Relative velocity profile and flow‐rate in sedimentation field‐flow fractionation
Identifieur interne : 001363 ( France/Analysis ); précédent : 001362; suivant : 001364Relative velocity profile and flow‐rate in sedimentation field‐flow fractionation
Auteurs : Michel Martin [France]Source :
- Journal of High Resolution Chromatography [ 0935-6304 ] ; 1996-09.
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Abstract
Although the classical retention theory is used for interpreting data or optimizing separations in sedimentation field‐flow fractionation (SedFFF), as in most other field‐flow fractionation techniques, the assumption of a parabolic flow profile on which this theory is based is not rigorously correct in SedFFF because of the curvature of the channel walls. In order to examine quantitatively the influence of this effect, the relative velocity profile in SedFFF is obtained by solving the Navier‐Stokes equation in cylindrical coordinates. Discrepancies found in the literature about the definition of the mean velocity in such channels are discussed. Relationships between mean velocity, flow‐rate and pressure gradient are given. Approximating the velocity profile by a third‐degree polynomial of the radial coordinate which provides the same slope as the exact profile at a reference wall, for small values of δ, the curvature ratio (ratio of the channel thickness to the mean curvature radius), shows that the adjustable parameter of the approximate profile, ν, is equal to ± δ/3, the sign depending on whether the reference wall is the inner or outer wall. The curvature ratio appears to be a good indicator of the error made on retention when using the straight channel approximation in retention theory. The error is quite small for typical SedFFF channels. It may have to be taken into account for precise determinations if thicker channels and/or miniaturized systems are used.
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DOI: 10.1002/jhrc.1240190902
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ISTEX:7C19EB145FAD2425CCBE3A3FDAB98D47FB1BE912Le document en format XML
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High Resol. Chromatogr.</title><idno type="ISSN">0935-6304</idno><idno type="eISSN">1521-4168</idno><imprint><publisher>Wiley Subscription Services, Inc., A Wiley Company</publisher><pubPlace>Hoboken</pubPlace><date type="published" when="1996-09">1996-09</date><biblScope unit="volume">19</biblScope><biblScope unit="issue">9</biblScope><biblScope unit="page" from="481">481</biblScope><biblScope unit="page" to="484">484</biblScope></imprint><idno type="ISSN">0935-6304</idno></series><idno type="istex">7C19EB145FAD2425CCBE3A3FDAB98D47FB1BE912</idno><idno type="DOI">10.1002/jhrc.1240190902</idno><idno type="ArticleID">JHRC1240190902</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0935-6304</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Curved Poiseulle flow</term><term>Curved channels</term><term>Flow‐rate</term><term>Sedimentation field‐flow fractionation</term><term>Velocity profile</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Although the classical retention theory is used for interpreting data or optimizing separations in sedimentation field‐flow fractionation (SedFFF), as in most other field‐flow fractionation techniques, the assumption of a parabolic flow profile on which this theory is based is not rigorously correct in SedFFF because of the curvature of the channel walls. In order to examine quantitatively the influence of this effect, the relative velocity profile in SedFFF is obtained by solving the Navier‐Stokes equation in cylindrical coordinates. Discrepancies found in the literature about the definition of the mean velocity in such channels are discussed. Relationships between mean velocity, flow‐rate and pressure gradient are given. Approximating the velocity profile by a third‐degree polynomial of the radial coordinate which provides the same slope as the exact profile at a reference wall, for small values of δ, the curvature ratio (ratio of the channel thickness to the mean curvature radius), shows that the adjustable parameter of the approximate profile, ν, is equal to ± δ/3, the sign depending on whether the reference wall is the inner or outer wall. The curvature ratio appears to be a good indicator of the error made on retention when using the straight channel approximation in retention theory. The error is quite small for typical SedFFF channels. It may have to be taken into account for precise determinations if thicker channels and/or miniaturized systems are used.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Île-de-France</li></region><settlement><li>Paris</li></settlement></list><tree><country name="France"><region name="Île-de-France"><name sortKey="Martin, Michel" sort="Martin, Michel" uniqKey="Martin M" first="Michel" last="Martin">Michel Martin</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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