Thermal Diffusion Column Theory for Liquids

EMERY, ALDEN H.

doi:10.1021/ie50593a029

Cited by 9 publications

(6 citation statements)

References 9 publications

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“…A rather complete mathematical treatment of the operation of Clusius-Dickel columns has been given by Jones and Furry (26). The separation of gaseous isotopes was of primary concern in the Furry-Jones treatment but recently-Emery (27) has introduced into their equations the strong temperature dependencies of viscosity and diffusion in liquids. Because of the extreme concentration dependence of viscosity and diffusion in the case of polymer solutions, it was decided in the present study to employ-a detailed mathematical description only in the extreme case of infinitely dilute solutions.…”

Section: Mathematical Treatmentsmentioning

confidence: 99%

“…which shows that the concentration in the column should vary exponentially with vertical distance for sufficiently dilute solutions. More than one value of 7 and -16will satisfy Equations (25) through (27), the values of y being the eigenvalues of Equation (25).…”

Section: Flow Problemmentioning

confidence: 99%

“…For a given solution to the hydrodynamic problem, the steady-state concentration as a function of both horizontal and vertical position in the column is given by Equation (30) with auxiliary conditions (26) and (27). P expresses the concentration as a function of the radial co-ordinate r and is independent of the vertical co-ordinate z, and y is related to the rate of diminution of concentration with z and is independent of r. If P is a solution of Equation (30) then any multiple of P is also a solution; the.…”

Section: Diffusion Problemmentioning

confidence: 99%

“…First, the relative differences in the diffusion coefficients of various size polymer molecules are reduced because of the strong concentration dependence of D for polymers. Second, increased concentration greatly magnifies the variation of solution viscosity across the annulus which in turn distorts the convection velocity profile in such a manner that the cold stream is broadened and the position of maximum downward velocity is shifted away from the cold wall (27). The position where ac/r = 0 will also be shifted away from the cold wall so that / must be reduced in this region resulting in a reduced fractionation effect.…”

Section: Concentration Effectmentioning

confidence: 99%

“…However, for the purpose of computing D' from experimental values of 7, the magnitude of P may be assumed arbitrary. Because P and its derivative are interrelated Velocity Profile of.Convection Streams U at the walls of the column'by Equation(26), a solution of'Equation (30) which satisfies condition(26) at both boundaries must necessarily satisfy the flow condition of Equation(27). Therefore, the diffusion problem reduces to a boundary value problem with only one adjustable parameter.…”

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confidence: 99%

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An evaluation of column thermal diffusion as a means of polymer characterization

Taylor¹

1964

J. Polym. Sci. A Gen. Pap.

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The mechanism of polymer fractionation in a Clusius‐Dickel thermal diffusion column was elucidated by a systematic study of the effects of important experimental factors on the separations attainable combined with an analytical description of column operation and recent theories of polymer thermal diffusion. Several polystyrene samples of known molecular weight distribution were studied in toluene and methyl ethyl ketone solvents at varying conditions of temperature gradient (up to 1050°C./cm.), mean temperature (20–45°C.), and concentration (up to 2.4 wt.‐%). The thermal diffusion column was of the concentric cylinder type, equipped with thirty sample ports. The degree of separation of polymer from solvent increased with temperature gradients below 40°C./cm., increased slightly with decreased mean temperature, increased markedly with starting concentration, and was greater in toluene at a given concentration. The degree of fractionation was found to increase rapidly with temperature gradient, and was largely independent of concentration in methyl ethyl ketone but increased strongly with concentration in toluene solutions. These effects were interpreted by means of a theoretical calculation of the influence of both ordinary and thermal diffusion on column behavior in conjunction with an evaluation of the radical concentration gradients. The experimental results are in accord with a recent theory of polymer thermal diffusion which predicts that the thermal diffusion coefficient should not be a strong function of molecular weight. The fractionation effect is apparently governed by differences in ordinary diffusion coefficients. The fractionation was greater for higher molecular weights.

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Section: Mathematical Treatmentsmentioning

confidence: 99%

Section: Flow Problemmentioning

confidence: 99%

Section: Diffusion Problemmentioning

confidence: 99%

Section: Concentration Effectmentioning

confidence: 99%

mentioning

confidence: 99%

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An evaluation of column thermal diffusion as a means of polymer characterization

Taylor¹

1964

J. Polym. Sci. A Gen. Pap.

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Thermal diffusion of liquids in columns

Hoffman

EMERY

1963

AIChE Journal

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If the roots of the discriminant (3A) are complex, a case which often arises in practical applications, one may write (3A) in two forms: and where When (6A) and ( 8 A ) are combinedWhen ( PREVIOUS WORKThe early studies of thermal diffusion were made in the single-stage, convection-free apparatus in which separations are very small. In 1938 Clusius and Dickel ( I ) devised the thermal diffusion column which acts as a multistage device and thus greatly magnifies the possible separations. In 1939 Furry, Jones, and Onsager ( 2 ) and, independently, Debye (3) published theories to explain the behavior of the column. A number of investigations followed which demonstrated the approximate validity of the theory of the column for gases.

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Papierthermodiffusion. Mit 7 Abbildungen

Vámos

Major

1961

J. Prakt. Chem.

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Es wurde ein neues Gerät und eine neue Arbeitsweise zur Trennung von geringen Mengen von Kohlenwasserstoffen entwickelt, durch Thermodiffusion im Papierstreifen, zwischen planparallelen, temperierten Oberflächen. Die Methode ermöglicht in gewissen Fällen, besonders bei hochsiedenden gesättigten Kohlenwasserstoffen Trennungen oder Anreicherungen, welche weder auf gaschromatographischem, noch auf adsorptions‐ oder papierchromatographischem Wege möglich sind. Es wurde außerdem gefunden, daß die auf Etalonsubstanzen bezogene Thermodiffusionsfaktoren für gewisse Stoffgruppen charakteristische Zahlen sind, und daher zur Identifizierung von Substanzen zugezogen werden können.

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Thermal Diffusion Column Theory for Liquids

Cited by 9 publications

References 9 publications

An evaluation of column thermal diffusion as a means of polymer characterization

An evaluation of column thermal diffusion as a means of polymer characterization

Thermal diffusion of liquids in columns

Papierthermodiffusion. Mit 7 Abbildungen

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