Approximate Analytical Solution to a Pore Network Model of Deactivation of Immobilized Glucose Isomerase in Packed-Bed Reactors Using Akbari-Ganji’s Method
DOI:
https://doi.org/10.26713/cma.v13i3.1805Keywords:
Mathematical modelling, Non-linear differential equation, Pore network model, Akbari–Ganji’s method, Numerical simulationAbstract
The main objective of this paper is to derive an approximate analytical solution for the mathematical model pertaining to deactivation of immobilized glucose in packed-bed reactors. The Akbari-Ganji’s method is applied to solve the previously developed mathematical model. The approximate analytical expressions corresponding to the concentration and current in the steady state condition have been derived for all values of parameters. Excellent agreement is obtained between the analytical solution and the numerical simulation. The analytical solution presented in this paper is presented for the first time. The results of this work will provide a better understanding of the mathematical model examined.
Downloads
References
V. Ananthaswamy and B. Seethalakshmi, Mathematical analysis of information dissemination model for social networking services, American Journal of Modeling and Optimization 3(1) (2015), 26 – 34, URL: http://pubs.sciepub.com/ajmo/3/1/4.
M. D. Benaiges, C. Sola and C. De Mas, Intrinsic kinetic constants of an immobilised glucose isomerase, Journal of Chemical Technology & Biotechnology 36(10) (1986), 480 – 486, DOI: 10.1002/jctb.280361008.
K. C. Chen and J. Y. Wu, Substrate protection of immobilized glucose isomerase, Biotechnology and Bioengineering 30(7) (1987), 817 – 824, DOI: 10.1002/bit.260300703.
M. Dadvar and M. Sahimi, Pore network model of deactivation of immobilized glucose isomerase in packed-bed reactors. Part III: Multiscale modelling, Chemical Engineering Science 58 (2003), 4935 – 4951, DOI: 10.1016/j.ces.2003.07.006.
A. Demir, S. Erman, B. Ozgur and E. Korkmaz, Analysis of the new homotopy perturbation method for linear and nonlinear problems, Boundary Value Problems 2013 (2013), Article number: 61, DOI: 10.1186/1687-2770-2013-61.
K. M. Dharmalingam and M. Veeramuni, Akbari-Ganji’s Method (AGM) for solving non-linear reaction - Diffusion equation in the electroactive polymer film, Journal of Electroanalytical Chemistry 844(1) (2019), 1 – 5, DOI: 10.1016/j.jelechem.2019.04.061.
J.-Y. Houng, H.-Y. Yu, K.-C. Chen and C. Tiu, Analysis of substrate protection of an immobilized glucose isomerase reactor, Biotechnology and Bioengineering 41(4) (1993), 451 – 458, DOI: 10.1002/bit.260410408.
R. A. Joy, A. Meena, S. Loghambal and L. Rajendran, A two-parameter mathematical model for immobilizedenzymes and homotopy analysis method, Natural Science 3 (2011), 556 – 565, DOI: 10.4236/ns.2011.37078.
M. Kirthiga, S. Balamurugan and L. Rajendran, Modelling of reaction-diffusion process at carbon nanotube-Redox enzyme composite modified electrode biosensor, Chemical Physics Letters 715 (2019), 20 – 28, DOI: 10.1016/j.cplett.2018.11.019.
M. Mahalakshmi, G. Hariharan and K. Kannan, The wavelet methods to linear and nonlinear reaction-diffusion model arising in mathematical chemistry, Journal of Mathematical Chemistry 51 (2013), 2361 – 2385, DOI: 10.1007/s10910-013-0216-x.
R. O. Marshall and E. R. Kooi, Enzymatic conversion of D-glucose to D-fructose, Science 125(3249) (1957), 648 – 649, DOI: 10.1126/science.125.3249.648.
S. Narmatha, V. Ananthaswamy and M. Rasi, Application of new approach to homotopy perturbation method in solving a system of nonlinear self-igniting reaction diffusion equations, Mathematics in Engineering, Science and Aerospace 12(1) (2021), 231 – 244, URL: http://nonlinearstudies.com/index.php/mesa/issue/view/192.
M. Rabbani, New homotopy perturbation method to solve non-linear problems, Journal of Mathematics and Computer Science 7(4) (2013), 272 – 275, DOI: 10.22436/jmcs.07.04.06.
A. K. Rostami, M. R. Akbari, D. D. Ganji and S. Heydari, Investigating Jeffery-Hamel flow with high magnetic field and nano particle by HPM and AGM, Central European Journal of Engineering 4 (2014), 357 – 370, DOI: 10.2478/s13531-013-0175-9.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.