A Semi-Analytical Study on Multiscale Porous Biocatalytic Electrodes in the Enzyme Reaction Process

Authors

  • V. Vijayalakshmi Research Centre and PG Department of Mathematics, The Madura College (affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India https://orcid.org/0009-0007-6314-1969
  • V. Ananthaswamy Research Centre and PG Department of Mathematics, The Madura College (affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India https://orcid.org/0000-0002-2938-8745
  • J. Anantha Jothi Research Centre and PG Department of Mathematics, The Madura College (affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India https://orcid.org/0009-0000-5280-4500

DOI:

https://doi.org/10.26713/cma.v15i3.2821

Keywords:

Bioelectrodes, Glucose oxidase, New Homotopy Perturbation Method (NHPM), Ananthaswamy-Sivasankari Method (ASM), Non-linear boundary value problem, Numerical Simulation

Abstract

A multiscale porous biocatalytic electrode’s oxidation of glucose is explained theoretically. The model that describes diffusion and response within a hydrogel film is composed by two non-linear differential equations. Approximate analytical findings of the glucose concentrations, current, and the oxidised mediator have been obtained via the new homotopy perturbation technique. Furthermore, an analytical calculation is performed to determine the ideal electrode thickness for the film by employing Ananthaswamy-Sivasankari Method (ASM). It also investigates how parameters affect current. Our approximate analytical expressions are validated by the numerical simulation (MATLAB).

Downloads

References

G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, 1st edition, Springer, Dordrecht, xiv + 354 pages (1993).

V. Ananthaswamy and S. Narmatha, Semi-analytical solution for surface coverage model in an electrochemical arsenic sensor using a new approach to homotopy perturbation method, International Journal of Modern Mathematical Sciences 17(2) (2019), 85 – 110.

V. Ananthaswamy, R. Shanthakumari and M. Subha, Simple analytical expressions of the nonlinear reaction diffusion process in an immobilized biocatalyst particle using the new homotopy perturbation method, Review of Bioinformatics and Biometrics 3 (2014), 22 – 28.

O. E. Barcia, E. D’Elia, I. Frateur, O. R. Mattos, N. Pébère and B. Tribollet, Application of the impedance model of de Levie for the characterization of porous electrodes, Electrochimica Acta 47(13-14) (2002), 2109 – 2116, DOI: 10.1016/S0013-4686(02)00081-6.

E. O. Barnes, X. Chen, P. Li and R. G. Compton, Voltammetry at porous electrodes: A theoretical study, Journal of Electroanalytical Chemistry 720-721 (2014), 92 – 100, DOI: 10.1016/j.jelechem.2014.03.028.

P. N. Bartlett and K. F. E. Pratt, Theoretical treatment of diffusion and kinetics in amperometric immobilized enzyme electrodes Part I: Redox mediator entrapped within the film, Journal of Electroanalytical Chemistry 397(1-2) (1995), 61 – 78, DOI: 10.1016/0022-0728(95)04236-7.

D.-S. Chan, D.-J. Dai and H.-S. Wu, Dynamic modeling of anode function in enzyme-based biofuel cells using high mediator concentration, Energies 5(7) (2012), 2524 – 2544, DOI: 10.3390/en5072524.

S. Cosnier, A. J. Gross, A. Le Goff and M. Holzinger, Recent advances on enzymatic glucose/oxygen and hydrogen/oxygen biofuel cells: Achievements and limitations, Journal of Power Sources 325 (2016), 252 – 263, DOI: 10.1016/j.jpowsour.2016.05.133.

T. Q. N. Do, M. Varniˇci´c, R. Hanke-Rauschenbach, T. Vidakovi´c-Koch and K. Sundmacher, Mathematical modeling of a porous enzymatic electrode with direct electron transfer mechanism, Electrochimica Acta 137 (2014), 616 – 626, DOI: 10.1016/j.electacta.2014.06.031.

J. Galceran, S. L. Taylor and P. N. Bartlett, Modelling the steady-state current at the inlaid disc microelectrode for homogeneous mediated enzyme catalysed reactions, Journal of Electroanalytical Chemistry 506(2) (2001), 65 – 81, DOI: 10.1016/S0022-0728(01)00503-4.

J.-H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, International Journal of Non-Linear Mechanics 35(1) (2000), 37 – 43, DOI: 10.1016/S0020-7462(98)00085-7.

J.-H. He, A simple perturbation approach to Blasius equation, Applied Mathematics and Computation 140(2-3) (2003), 217 – 222, DOI: 10.1016/S0096-3003(02)00189-3.

J.-H. He, Homotopy perturbation method: A new nonlinear analytical technique, Applied Mathematics and Computation 135(1) (2003), 73 – 79, DOI: 10.1016/S0096-3003(01)00312-5.

J.-H. He, Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering 178(3-4) (1999), 257 – 262, DOI: 10.1016/S0045-7825(99)00018-3.

J. H. He, Some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B 20(10) (2006), 1141 – 1199, DOI: 10.1142/S0217979206033796.

X. Ke, J. M. Prahl, J. I. D. Alexander and R. F. Savinell, Redox flow batteries with serpentine flow fields: Distributions of electrolyte flow reactant penetration into the porous carbon electrodes and effects on performance, Journal of Power Sources 384 (2018), 295 – 302, DOI: 10.1016/j.jpowsour.2018.03.001.

D. Leech, P. Kavanagh and W. Schuhmann, Enzymatic fuel cells: Recent progress, Electrochimica Acta 84 (2012) 223 – 234, DOI: 10.1016/j.electacta.2012.02.087.

A. Meena and L. Rajendran, Analysis of a pH-based potentiometric biosensor using the Homotopy perturbation method, Chemical Engineering & Technology 33(12) (2010), 1999 – 2007, DOI: 10.1002/ceat.200900580.

N. Mehala and L. Rajendran, Analysis of mathematical modelling on potentiometric biosensors, International Scholarly Research Notices 2014(1) (2014), 582675, DOI: 10.1155/2014/582675.

M. M. Mousa and S. F. Ragab, Applications of the homotopy perturbation method to linear and non-linear Schrödinger equations, Zeitschrift für Naturforschung A 63(3-4) (2008), 140 – 144, DOI: 10.1515/zna-2008-3-404.

B. Nam and R. T. Bonnecaze, Analytic models of the infinite porous rotating disk electrode, Journal of the Electrochemical Society 154(10) (2007), F191, DOI: 10.1149/1.2759834.

M. Rasi, K. Indira and L. Rajendran, Approximate analytical expressions for the steadystate concentration of substrate and cosubstrate over amperometric biosensors for different enzyme kinetics, International Journal of Chemical Kinetics 45(5) (2013), 322 – 336, DOI: 10.1002/kin.20768.

V. Vijayalakshmi, V. Ananthaswamy and J. A. Jothi, Semi-analytical study on non-isothermal steady R-D equation in a spherical catalyst and biocatalyst, CFD Letters 15(12) (2023), 60 – 76, DOI: 10.37934/cfdl.15.12.6076.

A.-M. Wazwaz, The variational iteration method for solving linear and nonlinear ODEs and scientific models with variable coefficients, Open Engineering 4(1) (2014), 64 – 71, DOI: 10.2478/s13531-013-0141-6.

H. Wen, K. Ramanujam and S. C. Barton, Multiscale carbon materials as supports for bioelectrodes, ECS Transactions 13(21) (2008), 67, DOI: 10.1149/1.3036212.

Downloads

Published

30-11-2024
CITATION

How to Cite

Vijayalakshmi, V., Ananthaswamy, V., & Jothi, J. A. (2024). A Semi-Analytical Study on Multiscale Porous Biocatalytic Electrodes in the Enzyme Reaction Process. Communications in Mathematics and Applications, 15(3), 1241–1254. https://doi.org/10.26713/cma.v15i3.2821

Issue

Vol. 15 No. 3 (2024)

Section

Research Article

License

Creative Commons Licence 4.0 by  

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.