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2013-03-02T08:00:23Z

Bot: Migrating 3 interwiki links, now provided by Wikidata on d:q3274587

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	~~Nice to satisfy you, I am Marvella Shryock. In her expert life she~~ is a ~~payroll clerk but she~~'s ~~always wanted her own business~~. ~~Puerto Rico~~ is ~~exactly where he's always been living but she needs~~ to ~~transfer because~~ of ~~her family members~~. ~~Body developing~~ is ~~what my family~~ and ~~I appreciate~~.<br><br>~~Here~~ is ~~my homepage std home test~~ ([~~http~~://~~kgmcscs~~.~~realmind~~.~~net~~/~~xe/467281 Click~~ on ~~kgmcscs~~.~~realmind~~.~~net~~])		'''Intrinsic viscosity''' <math>\left[ \eta \right]</math> is a measure of a solute's contribution to the [[viscosity]] <math>\eta</math> of a [[solution]]. It should not be confused with '''[[inherent viscosity]]''', which is the ratio of the natural logarithm of the relative viscosity to the mass concentration of the polymer. <ref>{{cite web\|title=Dilute Solution Viscosity of Polymers\|url=http://www.ptli.com/testlopedia/tests/iv-d2857.asp}}</ref>

			Intrinsic viscosity is defined as

			<math>
			\left[ \eta \right] = \lim_{\phi \rightarrow 0} \frac{\eta - \eta_{0}}{\eta_{0}\phi}
			</math>

			where <math>\eta_0</math> is the viscosity in the absence of the solute and <math>\phi</math> is the volume fraction of the solute in the solution. As defined here, the intrinsic viscosity <math>\left[ \eta \right]</math> is a dimensionless number. When the solute particles are [[rigid body\|rigid]] [[sphere]]s, the intrinsic viscosity equals <math>
			\frac{5}{2}</math>, as shown first by [[Albert Einstein]].

			In practical settings, <math>\phi</math> is usually solute mass concentration ('''c''', g/dL), and the units of intrinsic viscosity <math>\left[ \eta \right]</math> are deciliters per gram (dL/g), otherwise known as inverse concentration.

			==Formulae for rigid spheroids==

			Generalizing from spheres to [[spheroid]]s with an axial semiaxis <math>a</math> (i.e., the semiaxis of revolution) and equatorial semiaxes <math>b</math>, the intrinsic viscosity can be written

			:<math>
			\left[ \eta \right] =
			\left( \frac{4}{15} \right) (J + K - L) +
			\left( \frac{2}{3} \right) L +
			\left( \frac{1}{3} \right) M +
			\left( \frac{1}{15} \right) N
			</math>

			where the constants are defined

			:<math>
			M \ \stackrel{\mathrm{def}}{=}\ \frac{1}{a b^{4}} \frac{1}{J_{\alpha}^{\prime}}
			</math>

			:<math>
			K \ \stackrel{\mathrm{def}}{=}\ \frac{M}{2}
			</math>

			:<math>
			J \ \stackrel{\mathrm{def}}{=}\ K \frac{J_{\alpha}^{\prime\prime}}{J_{\beta}^{\prime\prime}}
			</math>

			:<math>
			L \ \stackrel{\mathrm{def}}{=}\ \frac{2}{a b^{2} \left( a^{2} + b^{2} \right)}
			\frac{1}{J_{\beta}^{\prime}}
			</math>

			:<math>
			N \ \stackrel{\mathrm{def}}{=}\ \frac{6}{a b^{2}}
			\frac{\left( a^{2} - b^{2} \right)}{a^{2} J_{\alpha} + b^{2} J_{\beta}}
			</math>

			The <math>J</math> coefficients are the '''Jeffery functions'''

			:<math>
			J_{\alpha} =
			\int_{0}^{\infty} \frac{dx}{\left( x + b^{2} \right) \sqrt{\left( x + a^{2} \right)^{3}}}
			</math>

			:<math>
			J_{\beta} =
			\int_{0}^{\infty} \frac{dx}{\left( x + b^{2} \right)^{2} \sqrt{\left( x + a^{2} \right)}}
			</math>

			:<math>
			J_{\alpha}^{\prime} =
			\int_{0}^{\infty} \frac{dx}{\left( x + b^{2} \right)^{3} \sqrt{\left( x + a^{2} \right)}}
			</math>

			:<math>
			J_{\beta}^{\prime} =
			\int_{0}^{\infty} \frac{dx}{\left( x + b^{2} \right)^{2} \sqrt{\left( x + a^{2} \right)^{3}}}
			</math>

			:<math>
			J_{\alpha}^{\prime\prime} =
			\int_{0}^{\infty} \frac{x\ dx}{\left( x + b^{2} \right)^{3} \sqrt{\left( x + a^{2} \right)}}
			</math>

			:<math>
			J_{\beta}^{\prime\prime} =
			\int_{0}^{\infty} \frac{x\ dx}{\left( x + b^{2} \right)^{2} \sqrt{\left( x + a^{2} \right)^{3}}}
			</math>

			==General ellipsoidal formulae==

			It is possible to generalize the intrinsic viscosity formula from [[spheroid]]s to arbitrary ellipsoids with semiaxes <math>a</math>, <math>b</math> and <math>c</math>.

			==Frequency dependence==

			The intrinsic viscosity formula may also be generalized to include a frequency dependence.

			==Applications==

			The intrinsic viscosity is very sensitive to the [[axial ratio]] of spheroids, especially of prolate spheroids. For example, the intrinsic viscosity can provide rough estimates of the number of subunits in a [[protein]] fiber composed of a helical array of proteins such as [[tubulin]]. More generally, intrinsic viscosity can be used to assay [[quaternary structure]]. In [[polymer chemistry]] intrinsic viscosity is related to [[molar mass]] through the [[Mark-Houwink equation]]. A practical method for the determination of intrinsic viscosity is with a [[Ubbelohde viscometer]].

			==References==
			<references />

			* Jeffery GB. (1922) "The Motion of Ellipsoidal Particles Immersed in a Viscous Fluid", ''Proc. Roy. Soc.'', '''A102''', 161-179.

			* Simha R. (1940) "The Influence of Brownian Movement on the Viscosity of Solutions", ''J. Phys. Chem.'', '''44''', 25-34.

			* Mehl JW, Oncley JL, Simha R. (1940) "Viscosity and the Shape of Protein Molecules", ''Science'', '''92''', 132-133.

			* Saito N. (1951) ''J. Phys. Soc. Japan'', '''6''', 297.

			* Scheraga HA. (1955) "Non-Newtonian Viscosity of Solutions of Ellipsoidal Particles", ''J. Chem. Phys.'', '''23''', 1526-1531.


			[[Category:Fluid dynamics]]
			[[Category:Viscosity]]

en>ZéroBot: r2.7.1) (Robot: Adding it:Raggio idrodinamico

2012-05-29T10:09:21Z

r2.7.1) (Robot: Adding it:Raggio idrodinamico

New page

Nice to satisfy you, I am Marvella Shryock. In her expert life she is a payroll clerk but she's always wanted her own business. Puerto Rico is exactly where he's always been living but she needs to transfer because of her family members. Body developing is what my family and I appreciate.<br><br>Here is my homepage std home test ([http://kgmcscs.realmind.net/xe/467281 Click on kgmcscs.realmind.net])

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en>Addbot: Bot: Migrating 3 interwiki links, now provided by Wikidata on d:q3274587

en>ZéroBot: r2.7.1) (Robot: Adding it:Raggio idrodinamico