A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics

Do, D. and Greenfield, P. (1981) A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics. Mathematical Biosciences, 54 1-2: 31-47.


Author Do, D.
Greenfield, P.
Title A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics
Journal name Mathematical Biosciences   Check publisher's open access policy
Publication date 1981-05
Sub-type Article
DOI 10.1016/0025-5564(81)90074-2
Volume number 54
Issue number 1-2
ISSN 0025-5564
Start page 31
End page 47
Total pages 17
Place of publication New York
Publisher Elsevier Science
Language eng
Subject 290600 Chemical Engineering
Abstract An approximate analytical technique employing a finite integral transform is developed to solve the reaction diffusion problem with Michaelis-Menten kinetics in a solid of general shape. A simple infinite series solution for the substrate concentration is obtained as a function of the Thiele modulus, modified Sherwood number, and Michaelis constant. An iteration scheme is developed to bring the approximate solution closer to the exact solution. Comparison with the known exact solutions for slab geometry (quadrature) and numerically exact solutions for spherical geometry (orthogonal collocation) shows excellent agreement for all values of the Thiele modulus and Michaelis constant.
Keyword finite integral transform technique
diffusion-reaction equation
Michaelis-Menten kinetics
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown
Additional Notes This is an author version of an article originally published as Do, D. & Greenfield, P. (1981) A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics. Mathematical Biosciences, 54 1-2: 31-47. Doi: 10.1016/0025-5564(81)90074-2 Copyright 1981 Elsevier. Allrights reserved. Single copies only may be downloaded and printed for a user’s personal research and study.

Document type: Journal Article
Sub-type: Article
Collection: School of Chemical Engineering Publications
 
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Created: Mon, 25 Jun 2007, 15:52:35 EST by Fei Yu