Multi-route reaction mechanism and steady-state flow: a MATLAB-based analysis

Abstract

This article presents the theoretical results for Multi-route reaction model of chemical kinetics. The steady-state approximation of the participating chemical species and the relationship between the common species in multi-routes mechanism is preserved. It has observed that some reaction routes complete their cycle before the others. The reason behind the reaction completion is the transition time of the species during the reaction. Graphical results obtained through MATLAB are used to describe the physical aspects of measurements.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

References

  1. Ali M, Shahzad M, Sultan F, Khan WA (2019) Physical assessments on the invariant region in multi-route reaction mechanism. Phys A. https://doi.org/10.1016/j.physa.2019.122499

    Article  Google Scholar 

  2. Aris R (1965) Prolegomena to the rational analysis of systems of chemical reactions. Arch Ration Mech Anal 19:81

    Article  Google Scholar 

  3. Constales D, Yablonsky GS, D'hooge DR et al (2016) Advanced data analysis and modelling in chemical engineering. Elsevier, Amsterdam

    Google Scholar 

  4. Gorban AN, Shahzad M (2011) The michaelis-menten-stueckelberg theorem. Entropy 13:966

    CAS  Article  Google Scholar 

  5. Maxwell JC (1867) On the dynamical theory of gases. Philos Trans R Soc Lond 157:49

    Google Scholar 

  6. Shahzad M, Sultan F (2018) Complex reactions and dynamics: advanced chemical kinetics. InTech Rijeka. https://doi.org/10.5772/intechopen.70502

    Article  Google Scholar 

  7. Shahzad M, Rehman S, Bibi R, Abdul Wahab H, Abdullah S, Ahmed S (2015a) Measuring the complex behavior of the SO2 oxidation reaction. Comput Ecol Softw 5:254

    Google Scholar 

  8. Shahzad M, Sajid M, Gulistan M, Arif H (2015b) Initially approximated quasi equilibrium manifold. J Chem Soc Pak 37:208–216

    Google Scholar 

  9. Shahzad M, Sultan F, Haq I et al (2016a) Computing the low dimension manifold in dissipative dynamical systems. The Nucleus 53:107–113

    Google Scholar 

  10. Shahzad M, Haq I, Sultan F et al (2016b) Slow manifolds in chemical kinetics. J Chem Soc Pak 38(05):828–835

    CAS  Google Scholar 

  11. Shahzad M, Sultan F, Ali M, Khan WA, Irfan M (2019a) Slow invariant manifold assessments in multi-route reaction mechanism. J Mol Liq 284:265–270

    CAS  Article  Google Scholar 

  12. Shahzad M, Sultan F, Haq I, Ali M, Khan WA (2019b) C-matrix and invariants in chemical kinetics: a mathematical concept. Pramana–J Phys. https://doi.org/10.1007/s12043-019-1723-5

    Article  Google Scholar 

  13. Shahzad M, Sultan F, Shah SIA, Ali M, Khan HA, Khan WA (2019c) Physical assessments on chemically reacting species and reduction schemes for the approximation of invariant manifolds. J Mol Liq 285:237–243. https://doi.org/10.1016/j.molliq.2019.03.031

    CAS  Article  Google Scholar 

  14. Shahzad M, Sultan F, Ali M, Khan WA, Mustafa S (2020) Modeling multi-route reaction mechanism for surfaces: a mathematical and computational approach. Appl Nanosci. https://doi.org/10.1007/s13204-020-01275-4

    Article  Google Scholar 

  15. Sultan F, Khan WA, Shahzad M, Ali M, Shah SIA (2019) 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

    Article  Google Scholar 

  16. Sultan F, Shahzad M, Ali M, Khan WA (2019) The reaction routes comparison with respect to Slow Invariant Manifold and equilibrium points. AIP Adv 9:015212. https://doi.org/10.1063/1.5050265

    CAS  Article  Google Scholar 

  17. Yaublonsky GS, Branco D, Marin GB, Constales D (2020) New invariant expensions in chemical kinetics. Entropy 22:373

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding authors

Correspondence to Faisal Sultan or Muhammad Shahzad.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sultan, F., Ali, M., Shahzad, M. et al. Multi-route reaction mechanism and steady-state flow: a MATLAB-based analysis. Appl Nanosci 10, 3287–3294 (2020). https://doi.org/10.1007/s13204-020-01410-1

Download citation

Keywords

  • Reaction mechanism
  • Steady state
  • Activation energy
  • Reaction routes