Computational analysis of the slow invariant manifold for single and multi-route reaction mechanisms

Document Type : Research Note

Authors

1 Department of Mathematics and Statistics, Hazara University, Mansehra 21300, Pakistan

2 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China.; Department of Mathematics, Mohi-ud-Din Islamic University, Nerian Sharif, 12010 Azad Jammu & Kashmir, Pakistan

Abstract

The complexity behavior lies in many natural phenomena’s, such as our ecosystems, the earth’s climate, the behavior of the animal group, living cells and our brain. Therefore, a new field of “systems chemistry” is emerging, which aims to capture the complexity observed in natural systems within a synthetic chemical framework. To understand the physical behavior of the chemical components in a reaction mechanism (system), we need to understand the overall (complete) reactions network as well as different available reaction-paths. We propose the development of a multi-route reaction mechanism for a complex chemical reaction mechanism which is unsolvable through a common way. Further, invariant manifold approximation has been constructed through the Quasi Equilibrium Manifold. The numerical results have been tabulated along with the graphical view through MATLAB

Keywords

References

References:
1. Shahzad, M., Sajid, M., Gulistan, M., and Arif, H. "Initially approximated quasi equilibrium manifold", Journal of the Chemical Society of Pakistan, 37, pp. 1-7 (2015).
2. Kooshkbaghi, M., Frouzakis, C.E., Boulouchos, K., and Karlin, I.V. "Spectral quasi-equilibrium manifold for chemical kinetics", J. Phys. Chem. A, 120, pp. 3406-4313 (2016).
3. Shahzad, M., Sultan, F., Haq, I., Ali, M., and Khan, W.A. "C-matrix and invariants in chemical kinetics: A mathematical concept", Pramana - J. Phys., 92(64) (2019). https://doi.org/10.1007/s12043-019-1723-5. 
4. Kooshkbaghi, M., Frouzakis, C.E., Chiavazzo, E., Boulouchos, K., and Karlin, I.V. "The global relaxation redistribution method for reduction of combustion kinetics", The Journal of Chemical Physics, 141, 044102 (2014).
5. Shahzad, M., Sultan, F., and Haq, I. "Computing the low dimension manifold in dissipative dynamical systems", The Nucleus, 53, pp. 107-113 (2016).
6. Shahzad, M., Rehman, S., Bibi, R., Wahab, H.A., Abdullah, S., and Ahmed, S. "Measuring the complex behavior of the SO2 oxidation reaction", Computational Ecology and Software, 5, pp. 254-260 (2015).
7. Aris, R. "Prolegomena to the rational analysis of systems of chemical reactions", Archive for Rational Mechanics and Analysis, 19, p. 81 (1965).
8. Constales, D., Yablonsky, G.S., D'hooge, D.R., Thybout, J.W., and Marin, G.B., Advanced Data Analysis and Modelling in Chemical Engineering, Elsevier (2016).
9. Maxwell, J.C. "On the dynamical theory of gases", Philosophical Transactions of the Royal Society of London, 157, p. 49 (1867).
10. Boltzmann, L., Weitere Studien uber das warmegleichgewicht unter Gasmolekulen, Springer (1970).
11. Gorban, A.N. and Shahzad, M. "The michaelismenten-stueckelberg theorem", Entropy, 13, p. 966 (2011).
12. Sultan, F., Shahzad, M., Ali, M., and Khan, W.A. "The reaction routes comparison with respect to slow invariant manifold and equilibrium points", AIP Advances, 9, 015212 (2019).https://doi.org/10.1063/1.5050265.
13. Sultan, F., Khan, W.A., Shahzad, M., Ali, M., and Shah, S.I.A. "Activation energy characteristics of chemically reacting species in multi-route complex reaction mechanism", Indian J. Phys. https://doi.org/10.1007/s12648-019-01624-2.
14. Shahzad, M., Sultan, F., Ali, M., Khan, W.A., and Irfan, M. "Slow invariant manifold assessments in multi-route reaction mechanism", J. Mol. Liq., 284, pp. 265-270 (2019).
15. Gorban, A.N. and Karlin, I.V. "Method of invariant manifold for chemical kinetics", Chem. Eng. Sci., 58, pp. 4751-4768 (2003).
16. Shahzad, M., Sultan, F., Shah, S.I.A., Ali, M., Khan, H.A., and Khan, W.A. "Physical assessments on chemically reacting species and reduction schemes for the approximation of invariant manifolds", J. Mol. Liq., 285, pp. 237-243, doi.org/10.1016/j.molliq.2019.03.031 (2019).
17. Shahzad, M., Haq, I., Sultan, F.,Wahab, A., Faizullah, F., and Rehman, G. "Slow manifolds in chemical kinetics", J. Chem. Soc. Pak., 38(05), pp. 828-835 (2016).
18. Shahzad, M. and Sultan, F., Complex Reactions and Dynamics: Advanced Chemical Kinetics, InTech, Rijeka (2018). DOI: 10.5772/intechopen.70502.
Scientia Iranica
Volume 27, Issue 3
Transactions on Chemistry and Chemical Engineering (C)
June 2020
Pages 1293-1299

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History

  • Receive Date: 06 April 2019
  • Revise Date: 21 November 2019
  • Accept Date: 14 April 2020

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