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This Week’s Citation Classic CC/NUMBER 26 IT SR. On shape factors for irregular particles—I. The steady state problem. 4~1Diffusion and reaction. C/tern. Eng. Sci. 6:262-8, 1957. [Mathematical Institute, Edinburgh, Scotland] The effectiveness of a catalyst particle with In writing up my findings I naturally includ- diffusion and first.order reaction is gov- ed an exposition of Thiele’s work and hap- erned by a parameter proportional to the pened to notice that the asymptotic effec- ‘size’ of the particle. If that size is taken to tiveness factors for plate, cylinder, and be the ratio of the volume to external sur- sphere could be made the same by taking face area, the effectiveness factors for all the characteristic dimension of the catalyst particle shapes come together asymptotical- particle as the ratio of its volume to its ex- ly and are reasonably close together over ternal surface area. the whole range. [The SCI® indicates that “The result slept in my notebook for five this paper has been cited over 145 times years and saw the light of day through the since 1961.) kind interest of KG. Denbigh while I was a lecturer in technical mathematics at Edin- burgh. In retrospect I seem to have done2 less than justice to Wheeler, whose paper I had — read in 1952, but had not reread in 1957. His argument is based on his model of pore Rutherford Aris structure and gives the characteristic parti- Department of Chemical Engineering cle size as the ratio of volume to area but and Materials Science multiplied by a tortuosity factor of sJ~for University of Minnesota pores. However, this factor could have been Minneapolis, MN 55455 absorbed into the definition of the rate con- stant to give my result. My arguments were mathematical, but, in this paper, somewhat3 less rigorous than those used later. A rather June 4, 1982 obvious conjecture that, of all shapes of pellet of equal volume, the sphere would be “The main idea of this paper arose when I the least effective was later proved4 very was working at the (then) Billingham Divi- elegantly by Luss and Amundson. sion of Imperial Chemical Industries in 1952. “The engineer’s enduring interest in in- I had been seconded to the catalyst section telligent fudge factors, which wrap up the to study methods of catalyst testing and results of a difficult calculation in simple ciuickly ran into the problem of diffusion form, must account for the paper being so limitation. A remarkable mathematical physi- often cited. Thiele’s original idea of the ef- cist, C.H. Bosanquet, was at Rillingham at fectiveness factor was a classic example of the time, who, when asked if a particular this, and my modification fudged in the fur- reaction were limited by diffusion, would ther complication of shape. Though the ma- enquire as to the conditions and then terials lay athand (in a problem of Bird, wander around his almost bare office mut- Stewart, and Lightfoot’s5preliminary version tering about orders of magnitude followed of Transport Phenomena ) in the late-i 950s, by one of the Rhodesian Ridgebacks he it was not until 1965 that the ultimate nor- brought into work. From time to time he malization of the Thiele modulus, account- would press the top of his head against the ing for the kinetics as well as the shape, was wall and come up with a ‘scarcely,’ published, independently and almost simul- ‘somewhat,’ or ‘severely.’ Whilst this was taneously, by Bischoff, Petersen, and myself great fun and very impressive (for a later (mention of this is made on page 41 of check of some of his judgments showed reference 3), The most recent citation of the them to be essentially correct under a strict paper (or rather of its result as given6 in interpretation of his words), it was a difficult reference 3) is by Yortsos and Tsotsis, who act to follow and it was with some relief that generalize the result for particles with vary- I discovered Thiele’s classic paper of 1939.1 ing activity.” 1. Thiele E W. Relation between catalytic activity and size of particle. md. Eng. Chem. 31:916-20, 1939. Icitation Classic. Current Contents/Engineering, Technology & Applied Sciences 10(2): 10, 8 January 1979.1 2. Wheeler A. Reaction rates and selectivity in catalyst pores. Advan. Catal. 3:249-300, 1951. 3. Ails R. The mathematical theory ofdiffusion andreaction in permeable catalysts. Oxford: Clarendon Press, 1973. 2 vols, . 4. Amunttson N R & Lust D. On a conjecture of Ails: proof and remarks. AICHEJ. t3:739-43, 1967. 5. Bird R B, Stewart WE & Llghtfool EN. Transport phenomena. New York: Wiley, 1960. 780 p. ICisation Classic. Current Contents/Engineering, Technology ~6Applied Sciences 10(38):12, 17 September 1979.] 6. Yorssos ~‘ C & l’solsls T T. Asymptotic behavior of the effectiveness factor ror variable activity catalysts. Chem. Eng. Sci, 37:237-43, 1982. 28 CURRENT CONTENTS® ET&AS ~ 1982 by lSl® p.

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