Multicomponent mass transfer in turbulent flow

Stewart, W. D. P.

doi:10.1002/aic.690190237

Cited by 24 publications

(5 citation statements)

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“…This method is well tested for stagnant 5lms (Smith and Taylor, 1983) and is suggested for situations not covered by detailed theory on net flux corrections. For information on these corrections, see Bird et al (19601, Prober and Stewart (19631, Stewart (1963, 1971. 1973), Stewart and Prober (1962).…”

Section: Discussionmentioning

confidence: 97%

“…This method is well tested for stagnant films (Smith and Taylor, 1983) and is suggested for situations not covered by detailed theory on net flux corrections. For information on these corrections, see Bird et al (1960), Prober and Stewart (1963), Stewart (1963Stewart ( , 1971Stewart ( , 1973), Stewart and Prober (1962) s cmtotal molar concentration, mol cm"3 A"1, Fickian diffusivity matrix, cm2 s"1 binary diffusion coefficient, cm2 s"1 eigenvalues, identical for D¿ and Dx, cm2 s*1 identity matrix column vector of molar fluxes relative to v*, mol ernes'"1 column vector of transformed fluxes defined in eq 47, mol cm"2 s"1 column vector of mass fluxes relative to v, g cm"2…”

Section: Discussionmentioning

confidence: 99%

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Comparison of matrix approximations for multicomponent transfer calculations

Young¹,

Stewart²

1986

Ind. Eng. Chem. Fund.

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Linearization and film models for multicomponent mass transfer predictions are summarized and compared with detailed boundary layer calculations. The linearization method is improved significantly by adjustment of the averaging rule for the reference state. Linearization is the most accurate of the approximation methods tested, both for steady and transient mass transfer operations. IntroductionMulticomponent mass transfer problems often arise in the design and simulation of chemical processes. Since the fundamental equations are coupled and nonlinear, these problems are normally done by approximate solution methods. The favored methods fall into two categories: (i) linearized solutions of the equations of change and (ii) exact solutions of one-dimensional models. This paper tests both approaches by comparisons with exact solutions for steady and transient multicomponent mass transfer problems. The effect of property-averaging methods on the accuracy of the approximations is also investigated.The linearized matrix theory of multicomponent mass transfer was developed independently by Stewart and Prober (1964) and by Toor (1964). In this theory the fluid

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Section: Discussionmentioning

confidence: 97%

Section: Discussionmentioning

confidence: 99%

Comparison of matrix approximations for multicomponent transfer calculations

Young¹,

Stewart²

1986

Ind. Eng. Chem. Fund.

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“…For discussions in this paper, we shall assume that the interface compositions are specified. The superscript on the matrix of mass transfer coefficients [k*y] serves as a reminder that these coefficients are themselves dependent on the interfacial rates of transfer of the n species Ni (Stewart, 1973).…”

Section: Conclusion and Significancementioning

confidence: 99%

A multicomponent film model incorporating a general matrix method of solution to the Maxwell‐Stefan equations

1976

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“…Multicomponent mass transfer at a fluid and solid interface can be found in many chemical engineering processes such as leaching, dissolution or crystallization, electrolysis, and adsorption, as well as chemical reactions involving solid reactants or porous catalysts. Consequently, it has long been a focus of studies in many different disciplines (Wendt, 1965;Woolf, 1972;Stewart and Prober, 1964;Stewart, 1973;Cussler, 1976;Anderson and Graf, 1976;Taylor, 1982;Smith and Taylor, 1983;Pinto and Graham, 1987). But most of the previous work centered either on the sole aspect of multicomponent diffusion or on the mathematical treatments of convective processes under welldefined conditions.…”

Section: Introductionmentioning

confidence: 99%

Dissolution equilibria and kinetics of fluorite and calcite mixtures

Knaebel

1989

AIChE Journal

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Minerals commonly contain impurities, and their dissolution involves complicated ionic equilibria and multicomponent mass transfer. This paper describes the experiments that were carried out and proposes a mechanism for dissolution behavior of fluorspar containing calcite as a major impurity in both batchwise and continuous packed-bed systems.The mechanism is based on analysis of coupled equilibria among the soluble species. Of more than eight potentially relevant species, only three (viz., F-, HCO,-, and Ca2+) are significant. The coupled flux equations for Fand HCO,are written in terms of "main" and "cross" mass transfer coefficients, with the concentration of Ca2+ being accounted for by electroneutrality. Only one main mass transfer coefficient needs to be determined experimentally; and other coefficients can be evaluated from it by means of simple diffusion coefficient ratios, which are determined independently. The Stanton number based on the main mass transfer coefficient is correlated with Reynolds number and the Schmidt number for packed bed dissolution.A comparison of the exact solution (Eq. 9) with the approximate solution (Eq. 10) is shown in Figure 1 for a range of aqueous carbon dioxide activities. Since the discrepancies are negligible except at very low concentration of aqueous carbon dioxide, the Vol. 35, No. 8 AICbE Journal 15 and 16 then become: open system of fluorspar dissolution equilibrium (viz., = 0.0013 mM) can be treated as a dilute ternary system consisting of F-, and Ca2+. *Obtained by recirculation of effluent at 500 mL/min. Other data were measured in zero-flow rate columns (column initially filled with distilled water). All the experiments were conducted after aging process was completed, i.e., after about 80 hours dissolution in the packed column (cf. Figure Al).

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Multicomponent mass transfer in turbulent flow

Abstract: = heat transfer 2 = mass transfer rn = maximum value n = minimum value 8

Cited by 24 publications

References 4 publications

Comparison of matrix approximations for multicomponent transfer calculations

Comparison of matrix approximations for multicomponent transfer calculations

A multicomponent film model incorporating a general matrix method of solution to the Maxwell‐Stefan equations

Dissolution equilibria and kinetics of fluorite and calcite mixtures

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