Ind. E n g . Chem. Res 1987,26, 1616-1621
1616
r = radial distance from center of tube R = radius of tube R- = very close to the tube wall Re,, = packed bed Reynolds number U, = slip velocity V , = bulk fluid velocity Greek Symbols @ = slip coefficient defined as U s / ~ w 8 = static contact angle p = viscosity p = density T = shear stress 7, T~~
7,
= wall shear stress = wall shear stress measured for nonwetting surface = wall shear stress measured for wetting surface
S u p p l e m e n t a r y Material Available: Tables of velocity profiles and pressure drop data at different Reynolds numbers and grain sizes, (6 pages). Ordering information is given o n a n y masthead page.
Literature Cited Adamson, A. W. Physical Chemistry of Surface, 3rd ed.; Wiley: New York, 1976. Apelian, D.; Luk, S.; Piccone, T.; Mutharasan, R. “Removal of Liquid and Solid Inclusions from Steel Melt”, Proceedings of the 5th International Iron and Steel Congress, Washington, DC, April 1986. Allen, T. 0.;Roberts, A. P. Production Operation, 2nd ed.; Oil & Gas Consultants: Tulsa, OK, 1982. Astarita, G.; Marruci, F.; Palumbo, G. Ind. Eng. Chem. Fundam. 1964, 3, 333. Bell, J. J . Comp. Mat. 1969, 3, 244. Blyler, L. L., Jr.; Hart, A. C., Jr. Polym. Eng. Sci. 1970, 10, 193. Bugliarello, G.; Kaupur, C.; Hsiao, G. Proceedings of the International Congress on Rheology; Lee, E. H., Copley, A. L. Eds.; Interscience: New York, 1964; Vol. 4, p 351. Brunn, P. Int. J . Multiphase Flow 1981, 7, 229. Carreau, P. J.; Bui, W. H.; Leroux, P. Rheol. Acta 1979, 18, 600. Cheng, D. C. H. Ind. Eng. Chem. Fundam. 1974,13, 394. Cheremisinoff, N. P. Fluid Flow-Pumps, Pipes and Channels; Ann Arbor Science: Ann Arbor, MI, 1981.
Cohen, Y.; Chang, C. Chem. Eng. Commun. 1984, 28, 73. Cox, R.; Brenner, H. Chem. Eng. Sci. 1968, 23, 147. Den Otter, J. L. Rheol. Acta 1965, 14, 329. George, W. K.; Lumley, J. L. J . Fluid Mech. 1973, 60, 321. Goldstein, S. Annual Review of Fluid Mechanics; Seans, W. R., Van Dyke, M. Eds.; Annual Reviews: Palo Alto, CA, 1969; Vol. 1, p 1. Test. Mat. 1920, 20, 451. Green, H. Proc. Am. SOC. Janssen, L. P. B. M. Rheol. Acta 1980, 19, 32. Karmis, A.; Goldsmith, H.; Mason, S. Can. J . Chem. Eng. 1966,44, 181.
Kraynik, A. M. Ph.D. Dissertation, Princeton University, Princeton, NJ, 1976. Kried, D. K.; Goldstein, R. J. Technical Report, 1974; University of Minnesota, Minneapolis. Maude, A. Br. J . Appl. Phys. 1959, 10, 371. Maude, A.; Whitmore, R. Br. J. Appl. Phys. 1956, 7, 98. Menawat, A.; Henry, J., Jr.; Siriwardne, R. J . Colloid Interface Sci. 1984, 101, 110. Metzner, A. B. Improved Oil Recovery by Surfactant and Polymer Flooding; Shah, D. D., Schechter, R. S., Eds.; Acadamic: New York, 1977. Metzner, A. B.; Cohen, Y.; Rangel-Nafaile, C. J . Non-Newtonian Fluid Mech. 1979, 5, 449. Mooney, M. J . Rheology 1931,2, 210. Pearson, J. T. A.; Petrie, C. J. S. Polymer Systems, Deformation and Flow, Proceedings of the 1966 Annual Conference of the British Society of Rheology; Wetton, R. E., Wholow, R. W., Eds.; Macmillan: London, 1968. Pilehvari, A. A. Ph.D. Dissertation, University of Tulsa, Tulsa, OK, 1984. Pinkava, J. Handbook of Laboratory Unit Operations for Chemists and Chemical Engineers; Bryant, J., Transl.; Gordon & Breach: New York, 1970. Ponter, A. B.; Taymour, N.; Dankyi, S. 0. Chem.-hg.-Tech. 1976, 48, 636. Russel, T. W. F.; Charles, M. E. Can. J . Chem. Eng. 1959, 18, 120. Scott Blair, G. W.; Crowther, E. M. J . Phys. Chem. 1929, 33, 321. Serge, G.; Siberberg, A. J . Fluid Mech. 1962, 14, 136. Rheol. 1972, 14, 351. Sheshadri, V.; Sutera, S. Trans. SOC. Vignogradov, G. V.; Froishteter, G. B.; Trilisky, K. K. Rheol. Acta 1978, 17, 156. Received for review October 15, 1985 Revised manuscript received January 18, 1987 Accepted April 15, 1987
Impact of the Catalytic Activity Profile on Observed Multiplicity Features: CO Oxidation on Pt/Al,O, Michael P. Haroldt and Dan Luss* Department of Chemical Engineering, University of Houston, Houston, Texas 77004
The observed multiplicity features of a catalytic pellet in which an isothermal Langmuir-Hinshelwood reaction occurs are sensitive to the distribution of the catalytic components. Specifically, surface migration of the catalytic components may change the range of reactant concentrations or temperatures over which rate multiplicity occurs or shift the maximal rate outside the concentration region in which multiple solutions occur’. These changes in the multiplicity features may be used to detect qualitative changes in the metal concentration profile without having to carry out a destructive test. The supported metal profile of many industrial precious metal catalysts is nonuniform. This catalytic a c t i v i t y profile may affect considerably the observed catalytic activity. Previous studies have shown that the p e r f o r m a n c e may be optimized by the use of a nonuniform catalytic activitv mofile. For Dositive-order reactions. the catalvtic -
A
* To whom correspondence should be addressed. ‘Presently at the Department of Chemical Engineering, University of Massachusetts, Amherst, MA 01003.
activity should be concentrated near the s u r f a c e to minimize the detrimental influence of intraparticle diffusional limitations ( C a r b e r r y and Minhas, 1969). A number of investigators have studied the interaction between a reaction rate which exhibits a m a x i m u m for an intermediate c o n c e n t r a t i o n (ex.. bimolecular Langmuir-Hinshelwood kinetics), pore digusion, and nonunifgrm catalytic activity ( W e i and Becker, 1974; Villadsen, 1976; Becker and Wei, 1976, 1977; Hegedus et al., 1977, 1979; Morbidelli et al., 1982; Morbidelli and Varma, 1982; W o n g and Szepe, 1982).
0888-5885/87/2626-1616$01.50/0 0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 1617 1.0 -
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