翻訳と辞書 Words near each other ・ Thiel Foundation ・ Thiel Mountains ・ Thiel Trough ・ Thiel-Behnke dystrophy ・ Thiel-sur-Acolin ・ Thielavia ・ Thielavia subthermophila ・ Thielaviopsis ・ Thielaviopsis basicola ・ Thielaviopsis ceramica ・ Thielbeer ・ Thiele ・ Thiele (Aar) ・ Thiele and Ladiges' taxonomic arrangement of Banksia ・ Thiele Highway ・ Thiele modulus ・ Thiele tube ・ Thiele's interpolation formula ・ Thiele/Small ・ Thieleella ・ Thieleherpia ・ Thieleman J. van Braght ・ Thielemann ・ Thielen ・ Thielenbruch (KVB) ・ Thielenplatz/Schauspielhaus (Hanover Stadtbahn station) ・ Thielert ・ Thielert Centurion ・ Thielle ・ Thielle-Wavre Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Thiele modulus ： ウィキペディア英語版 Thiele modulus The Thiele modulus was developed by E.W. Thiele in his paper 'Relation between catalytic activity and size of particle' in 1939.〔Thiele, E.W. Relation between catalytic activity and size of particle. Industrial and Engineering Chemistry, 31 (1939), pp. 916–920〕 Thiele reasoned that with a large enough particle, the reaction rate is so rapid that diffusion forces are only able to carry product away from the surface of the catalyst particle. Therefore, only the surface of the catalyst would be experiencing any reaction. The Thiele Modulus was then developed to describe the relationship between diffusion and reaction rate in porous catalyst pellets with no mass transfer limitations. This value is generally used in determining the effectiveness factor for catalyst pellets. The Thiele modulus is represented by different symbols in different texts, but is defined in Hill〔Hill, C. An Introduction to Chemical Engineering and Reactor Design. John Wiley & Sons, Inc. 1977, 440-446.〕 as ''hT''. : $h^2\_\; =\; \backslash dfrac$ == Overview == The derivation of the Thiele Modulus (from Hill) begins with a material balance on the catalyst pore. For a first-order irreversible reaction in a straight cylindrical pore at steady state: $r^2\backslash left\; (\; -D\_c\; \backslash frac\; \backslash right\; )\_x\; =\; r^2\backslash left\; (\; -D\_c\; \backslash frac\; \backslash right\; )\_+\backslash left\; (\; 2rx\; \backslash right\; )\backslash left\; (\; k\_1C\; \backslash right\; )$ where $D\_c$ is a diffusivity constant, and $k\_1$ is the rate constant. Then, turning the equation into a differential by dividing by $x$ and taking the limit as $x$ approaches 0, $D\_c\backslash left\; (\backslash frac\; \backslash right\; )\; =\; \backslash frac$ This differential equation with the following boundary conditions: $C=C\_o\; \backslash text\; x=0$ and $\backslash frac\; =\; 0\; \backslash text\; x=\; L$ where the first boundary condition indicates a constant external concentration on one end of the pore and the second boundary condition indicates that there is no flow out of the other end of the pore. Plugging in these boundary conditions, we have $\backslash frac\; =\; \backslash left\; (\backslash frac\; \backslash right)\; C$ The term on the right side multiplied by C represents the square of the Thiele Modulus, which we now see rises naturally out of the material balance. Then the Thiele modulus for a first order reaction is: $h^2\_T=\backslash frac$ From this relation it is evident that with large values of $h\_T$, the rate term dominates, and the reaction is fast while slow diffusion limits the overall rate. Smaller values of the Thiele modulus represent slow reactions with fast diffusion. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Thiele modulus」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.