{"title":"Theoretical analysis of Langmuir–Hinshelwood kinetics: Hyperbolic function and Akbari–Ganji’s method","authors":"M. Karthiyayini, P. Jeyabarathi, L. Rajendran","doi":"10.1007/s11144-025-02802-6","DOIUrl":null,"url":null,"abstract":"<div><p>Reaction–diffusion processes, including Langmuir’s absorption kinetics and chemical reactions in porous catalysts, have been discussed. This model’s non-linear reaction–diffusion equation includes a non-linear term associated with Langmuir–Hinshelwood kinetics. Simple analytical expressions of the reactant concentration for all kinetic and adsorption parameters are reported using the hyperbolic function and the Akbari–Ganji method. The impact of different parameters on concentration is also discussed. The simple expression of the effectiveness factor is also obtained for general geometry and all reaction orders. A satisfactory agreement is observed when our theoretical results are compared with the simulation results. Our analytical results demonstrate a notable agreement with simulation outcomes, underscoring the effectiveness and reliability of our proposed methodology.</p></div>","PeriodicalId":750,"journal":{"name":"Reaction Kinetics, Mechanisms and Catalysis","volume":"138 3","pages":"1221 - 1239"},"PeriodicalIF":1.7000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reaction Kinetics, Mechanisms and Catalysis","FirstCategoryId":"92","ListUrlMain":"https://link.springer.com/article/10.1007/s11144-025-02802-6","RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Reaction–diffusion processes, including Langmuir’s absorption kinetics and chemical reactions in porous catalysts, have been discussed. This model’s non-linear reaction–diffusion equation includes a non-linear term associated with Langmuir–Hinshelwood kinetics. Simple analytical expressions of the reactant concentration for all kinetic and adsorption parameters are reported using the hyperbolic function and the Akbari–Ganji method. The impact of different parameters on concentration is also discussed. The simple expression of the effectiveness factor is also obtained for general geometry and all reaction orders. A satisfactory agreement is observed when our theoretical results are compared with the simulation results. Our analytical results demonstrate a notable agreement with simulation outcomes, underscoring the effectiveness and reliability of our proposed methodology.
期刊介绍：
Reaction Kinetics, Mechanisms and Catalysis is a medium for original contributions in the following fields:
-kinetics of homogeneous reactions in gas, liquid and solid phase;
-Homogeneous catalysis;
-Heterogeneous catalysis;
-Adsorption in heterogeneous catalysis;
-Transport processes related to reaction kinetics and catalysis;
-Preparation and study of catalysts;
-Reactors and apparatus.
Reaction Kinetics, Mechanisms and Catalysis was formerly published under the title Reaction Kinetics and Catalysis Letters.
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