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Diffusion of methylene blue in glass fibers - Application of the shrinking core model

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

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:Adsorption; Cylinders (shapes); Diffusion; Functions; Glass; Glass fibers; Sensitivity analysis; Shrinkage; Sorption; Analytical solutions; Approximate analytical solutions; Concentration dependents; Diffusion phenomenon; Diffusivities; Dye concentrations; Exponential functions; Fluid reactions; Global minimizations; Heat diffusions; Heterogeneous solids; Mathematical model; Methylene blue dyes; Parametric sensitivities; Shrinking core model; Solid cylinders; Sorption of methylene blue; Temperature-dependent thermal conductivities; Theoretical equations; Mathematical models
Subjects:T Technology > TP Chemical technology
Departments / MOR / COE:Departments > Chemical Engineering
ID Code:2860
Deposited By: Prof Dr Binay Kanti Dutta
Deposited On:29 Sep 2010 03:17
Last Modified:19 Jan 2017 08:25

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