJC1wC&pg=RA1-PA186&dq=centrifuge+earthquake#PRA1-PA135,M1  |isbn=0-415-41586-1 |year=2006 |publisher=Taylor & Francis}}</ref>
 
=== Commercial applications ===
* Centrifuges with a batch weight of up to 2,200&nbsp;kg per charge are used in the sugar industry to separate the [[sugar]] crystals from the [[mother liquor]].<ref>[http://www.bma-automation.com/Zentrifugensteuerung.2066.0.html?id=2066&L=1 article on centrifugal controls, retrieved on June 5, 2010]</ref>
* Standalone centrifuges for drying (hand-washed) clothes &ndash; usually with a water outlet.
* Centrifuges are used in the attraction [[Mission: SPACE]], located at [[Epcot]] in [[Walt Disney World]], which propels riders using a combination of a centrifuge and a [[motion simulator]] to simulate the feeling of going into [[space]].
* In [[soil mechanics]], centrifuges utilize centrifugal acceleration to match soil stresses in a scale model to those found in reality.
* Large industrial centrifuges are commonly used in [[water]] and [[wastewater]] treatment to dry [[sludge]]s. The resulting dry product is often termed '''cake''', and the water leaving a centrifuge after most of the solids have been removed is called '''centrate'''.
* Large industrial centrifuges are also used in the [[oil industry]] to remove solids from the [[drilling fluid]].
* Disc-stack centrifuges used by some companies in [[Oil Sands]] industry to separate small amounts of water and solids from [[bitumen]]
* Centrifuges are used to separate cream (remove fat) from milk; see [[Separator (milk)]].
 
==References and notes==
{{Reflist}}
 
==Further reading==
*[http://www.civil.ubc.ca/liquefaction/Publications/flow%20liq_Naesgaard%20et%20al%20version31.pdf Naesgaard ''et al.'', ''Modeling flow liquefaction, its mitigation, and comparison with centrifuge tests'']
 
== See also ==
* [[Lamm equation]]
* [[Sedimentation]]
* [[Centrifugal force]]
* [[Centrifugation]]
* [[Gas centrifuge]]
* [[Sedimentation coefficient]]
* [[Clearing factor]]
* [[Hydroextractor]]
 
== External links ==
{{Commons category|Centrifuges}}
{{Wiktionary|centrifuge}}
*[http://www.djblabcare.co.uk/djb/info/6/user_tools RCF Calculator and Nomograph]
*[http://www.changbioscience.com/cell/rcf.html Centrifugation Rotor Calculator]
*[http://vlp.mpiwg-berlin.mpg.de/technology/search?-max=10&-title=1&-op_varioid=numerical&varioid=3 Selection of historical centrifuges] in the Virtual Laboratory of the [[Max Planck Institute for the History of Science]]
 
[[Category:Centrifuges|Centrifuges]]

Latest revision as of 17:44, 5 December 2014

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Endocrinologic Impotence: Endocrinologic impotence occurs due to an imbalance of sex hormones in the blood stream. High blood pressure is one of the major set back that has direct impact on corpa covernosa. This medication may take up to four weeks to become fully effective, if used properly. You should not take Cialis if you are taking a nitrate drug for chest pain or heart problems, including nitroglycerin. Guys who have achieved this are invaluable to research because they have served as the missing control group in studies; those without the effects of internet pornography: Previously, researchers couldn't find ANY guys who were not surfing pornography.

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