Magic angle - Revision history

en>Tom.Reding: WP:GenFixes (page/s, endash, , unicodify, and/or concising wikilinks, etc.), et al., ed., ref cleanup using AWB

2015-01-12T20:35:29Z

WP:GenFixes (page/s, endash, &nbsp, unicodify, and/or concising wikilinks, etc.), et al., ed., ref cleanup using AWB

← Older revision		Revision as of 22:35, 12 January 2015
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	[~~[Image~~:~~Taylor cone photo.jpg\|thumb\|right\|250 px\|Photograph of a meniscus of polyvinyl alcohol in aqueous solution showing a fibre drawn from a Taylor cone by the process of electrospinning.]]~~		I good psychic ([http://chorokdeul.co.kr/index.php?document_srl=324263&mid=customer21 chorokdeul.co.kr]) would like to introduce myself to you, I am Jayson Simcox but I don't like when people use my full title. Office supervising is my profession. For years he's been residing in Alaska and he doesn't plan on altering it. It's [http://test.jeka-nn.ru/node/129 online psychic chat] not a common thing but what she likes doing is to perform domino but she doesn't have the time recently.<br><br>my web blog: email psychic readings; [http://clothingcarearchworth.com/index.php?document_srl=441551&mid=customer_review find more information],
	A '''Taylor cone''' refers to the cone observed in [[electrospinning]], [[electrospray]]ing and hydrodynamic spray processes from which a jet of charged particles emanates above a threshold voltage. Aside from [[electrospray ionization]] in [[mass spectrometry]], the Taylor cone is important in [[FEEP]] and [[colloid thruster]]s used in fine control and high efficiency (low power) thrust of spacecraft.

	~~== History ==~~

	This cone was described by Sir [[Geoffrey Ingram Taylor]] in 1964 before electrospray was "discovered".<ref>{{cite journal \| author = Sir Geoffrey Taylor \| year = 1964 \| title = Disintegration of Water Droplets in an Electric Field \| journal = [[Proceedings of the Royal Society A]] \| volume = 280 \| pages = 383 \| issue = 1382 \| doi = 10.1098/~~rspa.1964~~.~~0151 \| jstor=2415876\|bibcode = 1964RSPSA~~.~~280..383T }}<~~/~~ref> This work followed on the work of Zeleny<ref>{{cite journal\| author=Zeleny, J~~. ~~\|title~~ = ~~The Electrical Discharge from Liquid Points, and a Hydrostatic Method of Measuring the Electric Intensity at Their Surfaces. \| journal~~ = ~~[[Physical Review]] \| year = 1914 \| volume = 3\| issue=2 \| pages = 69 \| doi = 10~~.~~1103/PhysRev~~.~~3.69\|bibcode = 1914PhRv....3...69Z }}</ref> who, in 1917,<ref>{{cite journal\| author=Zeleny, John \|title = Instability of electrified liquid surfaces. \| journal = [[Physical Review]~~] \| year = 1917 \| volume = 10\| issue=1 \| pages = 1–6 \| doi = 10.1103/PhysRev.10.1\|bibcode = Bibcode 1917PhRv...10....1Z }}</ref> photographed a cone-jet of glycerine under high electric field and the work of several others: Wilson and Taylor (1925),~~<ref>{{cite journal\|title=The bursting of soap bubbles in a uniform electric field\|journal=Proc. Cambridge Philos. Soc.\|year=1925\|first=C. T.\|last=Wilson\|coauthors= G.~~ I ~~Taylor\|volume=22\|issue=5\|pages=728\|id= \|url=\|format=\|accessdate=\|doi=10.1017/S0305004100009609 \|bibcode = 1925PCPS...22..728W }}</ref> Nolan (1926)<ref>{{cite journal\|~~title~~= \|journal=Proc~~. R. ~~Ir. Acad. Sect. A\|year=1926\|first=J. J.\|last=Nolan\|coauthors=\|volume=37\|issue=\|pages=28\|id= \|url=\|format=\|accessdate= }}</ref>~~ and ~~Macky (1931).<ref name=~~'~~rspa~~.~~1931.0168~~'~~>{{cite journal\|title=Some Investigations on the Deformation and Breaking of Water Drops in Strong Electric Fields\|journal=~~[~~[Proceedings of the Royal Society A]]\|date=October 1, 1931\|first=W. A.\|last=Macky\|coauthors=\|volume=133\|issue=822\|pages=565–587\|doi= 10.1098/rspa.1931.0168\|bibcode = 1931RSPSA.133..565M }}\|url=~~http://~~www.journals.royalsoc.ac.uk/content/c6188343042555vw/fulltext~~.~~pdf\|format=PDF\|accessdate=2007-10~~-~~25</ref> Taylor was primarily interested in the behavior of water droplets in strong electric fields, such as in thunderstorms.~~

	~~== Taylor cone formation ==~~
	~~[[Image:Taylor cone.jpg\|thumb\|right\|300 px\|Electrospray diagram depicting the Taylor cone, jet and plume]]~~
	When a small volume of electrically conductive liquid is exposed to an electric field, the shape of liquid starts to deform from the shape caused by surface tension alone. As the voltage is increased the effect of the electric field becomes more prominent and as it approaches exerting a similar amount of force on the droplet as the surface tension does a cone shape begins to form with convex sides and a rounded tip. This approaches the shape of a [[Cone (geometry)\|cone]] with a whole angle (width) of 98.6°.<ref>{{cite journal \| author = Sir Geoffrey Taylor \| year = 1964 \| title = Disintegration of Water Droplets in an Electric Field \| journal = [[Proceedings of the Royal Society A]] \| volume = 280 \| pages = 392 \| issue = 1382 \| doi = 10.~~1098~~/~~rspa.1964.0151 \| jstor=2415876\|bibcode = 1964RSPSA.280..383T }}<~~/~~ref> When a certain threshold voltage has been reached the slightly rounded tip inverts and emits a jet of liquid. This is called a cone-jet and is the beginning of the [[electrospray~~]~~]ing process in which ions may be transferred to the gas phase. It is generally found that in order to achieve~~ a ~~stable cone-jet a slightly higher than threshold voltage must be used. As the voltage~~ is ~~increased even more other modes of droplet disintegration are found. The term Taylor cone can specifically refer~~ to the ~~theoretical limit of a perfect cone of exactly the predicted angle or generally refer to the approximately conical portion of a cone-jet after the electrospraying process has begun.~~

	~~== Theory ==~~

	Sir [[Geoffrey Ingram Taylor]] in 1964 described this phenomenon, theoretically derived based on general assumptions that the requirements to form a perfect cone under such conditions required a semi-vertical angle of 49.3° (a whole angle of 98.6°) and demonstrated that the shape of such a cone approached the theoretical shape just before jet formation. ~~This angle is known as the '''Taylor angle'''. This angle is more precisely <math>\pi-\theta _0\,</math> where <math>\theta _0\,~~<~~/math~~> ~~is the first zero of~~ <~~math~~>~~P _{1/2} (\cos\theta _0)\,</math> (the [[Legendre polynomial]] of order 1/2).~~

	~~Taylor's derivation is based on two assumptions~~: ~~(1) that the surface of the cone is an equipotential surface and (2) that the cone exists in a steady state equilibrium. To meet both of these criteria the electric field must have~~ [~~[azimuth]]al symmetry and have <math>\sqrt{R}\,</math> dependence to counter the surface tension to produce the cone. The solution to this problem is:~~

	:~~<math>V=V_0+AR^{1/2}P _{1/2} (\cos\theta _0)\,</math>~~

	~~where <math>V=V_0\,<~~/~~math> (equipotential surface) exists at a value of <math>\theta _0<~~/~~math> (regardless of R) producing an equipotential cone~~. ~~The angle necessary for <math>V=V_0\,<~~/~~math> for all R is a zero of <math>P _{1/2} (\cos\theta _0)\,</math> between 0 and <math>\pi\,</math> which there is only one at 130~~.~~7099°. The complement of this angle is the Taylor angle.~~

	== ~~References ==~~
	~~{{reflist}}~~

	~~==External links==~~

	~~[[Category:Mass spectrometry]~~]

en>ChrisGualtieri: General Fixes using AWB

2013-10-22T01:11:25Z

General Fixes using AWB

← Older revision		Revision as of 03:11, 22 October 2013
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	~~The writer~~'s ~~title is Christy~~. ~~Since he~~ was ~~eighteen he's been working as~~ an ~~info officer but he plans~~ on ~~changing it~~. ~~For many years he's been living~~ in ~~Mississippi~~ and ~~he doesn~~'~~t strategy~~ on ~~changing~~ it. It~~'s not~~ a ~~common thing but what I like doing~~ is to ~~climb but I don~~'t have the ~~time lately~~.<br><br>~~Here~~ is ~~my homepage best psychics~~ (~~[http:~~//~~isaworld~~.pe.~~kr/?document_srl~~=~~392088 please click the next website~~])		[[Image:Taylor cone photo.jpg\|thumb\|right\|250 px\|Photograph of a meniscus of polyvinyl alcohol in aqueous solution showing a fibre drawn from a Taylor cone by the process of electrospinning.]]
			A '''Taylor cone''' refers to the cone observed in [[electrospinning]], [[electrospray]]ing and hydrodynamic spray processes from which a jet of charged particles emanates above a threshold voltage. Aside from [[electrospray ionization]] in [[mass spectrometry]], the Taylor cone is important in [[FEEP]] and [[colloid thruster]]s used in fine control and high efficiency (low power) thrust of spacecraft.

			== History ==

			This cone was described by Sir [[Geoffrey Ingram Taylor]] in 1964 before electrospray was "discovered".<ref>{{cite journal \| author = Sir Geoffrey Taylor \| year = 1964 \| title = Disintegration of Water Droplets in an Electric Field \| journal = [[Proceedings of the Royal Society A]] \| volume = 280 \| pages = 383 \| issue = 1382 \| doi = 10.1098/rspa.1964.0151 \| jstor=2415876\|bibcode = 1964RSPSA.280..383T }}</ref> This work followed on the work of Zeleny<ref>{{cite journal\| author=Zeleny, J. \|title = The Electrical Discharge from Liquid Points, and a Hydrostatic Method of Measuring the Electric Intensity at Their Surfaces. \| journal = [[Physical Review]] \| year = 1914 \| volume = 3\| issue=2 \| pages = 69 \| doi = 10.1103/PhysRev.3.69\|bibcode = 1914PhRv....3...69Z }}</ref> who, in 1917,<ref>{{cite journal\| author=Zeleny, John \|title = Instability of electrified liquid surfaces. \| journal = [[Physical Review]] \| year = 1917 \| volume = 10\| issue=1 \| pages = 1–6 \| doi = 10.1103/PhysRev.10.1\|bibcode = Bibcode 1917PhRv...10....1Z }}</ref> photographed a cone-jet of glycerine under high electric field and the work of several others: Wilson and Taylor (1925),<ref>{{cite journal\|title=The bursting of soap bubbles in a uniform electric field\|journal=Proc. Cambridge Philos. Soc.\|year=1925\|first=C. T.\|last=Wilson\|coauthors= G. I Taylor\|volume=22\|issue=5\|pages=728\|id= \|url=\|format=\|accessdate=\|doi=10.1017/S0305004100009609 \|bibcode = 1925PCPS...22..728W }}</ref> Nolan (1926)<ref>{{cite journal\|title= \|journal=Proc. R. Ir. Acad. Sect. A\|year=1926\|first=J. J.\|last=Nolan\|coauthors=\|volume=37\|issue=\|pages=28\|id= \|url=\|format=\|accessdate= }}</ref> and Macky (1931).<ref name='rspa.1931.0168'>{{cite journal\|title=Some Investigations on the Deformation and Breaking of Water Drops in Strong Electric Fields\|journal=[[Proceedings of the Royal Society A]]\|date=October 1, 1931\|first=W. A.\|last=Macky\|coauthors=\|volume=133\|issue=822\|pages=565–587\|doi= 10.1098/rspa.1931.0168\|bibcode = 1931RSPSA.133..565M }}\|url=http://www.journals.royalsoc.ac.uk/content/c6188343042555vw/fulltext.pdf\|format=PDF\|accessdate=2007-10-25</ref> Taylor was primarily interested in the behavior of water droplets in strong electric fields, such as in thunderstorms.

			== Taylor cone formation ==
			[[Image:Taylor cone.jpg\|thumb\|right\|300 px\|Electrospray diagram depicting the Taylor cone, jet and plume]]
			When a small volume of electrically conductive liquid is exposed to an electric field, the shape of liquid starts to deform from the shape caused by surface tension alone. As the voltage is increased the effect of the electric field becomes more prominent and as it approaches exerting a similar amount of force on the droplet as the surface tension does a cone shape begins to form with convex sides and a rounded tip. This approaches the shape of a [[Cone (geometry)\|cone]] with a whole angle (width) of 98.6°.<ref>{{cite journal \| author = Sir Geoffrey Taylor \| year = 1964 \| title = Disintegration of Water Droplets in an Electric Field \| journal = [[Proceedings of the Royal Society A]] \| volume = 280 \| pages = 392 \| issue = 1382 \| doi = 10.1098/rspa.1964.0151 \| jstor=2415876\|bibcode = 1964RSPSA.280..383T }}</ref> When a certain threshold voltage has been reached the slightly rounded tip inverts and emits a jet of liquid. This is called a cone-jet and is the beginning of the [[electrospray]]ing process in which ions may be transferred to the gas phase. It is generally found that in order to achieve a stable cone-jet a slightly higher than threshold voltage must be used. As the voltage is increased even more other modes of droplet disintegration are found. The term Taylor cone can specifically refer to the theoretical limit of a perfect cone of exactly the predicted angle or generally refer to the approximately conical portion of a cone-jet after the electrospraying process has begun.

			== Theory ==

			Sir [[Geoffrey Ingram Taylor]] in 1964 described this phenomenon, theoretically derived based on general assumptions that the requirements to form a perfect cone under such conditions required a semi-vertical angle of 49.3° (a whole angle of 98.6°) and demonstrated that the shape of such a cone approached the theoretical shape just before jet formation. This angle is known as the '''Taylor angle'''. This angle is more precisely <math>\pi-\theta _0\,</math> where <math>\theta _0\,</math> is the first zero of <math>P _{1/2} (\cos\theta _0)\,</math> (the [[Legendre polynomial]] of order 1/2).

			Taylor's derivation is based on two assumptions: (1) that the surface of the cone is an equipotential surface and (2) that the cone exists in a steady state equilibrium. To meet both of these criteria the electric field must have [[azimuth]]al symmetry and have <math>\sqrt{R}\,</math> dependence to counter the surface tension to produce the cone. The solution to this problem is:

			:<math>V=V_0+AR^{1/2}P _{1/2} (\cos\theta _0)\,</math>

			where <math>V=V_0\,</math> (equipotential surface) exists at a value of <math>\theta _0</math> (regardless of R) producing an equipotential cone. The angle necessary for <math>V=V_0\,</math> for all R is a zero of <math>P _{1/2} (\cos\theta _0)\,</math> between 0 and <math>\pi\,</math> which there is only one at 130.7099°. The complement of this angle is the Taylor angle.

			== References ==
			{{reflist}}

			==External links==

			[[Category:Mass spectrometry]]

en>DeMk9D76: Expanding article

2012-07-18T21:28:09Z

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