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  • 1
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 74 (1970), S. 2245-2249 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Analytic expressions for the velocity profile and distribution of neutrally buoyant particles in laminar flow were obtained as functions of the radial distance. A modified Einstein viscosity model and the hypothesis that the total force on all the particles flowing in the tube is a minimum were used. The methods of the variational calculus were used in the mathematical development. A velocity profile differing only slightly from the parabolic form of that for Hagan-Poiseuille flow was obtained. For particle distribution the equations developed predict a maximum concentration along the center-line for some flows and a maximum concentration in a ring some distance from the center line in other flows. Both of these concentration profiles have been observed experimentally. Quantitative predictions from the equations derived must await further experimental work to permit calculation of the parameters included in the equations.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 35 (1973), S. 577-589 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Analytic expressions for the velocity profile and particle distribution of a dilute suspension in flow were obtained as functions of radial distance. Einstein's linear viscosity model and the hypothesis of “minimum energy dissipation” were used. The methods of variational calculus were applied during the mathematical development. A parabolic velocity profile, which is a modified form of that for Hagen-Poiseuille flow, and a uniform particle distribution were obtained. An attempt is made to explain the results in light of some of the widely held theories on suspension flow and the rather severe limitations of Einstein's viscosity model. A suggestion for future work is made for improving the results of the present.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 17 (1971), S. 1234-1240 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Analytic expressions for the concentration distribution of reactant and for effectiveness factor have been obtained for zero-order catalytic reactions of the type A → bB. They can be summarized for various physical forms of catalyst to be \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm ln}\,\frac{{{\rm 1}\,{\rm + }\,mC}}{{1\, + \,m}}\, = \, - M_i \,\left\{ {f(\xi)\, - \frac{{g(\xi)}}{{g(\xi _e)}}.\,h\,\left({\xi _{e'} \,\frac{{K_e }}{K}} \right)} \right\} $$\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$$ \eta '\, = \,1\, + \,h\,\left({\xi _{e'} \frac{{K_e }}{K}} \right)/\,2g(\xi _e)\, = \,1\, - \,\xi _e^i $$\end{document} where \documentclass{article}\pagestyle{empty}\begin{document}$$ f(\xi),\,g(\xi),\,h\left({\xi _{e'} \,\frac{{K_e }}{K}} \right) $$\end{document}, and Mi are differently defined for thin-disk (i = 1), infinite-cylinder (i = 2), and spherical (i = 3) geometries. The results are also presented graphically for rapid calculation of these quantities. The phenomenon of reactant exhaustion associated with a zero-order reaction and the criteria for its occurrence are also discussed.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 19 (1973), S. 832-839 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Asymptotic analytic expressions for the concentration and temperature profiles as well as effectiveness factor inside porous, thin-disk shaped catalyst particles have been developed for zeroth-order exothermic reaction with reactant-to-product volume change. The individual and combinative effects of volume-change, Thiele and thermal Thiele moduli, and of the dimensionless activation energy are discussed. As expected, the expressions revert to those for the corresponding isothermal and constant-volume cases. Errors arising from the approximation were calculated and found to be quite acceptable.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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