Liquid-Phase Mass Transfer at Low Reynolds Numbers

Williamson, J. E.; Bazaire, K. E.; Geankoplis, C. J.

doi:10.1021/i160006a007

Cited by 173 publications

(75 citation statements)

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“…The material balance equation of an individual enantiomer j ((R)-, (S)-OH) in the porous support matrix is then given by Pore diffusion Eq. (3) is coupled with the external bulk concentrations in the organic solvent stream flowing through the packed bed reactor through the following boundary condition, where k, is the external liquid-solid mass transfer coefficient, estimated from a correlation given by Williamson, Bazaire, and Geankoplis (1963) for mass transfer in packed beds at low Reynolds numbers.…”

Section: ( 5 )mentioning

confidence: 99%

Stereoselective bioconversions in continuously operated fixed bed reactors: Modeling and process optimization

Indlekofer

Brotz

Bauer

et al. 1996

Biotechnol. Bioeng.

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Section: ( 5 )mentioning

confidence: 99%

Stereoselective bioconversions in continuously operated fixed bed reactors: Modeling and process optimization

Indlekofer

Brotz

Bauer

et al. 1996

Biotechnol. Bioeng.

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“…The analysis by Powers et al also showed that dissolution is sensitive to the mass transfer coefficient correlation. Simulations using (2) and an earlier measurement by Williamson et al [1963] were compared; however, they are the same correlation, with the only difference being that Williamson et al [1963] used a constant porosity.…”

Section: Mass Transfer Coefficientmentioning

confidence: 99%

Mass transfer from nonaqueous phase organic liquids in water‐saturated porous media

Geller

1993

Water Resources Research

228

155

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Results of dissolution experiments with trapped nonaqueous phase liquids (NAPLs) are modeled by a mass transfer analysis. The model represents the NAPL as isolated spheres that shrink with dissolution and uses a mass transfer coefficient correlation reported in the literature for dissolving spherical solids. The model accounts for the reduced permeability of a region of residual NAPL relative to the permeability of the surrounding clean media that causes the flowing water to partially bypass the residual NAPL. The dissolution experiments with toluene alone and a benzene-toluene mixture were conducted in a water-saturated column of homogeneous glass beads over a range of Darcy velocities from 0.5 to 10 m d −1 . The model could represent the observed effluent concentrations as the NAPL underwent complete dissolution. The changing pressure drop across the column was predicted following an initial period of NAPL reconfiguration. The fitted NAPL sphere diameters of 0.15 to 0.40 cm are consistent with the size of NAPL ganglia observed by others and are the smallest at the largest flow velocity.

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“…When mass transfer in the fluid phase is the controlling step, therefore, the usual design relationships' for mass transfer in packed beds (Gupta and Thodos, 1962;Wilson and Geankoplis, 1966;Williamson et al, 1963) are either unsuitable on account of the absence of a Grashof number, or do not cover (Karabelas et-al., 1971) the low Schmidt numbers (-10) which characterize diffusion of light organic solutes in supercritical fluids. (molecular weight -100) in supercritical fluids (Sc = v/ ).…”

Section: 1: Physical Properties and Mass Transfer Mechanismmentioning

confidence: 99%

Diffusion and mass transfer in supercritical fluids

1986

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The different behavior of fluid density and viscosity in going from the dilute gas to the dense fluid state gives rise to kinematic viscosities which, in the near supercritical region, are lower than for liquid metals. As a consequence, the relative importance of natural convection (as measured by the ratio of buyoant to inertial forces) is two orders of magnitude higher in a supercritical fluid (at constant Reynolds number) than in normal liquids.Binary diffusion coefficients of nonvolatile solutes in supercritical fluids were measured with a technique that involved laminar flow and diffusion in a rectangular channel. The solution to this hydrodynamic problem is presented. By varying the inclination of the solute source plane with respect to the horizontal position, apparent diffusion coefficients were measured that were up to six times higher than the “true” coefficients.Experimental binary diffusion coefficients, including published literature data, were analyzed in the light of hydrodynamic (Stokes‐Einstein) theory. The analysis suggests that under the high‐density, low‐viscosity conditions that characterize supercritical fluids, hydrodynamic behavior at the molecular level is approached, and can be used as a basis for data extrapolation.

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Liquid-Phase Mass Transfer at Low Reynolds Numbers

Cited by 173 publications

References 1 publication

Stereoselective bioconversions in continuously operated fixed bed reactors: Modeling and process optimization

Stereoselective bioconversions in continuously operated fixed bed reactors: Modeling and process optimization

Mass transfer from nonaqueous phase organic liquids in water‐saturated porous media

Diffusion and mass transfer in supercritical fluids

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