Diffusion of methylene blue in glass fibers - Application of the shrinking core model
Diffusion of mass in a solid cylinder with concentration dependent diffusivity (or temperature-dependent thermal conductivity in case of heat diffusion) does not admit of an analytical solution except in special cases. The 'shrinking core model' has been used to develop an approximate anal...
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| Format: | Article |
| Language: | English |
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2009
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| Online Access: | http://scholars.utp.edu.my/id/eprint/2860/ http://scholars.utp.edu.my/id/eprint/2860/1/Diffusion-of-methylene-blue-in-glass-fibers---Application-of-the-shrinking-core-model_2009_Applied-Mathematical-Modelling.pdf |
| _version_ | 1848659316893024256 |
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| author | B.K., Dutta D., Sarkar S., Chakrabarti |
| author_facet | B.K., Dutta D., Sarkar S., Chakrabarti |
| author_sort | B.K., Dutta |
| building | UTP Institutional Repository |
| collection | Online Access |
| description | Diffusion of mass in a solid cylinder with concentration dependent diffusivity (or temperature-dependent thermal conductivity in case of heat diffusion) does not admit of an analytical solution except in special cases. The 'shrinking core model' has been used to develop an approximate analytical solution in certain circumstances. The model, generally useful to describe heterogeneous solid-fluid reactions, is applied to theoretically analyze the adsorption-diffusion phenomena of methylene blue dye in a glass fiber in the present work. Theoretical equations have been derived for the case of diffusivity as an exponential function of concentration. The diffusivity parameters are evaluated by global minimization of the error between the experimental and the theoretical concentration history. Other forms of diffusivity, namely constant diffusivity and diffusivity varying linearly with concentration are found to involve larger errors. A parametric sensitivity analysis of the error has been done. The shrinking core model could satisfactorily interpret the experimental dye concentration profile in the substrate. © 2008 Elsevier Inc. All rights reserved.
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| first_indexed | 2025-11-13T07:28:30Z |
| format | Article |
| id | oai:scholars.utp.edu.my:2860 |
| institution | Universiti Teknologi Petronas |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-13T07:28:30Z |
| publishDate | 2009 |
| recordtype | eprints |
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| spelling | oai:scholars.utp.edu.my:28602017-01-19T08:25:37Z http://scholars.utp.edu.my/id/eprint/2860/ Diffusion of methylene blue in glass fibers - Application of the shrinking core model B.K., Dutta D., Sarkar S., Chakrabarti TP Chemical technology Diffusion of mass in a solid cylinder with concentration dependent diffusivity (or temperature-dependent thermal conductivity in case of heat diffusion) does not admit of an analytical solution except in special cases. The 'shrinking core model' has been used to develop an approximate analytical solution in certain circumstances. The model, generally useful to describe heterogeneous solid-fluid reactions, is applied to theoretically analyze the adsorption-diffusion phenomena of methylene blue dye in a glass fiber in the present work. Theoretical equations have been derived for the case of diffusivity as an exponential function of concentration. The diffusivity parameters are evaluated by global minimization of the error between the experimental and the theoretical concentration history. Other forms of diffusivity, namely constant diffusivity and diffusivity varying linearly with concentration are found to involve larger errors. A parametric sensitivity analysis of the error has been done. The shrinking core model could satisfactorily interpret the experimental dye concentration profile in the substrate. © 2008 Elsevier Inc. All rights reserved. 2009 Article PeerReviewed application/pdf en http://scholars.utp.edu.my/id/eprint/2860/1/Diffusion-of-methylene-blue-in-glass-fibers---Application-of-the-shrinking-core-model_2009_Applied-Mathematical-Modelling.pdf B.K., Dutta and D., Sarkar and S., Chakrabarti (2009) Diffusion of methylene blue in glass fibers - Application of the shrinking core model. Applied Mathematical Modelling, 33 (6). pp. 2874-2881. ISSN 0307904X http://www.scopus.com/inward/record.url?eid=2-s2.0-60249085726&partnerID=40&md5=3256bae726048729ddf1e0491777a324 10.1016/j.apm.2008.08.019 10.1016/j.apm.2008.08.019 10.1016/j.apm.2008.08.019 |
| spellingShingle | TP Chemical technology B.K., Dutta D., Sarkar S., Chakrabarti Diffusion of methylene blue in glass fibers - Application of the shrinking core model |
| title | Diffusion of methylene blue in glass fibers - Application of the shrinking core model
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| title_full | Diffusion of methylene blue in glass fibers - Application of the shrinking core model
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| title_fullStr | Diffusion of methylene blue in glass fibers - Application of the shrinking core model
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| title_full_unstemmed | Diffusion of methylene blue in glass fibers - Application of the shrinking core model
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| title_short | Diffusion of methylene blue in glass fibers - Application of the shrinking core model
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| title_sort | diffusion of methylene blue in glass fibers - application of the shrinking core model |
| topic | TP Chemical technology |
| url | http://scholars.utp.edu.my/id/eprint/2860/ http://scholars.utp.edu.my/id/eprint/2860/ http://scholars.utp.edu.my/id/eprint/2860/ http://scholars.utp.edu.my/id/eprint/2860/1/Diffusion-of-methylene-blue-in-glass-fibers---Application-of-the-shrinking-core-model_2009_Applied-Mathematical-Modelling.pdf |