On the dispersion of a solute in a fluid flowing through a tube

Aris, Rutherford

doi:10.1098/rspa.1956.0065

Cited by 2,249 publications

(513 citation statements)

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“…In eq (14), K is the dispersion coefficient, R is the radius of the diffusion tube and v is the axial velocity of the solvent averaged over the cross section of the tube. The standard relative uncertainties appearing on the right of eq (15) As expected, the diffusion coefficient increases with increasing temperature and declines with increasing pressure.…”

Section: Resultsmentioning

confidence: 99%

“…7,11 This technique exploits the combined effects of axial dispersion, primarily due to a parabolic velocity profile, and radial dispersion, due to molecular diffusion, on a solute in laminar flow. These combined effects produce a Gaussian concentration distribution which when treated with the approach of Taylor 13 and Aris 14 yields the diffusion coefficient. The technique is relatively quick, is based upon a rigorous working equation, and allows measurements to be performed under extreme conditions of temperature and pressure.…”

Section: Introductionmentioning

confidence: 99%

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Diffusion Coefficients of Carbon Dioxide in Eight Hydrocarbon Liquids at Temperatures between (298.15 and 423.15) K at Pressures up to 69 MPa

et al. 2016

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We report experimental measurements of the mutual diffusion coefficients in binary systems comprising CO2 + liquid hydrocarbon measured at temperatures between (298.15 and 423.15) K and at pressures up to 69 MPa. The hydrocarbons studied were the six normal alkanes hexane, heptane, octane, decane, dodecane and hexadecane, one branched alkane, 2,6,10,15,19,23-hexamethyltetracosane (squalane), and methylbenzene (toluene). The measurements were performed by the Taylor Dispersion method at effectively infinite dilution of CO2 in the alkane, and the results have a typical standard relative uncertainty of 2.6 %. Pressure was found to have a major impact, reducing the diffusion coefficient at a given temperature by up to 55 % over the range of pressures investigated. A correlation based on the Stokes-Einstein model was investigated in which the effective hydrodynamic radius of CO2 was approximated by a linear function of the reduced molar volume of the solvent. This represented the data for the normal alkanes only with an average absolute relative deviation (AAD) of 5 %. A new universal correlation, based on the rough-hard-sphere theory, was also developed which was able to correlate all the experimental data as a function of reduced molar volume with an AAD of 2.5 %.2

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Diffusion Coefficients of Carbon Dioxide in Eight Hydrocarbon Liquids at Temperatures between (298.15 and 423.15) K at Pressures up to 69 MPa

et al. 2016

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“…ESI-MS is used to monitor the Taylor dispersion of an initially sharp boundary between two analyte solutions of different concentration in a laminar flow tube [67][68][69][70][71][72]. Under laminar flow conditions, the velocity profile in a circular tube is given by…”

Section: Diffusion Studiesmentioning

confidence: 99%

Diffusion measurements by electrospray mass spectrometry for studying solution-phase noncovalent interactions

Clark

Konermann

2003

J. Am. Soc. Mass Spectrom.

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This study describes a novel approach for monitoring noncovalent interactions in solution by electrospray mass spectrometry (ESI-MS). The technique is based on measurements of analyte diffusion in solution. Diffusion coefficients of a target macromolecule and a potential low molecular weight binding partner are determined by measuring the spread of an initially sharp boundary between two solutions of different concentration in a laminar flow tube (Taylor dispersion), as described in Rapid Commun. Mass Spectrom. 2002Spectrom. , 16, 1454Spectrom. -1462. In the absence of noncovalent interactions, the measured ESI-MS dispersion profiles are expected to show a gradual transition for the macromolecule and a steep transition for the low molecular weight compound. However, if the two analytes form a noncovalent complex in solution the dispersion profiles of the two species will be very similar, since the translational diffusion of the small compound is determined by the slow Brownian motion of the macromolecule. In contrast to conventional ESI-MS-based techniques for studying noncovalent complexes, this approach does not rely on the preservation of solution-phase interactions in the gas phase. On the contrary, "harsh" conditions at the ion source are required to disrupt any potential gasphase interactions between the two species, such that their dispersion profiles can be monitored separately. The viability of this technique is demonstrated in studies on noncovalent heme-protein interactions in myoglobin. Tight noncovalent binding is observed in solutions of pH 10, both in the absence and in the presence of 30% acetonitrile. In contrast, a significant disruption of the noncovalent interactions is seen at an acetonitrile content of 50%. Under these conditions, the diffusion coefficient of heme in the presence of myoglobin is only slightly lower than that of heme in a protein-free solution. A breakdown of the noncovalent interactions is also observed in aqueous solution of pH 2.4, where myoglobin is known to adopt an acid-unfolded conformation. (J Am Soc Mass Spectrom 2003, 14, 430 -441)

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“…[13] For a passive solute with total mass, m, the Nth spatial moment of the distribution of the resident concentration, c(x; t) (defined as the mass of the solute per unit volume of aqueous solution) is given after Aris [1956] as:…”

Section: Concentration Spatial Momentsmentioning

confidence: 99%

Block‐effective macrodispersion in variably saturated heterogeneous formations

Russo

2003

Water Resources Research

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[1] Numerical models are frequently used in order to quantify the effect of the spatial heterogeneity in the formation hydraulic properties on field-scale solute transport. Because of practical constraints it is common to discretize the flow domain into relatively large numerical cells, with characteristic length scales, ' 1 , ' 2 , ' 3 , comparable with those of the formation heterogeneity, I 1 , I 2 , I 3 , leading to a loss in the velocity variability, and, concurrently, in solute spreading. We analyzed block-effective dispersion coefficients, D 0 ij (i, j = 1, 2, 3), required to compensate for this loss in three-dimensional, variably saturated heterogeneous formations under conditions of steady state, gravity-dominated, unsaturated flow. The results that the principal components of D 0 ij are controlled by the ratio ' 0 = ' 2 /I 2 = ' 3 /I 3 , that they may reach their ergodic limits if ' 0 is sufficiently large, and that their tendency to their asymptotic limits with increasing scaled travel time, t 0 , is inversely related to ' 0 , are in agreement with previous results for saturated flow. New findings suggest that under unsaturated flow conditions, both the time required to reach the asymptotic limits of D 0 ij and the length scale needed to reach the ergodic limits of D 0 ij depend on soil stratification, soil texture, and mean soil water saturation and differ for the longitudinal and the transverse components of D 0 ij .

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On the dispersion of a solute in a fluid flowing through a tube

Cited by 2,249 publications

References 1 publication

Diffusion Coefficients of Carbon Dioxide in Eight Hydrocarbon Liquids at Temperatures between (298.15 and 423.15) K at Pressures up to 69 MPa

Diffusion Coefficients of Carbon Dioxide in Eight Hydrocarbon Liquids at Temperatures between (298.15 and 423.15) K at Pressures up to 69 MPa

Diffusion measurements by electrospray mass spectrometry for studying solution-phase noncovalent interactions

Block‐effective macrodispersion in variably saturated heterogeneous formations

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