Adomian decomposition method solution of population balance equations for aggregation, nucleation, growth and breakup processes

Applied Mathematical Modelling

Volumn 39, Issue 7, 2015, Pages 1975-1984

  Hasseine, A ^a   Bart, H J ^b  

^a UNIVERSITY OF BISKRA   (Algeria)

^b University of Koblenz Landau   (Germany)

Author keywords

Adomian decomposition method (ADM); Population balance equation (PBE); Projection method

Indexed keywords

AGGLOMERATION; DISTRIBUTION FUNCTIONS; NUCLEATION; PARTICLE SIZE; PARTICLE SIZE ANALYSIS;

ADOMIAN DECOMPOSITION METHOD; ADOMIAN DECOMPOSITION METHODS; COLLOCATION TECHNIQUES; DIFFERENTIAL POPULATIONS; NON-LINEAR AGGREGATION; NUMERICAL TECHNIQUES; POPULATION BALANCE EQUATION; PROJECTION METHOD;

POPULATION STATISTICS;

EID: 84933675204     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2014.09.027     Document Type: Article

References (29)

1. Ramkrishna D. The status of population balances. Rev. Chem. Eng. 1985, 3:49-95.
2. Kostoglou M., Karabelas A.J. Evaluation of zero order methods for simulating particle coagulation. J. Colloidal Interface Sci. 1994, 613:420-431.
3. Kumar S., Ramkrishna D. On the solution of population balance equations by discretization - I. A fixed pivot technique. Chem. Eng. Sci. 1996, 51:1311-1332.
4. Kumar S., Ramkrishna D. On the solution of population balance equations by discretization-II. A moving pivot technique. Chem. Eng. Sci. 1996, 51:1333-1342.
5. Kumar S., Ramkrishna D. On the solution of population balance equations by discretization-III. nucleation, growth and aggregation of particles. Chem. Eng. Sci. 1997, 52:4659-4679.
6. Hasseine A., Bellagoun A., Bart H.-J. Analytical solution of the droplet breakup equation by the Adomian decomposition method. Appl. Math. Comput. 2011, 218:2249-2258.
7. Dehghan M., Shakeri F. The use of the decomposition procedure of Adomian for solving a delay differential equation arising in electrodynamics. Phys. Scr. 2008, 78:1-11.
8. Dehghan M., Salehi R. The use of variational iteration method and Adomian decomposition method to solve the Eikonal equation and its application in the reconstruction problem. Int. J. Numer. Methods Biomedical. Eng. 2011, 27:524-540.
9. Dehghan M., Heris J.M., Saadatmandi A. Application of semi-analytic methods for the Fitzhugh-Nagumo equation, which models the transmission of nerve impulses. Math. Methods Appl. Sci. 2010, 33:1384-1398.
10. Dehghan M., Shakourifar M., Hamidi A. The solution of linear and nonlinear systems of Volterra functional equations using Adomian-Pade technique. Chaos, Solitons Fractals 2009, 39:2509-2521.
11. Dehghan M., Hamidi A., Shakourifar M. The solution of coupled Burgers equations using Adomian-Pade technique. Appl. Math. Comput. 2007, 189:1034-1047.
12. Dehghan M., Salehi R. Solution of a nonlinear time-delay model in biology via semi-analytical approaches. Comput. Phys. Commun. 2010, 181:1255-1265.
13. Shakeri F., Dehghan M. Application of the decomposition method of Adomian for solving the pantograph equation of order m. Z. Naturforsch. 2010, 65a:453-460.
14. Dehghan M., Tatari M. Finding approximate solutions for a class of third-order non-linear boundary value problems via the decomposition method of Adomian. Int. J. Comput. Math. 2010, 87:1256-1263.
15. Alipanah A., Dehghan M. Solution of population balance equations via rationalized Haar functions. Kybernetes. 2008, 37:1189-1196.
16. Sandu A., Borden C. A framework for the numerical treatment of aerosol dynamics. Appl. Num. Math. 2003, 45:475-497.
17. Valentas K.J., Amundson A.R. Breakup and coalescence in dispersed phase systems. Ind. Eng. Chem. Fundam. 1966, 5:533-542.
18. Podgórska W., Bałdyga J. Scale-up effects on the drop size distribution of liquid liquid dispersions in agitated vessels. Chem. Eng. Sci. 2001, 56:741-746.
19. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method 1994, Kluwer Academic, Dordrecht.
20. Adomian G., Rach R. On linear and nonlinear integro-differential equations. J. Math. Anal. Appl. 1986, 113:199-201.
21. Wazwaz A.M. Partial Differential Equations and Solitary Waves Theory 2009, Higher Education Press, Beijing, and Springer, Berlin.
22. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method 1995, Kluwer.
23. Abbaoui K., Cherruault Y. Convergence of Adomian's method applied to differential equations. Comput. Math. Appl. 1994, 28:103-109.
24. Abbaoui K., Cherruault Y. New ideas for proving convergence of decomposition methods. Comput. Math. Appl. 1995, 29:103-108.
25. Cherruault Y., Adomian G. Decomposition method: a new proof of convergence. Math. Comput. Model. 1993, 18:103-106.
26. A. Sandu, Piecewise polynomial solutions of aerosol dynamic equations, Computer Science technical report CS-TR-04-01, Virginia Polytechnic Institute and State University, Jan. 2004.
27. Scott W.T. Analytic studies of cloud droplet coalescence. J. Atmos. Sci. 1968, 25:54-65.
28. Gelbard F., Seinfield J.H. Numerical solution of the dynamic equation for particulate systems. J. Comp. Phys. 1978, 28:357-375.
29. Liu Y., Cameron I.T. A new wavelet-based method for the solution of the population balance equation. Chem. Eng. Sci. 2001, 56:5283-5294.