A kinetic non-steady state analysis of immobilized enzyme systems with external mass transfer resistance

M. Sivakumar; M. Mallikarjuna; R. Senthamarai; M. Sivakumar; M. Mallikarjuna; R. Senthamarai

doi:10.3934/math.2024882

AIMS Mathematics

2024, Volume 9, Issue 7: 18083-18102. doi: 10.3934/math.2024882

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Research article

A kinetic non-steady state analysis of immobilized enzyme systems with external mass transfer resistance

1.
Department of Mathematics, College of Science and Humanities, SRM Institute of Science and Technology, Vadapalani, Chennai 600026, Tamilnadu, India
2.
Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamilnadu, India

Received: 20 March 2024 Revised: 26 April 2024 Accepted: 29 April 2024 Published: 28 May 2024
MSC : 35A22, 35A35, 35G31, 97M60

The goal of this paper is to utilize the homotopy perturbation method (HPM) and Laplace transform to provide an approximate analytical expression to the non-linear time-dependent reaction diffusion equation arising in a mathematical model of an immobilized enzyme system with external mass transfer resistance. This mathematical model is a non-steady, non-linear reaction diffusion equation based on Michaelis–Menten kinetics. Approximate analytical expressions are also provided for various geometries of the enzyme catalytic pellets, namely, planar, cylindrical, and spherical. Obtained semi-analytical expressions are proven to fit for all the parameters appearing in the system and for all the geometries of enzyme catalytic pellets. When comparing the numerical and approximate analytical solutions, satisfactory results are obtained. Also, approximate analytical expressions of the effectiveness factor (EF) of the immobilized system are presented, and the effect of parameters on the EF is also analyzed.
- mathematical modelling,
- immobilized enzyme,
- Michaelis–Menten kinetics,
- homotopy perturbation method,
- Laplace transform technique
Citation: M. Sivakumar, M. Mallikarjuna, R. Senthamarai. A kinetic non-steady state analysis of immobilized enzyme systems with external mass transfer resistance[J]. AIMS Mathematics, 2024, 9(7): 18083-18102. doi: 10.3934/math.2024882

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Abstract

The goal of this paper is to utilize the homotopy perturbation method (HPM) and Laplace transform to provide an approximate analytical expression to the non-linear time-dependent reaction diffusion equation arising in a mathematical model of an immobilized enzyme system with external mass transfer resistance. This mathematical model is a non-steady, non-linear reaction diffusion equation based on Michaelis–Menten kinetics. Approximate analytical expressions are also provided for various geometries of the enzyme catalytic pellets, namely, planar, cylindrical, and spherical. Obtained semi-analytical expressions are proven to fit for all the parameters appearing in the system and for all the geometries of enzyme catalytic pellets. When comparing the numerical and approximate analytical solutions, satisfactory results are obtained. Also, approximate analytical expressions of the effectiveness factor (EF) of the immobilized system are presented, and the effect of parameters on the EF is also analyzed.

References

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