Numerical Modeling of Three-Phase Mass Transition with an Application in Atmospheric Chemistry

Affiliation(s)

Department of Analytical Chemistry and Computer Chemistry, University of Plovdiv, Plovdiv, Bulgaria.

Department of Informatics and Statistics, University of Food Technology, Plovdiv, Bulgaria.

Department of Analytical Chemistry and Computer Chemistry, University of Plovdiv, Plovdiv, Bulgaria.

Department of Informatics and Statistics, University of Food Technology, Plovdiv, Bulgaria.

ABSTRACT

This work presents a software tool for modeling of mass transfer physicochemical processes occurring in the atmosphere. The implemented algorithms provide an efficient theoretical frame for the interpretation of the results obtained from Coated Wall Flow Tube (CWFT) reactor experiments, which is one of the most adequate techniques to study heterogeneous kinetics. The numerical simulations are based on the fundamental Langmuir adsorption theory by ordinary differential equations and the second Fick’s law described by partial differential equations. The main application of the system is to estimate the basic parameters that characterize the processes. The best parameter estimation is found by minimizing the difference between experimental signals from the CWFT reactors and the obtained numerical simulations. A numerical example for an experimental data fit is given.

Cite this paper

N. Kochev, A. Terziyski and M. Milev, "Numerical Modeling of Three-Phase Mass Transition with an Application in Atmospheric Chemistry,"*Applied Mathematics*, Vol. 4 No. 8, 2013, pp. 100-106. doi: 10.4236/am.2013.48A014.

N. Kochev, A. Terziyski and M. Milev, "Numerical Modeling of Three-Phase Mass Transition with an Application in Atmospheric Chemistry,"

References

[1] P. Behr, A. Terziyski and R. Zellner, “Reversible Gas Ad sorption in Coated Wall Flow Tube Reactors. Model Simulations for Langmuir Kinetics,” Zeitschrift für Phy sikalische Chemie, Vol. 218, No. 11, 2004, pp. 1307-1327. doi:10.1524/zpch.218.11.1307.50806

[2] P. Behr, A. Terziyski and R. Zellner, “Acetone Adsor ption on Ice Surfaces in the Temperature Range T = 190 220 K: Evidence for Aging Effects Due to Crystallogra phic Changes of the Adsorption Sites,” The Journal of Physical Chemistry A, Vol. 110, No. 26, 2006, pp. 8098-8107. doi:10.1021/jp0563742

[3] R. A. Cox, M. A. Fernandez, A. Symington, M. Ullerstam and J. P. D. Abbatt, “A Kinetic Model for Uptake of HNO3 and HCl on Ice in a Coated Wall Flow System,” Physical Chemistry Chemical Physics, Vol. 7, No. 19, 2005, pp. 3434-3442. doi:10.1039/b506683b

[4] W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, “Numerical Recipes in FORTRAN Example Book,” Cambridge University Press, Cambridge, 1992.

[5] K. Morton and D. Mayers, “Numerical Solution of Partial Differential Equations: An Introduction,” 2nd Edition, Cam bridge University Press, Cambridge, 2005. doi:10.1017/CBO9780511812248

[6] G. Smith, “Numerical Solution of Partial Differential Equa tions: Finite Difference Methods,” Oxford University Press, Oxford, 1985.

[7] V. Alexiades, “Overcoming the Stability Restriction of Ex plicit Schemes via Super-Time-Stepping,” Proceedings of Dynamic Systems and Applications, Vol. 2, Dynamic Pub lishers, 1996, pp. 39-44.

[8] M. Milev and A. Tagliani, “Efficient Implicit Scheme with Positivity Preserving and Smoothing Properties,” Jour nal of Computational and Applied Mathematics, Vol. 243, 2013, pp. 1-9. doi:10.1016/j.cam.2012.09.039

[9] J. C. Ndogmo and D. B. Ntwiga, “High-Order Accurate Implicit Methods for Barrier Option Pricing,” Applied Mathematics and Computation, Vol. 218, No. 5, 2011, pp. 2210-2224. doi:10.1016/j.amc.2011.07.037

[10] J. Strikwerda, “Finite Difference Schemes and Partial Differential Equations,” 2nd Edition, SIAM: Society for Industrial and Applied Mathematics, 2004. doi:10.1137/1.9780898717938

[11] A. Terziyski and N. Kochev, “Distributed Software Sys tem for Data Evaluation and Numerical Simulations of Atmospheric Processes,” Numerical Methods and Appli cations, Lecture Notes in Computer Science, Vol. 6046, 2011, pp. 182-189.

[12] C. A. Varotsos and R. Zellner, “A New Modeling Tool for the Diffusion of Gases in Ice or Amorphous Binary Mixture in the Polar Stratosphere and the Upper Tropo sphere,” Atmospheric Chemistry and Physics, Vol. 10, No. 6, 2010, pp. 3099-3105.

[13] R. Sander, “Compilation of Henry’s Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry,” Version 3, 1999. http://www.henrys-law.org

[14] R. Atkinson, D. L. Baulch, R. A. Cox, J. N. Crowley, R. F. Hampson, R. G. Hynes, M. E. Jenkin, M. J. Rossi, J. Troe and T. J. Wallington, “Evaluated Kinetic and Pho tochemical Data for Atmospheric Chemistry: Volume IV—Gas Phase Reactions of Organic Halogen Species,” Atmospheric Chemistry and Physics, Vol. 8, No. 15, 2008, pp. 4141-4496. doi:10.5194/acp-8-4141-2008

[1] P. Behr, A. Terziyski and R. Zellner, “Reversible Gas Ad sorption in Coated Wall Flow Tube Reactors. Model Simulations for Langmuir Kinetics,” Zeitschrift für Phy sikalische Chemie, Vol. 218, No. 11, 2004, pp. 1307-1327. doi:10.1524/zpch.218.11.1307.50806

[2] P. Behr, A. Terziyski and R. Zellner, “Acetone Adsor ption on Ice Surfaces in the Temperature Range T = 190 220 K: Evidence for Aging Effects Due to Crystallogra phic Changes of the Adsorption Sites,” The Journal of Physical Chemistry A, Vol. 110, No. 26, 2006, pp. 8098-8107. doi:10.1021/jp0563742

[3] R. A. Cox, M. A. Fernandez, A. Symington, M. Ullerstam and J. P. D. Abbatt, “A Kinetic Model for Uptake of HNO3 and HCl on Ice in a Coated Wall Flow System,” Physical Chemistry Chemical Physics, Vol. 7, No. 19, 2005, pp. 3434-3442. doi:10.1039/b506683b

[4] W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, “Numerical Recipes in FORTRAN Example Book,” Cambridge University Press, Cambridge, 1992.

[5] K. Morton and D. Mayers, “Numerical Solution of Partial Differential Equations: An Introduction,” 2nd Edition, Cam bridge University Press, Cambridge, 2005. doi:10.1017/CBO9780511812248

[6] G. Smith, “Numerical Solution of Partial Differential Equa tions: Finite Difference Methods,” Oxford University Press, Oxford, 1985.

[7] V. Alexiades, “Overcoming the Stability Restriction of Ex plicit Schemes via Super-Time-Stepping,” Proceedings of Dynamic Systems and Applications, Vol. 2, Dynamic Pub lishers, 1996, pp. 39-44.

[8] M. Milev and A. Tagliani, “Efficient Implicit Scheme with Positivity Preserving and Smoothing Properties,” Jour nal of Computational and Applied Mathematics, Vol. 243, 2013, pp. 1-9. doi:10.1016/j.cam.2012.09.039

[9] J. C. Ndogmo and D. B. Ntwiga, “High-Order Accurate Implicit Methods for Barrier Option Pricing,” Applied Mathematics and Computation, Vol. 218, No. 5, 2011, pp. 2210-2224. doi:10.1016/j.amc.2011.07.037

[10] J. Strikwerda, “Finite Difference Schemes and Partial Differential Equations,” 2nd Edition, SIAM: Society for Industrial and Applied Mathematics, 2004. doi:10.1137/1.9780898717938

[11] A. Terziyski and N. Kochev, “Distributed Software Sys tem for Data Evaluation and Numerical Simulations of Atmospheric Processes,” Numerical Methods and Appli cations, Lecture Notes in Computer Science, Vol. 6046, 2011, pp. 182-189.

[12] C. A. Varotsos and R. Zellner, “A New Modeling Tool for the Diffusion of Gases in Ice or Amorphous Binary Mixture in the Polar Stratosphere and the Upper Tropo sphere,” Atmospheric Chemistry and Physics, Vol. 10, No. 6, 2010, pp. 3099-3105.

[13] R. Sander, “Compilation of Henry’s Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry,” Version 3, 1999. http://www.henrys-law.org

[14] R. Atkinson, D. L. Baulch, R. A. Cox, J. N. Crowley, R. F. Hampson, R. G. Hynes, M. E. Jenkin, M. J. Rossi, J. Troe and T. J. Wallington, “Evaluated Kinetic and Pho tochemical Data for Atmospheric Chemistry: Volume IV—Gas Phase Reactions of Organic Halogen Species,” Atmospheric Chemistry and Physics, Vol. 8, No. 15, 2008, pp. 4141-4496. doi:10.5194/acp-8-4141-2008