Entropic lattice Boltzmann method for crystallization processes

Chemical Engineering Science

Volumn 65, Issue 13, 2010, Pages 3928-3936

  Majumder, Aniruddha ^a   Kariwala, Vinay ^a   Ansumali, Santosh ^a,b   Rajendran, Arvind ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b JAWAHARLAL NEHRU CENTRE FOR ADVANCED SCIENTIFIC RESEARCH   (India)

Author keywords

Crystallization; Dynamic simulation; High resolution method; Lattice Boltzmann method; Particulate process; Population balance

Indexed keywords

CRYSTALLIZATION DYNAMICS; HIGH-RESOLUTION METHODS; LATTICE BOLTZMANN METHOD; PARTICULATE PROCESS; POPULATION BALANCES;

COMPUTER SIMULATION; CRYSTALLIZATION;

DROP FORMATION;

EID: 77953133156     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2010.03.030     Document Type: Article

References (45)

1. Alopaeus V., Laakkonen M., and Aittamaa J. Solution of population balances with growth and nucleation by high order moment-conserving method of classes. Chem. Eng. Sci. 62 8 (2007) 2277-2289
2. Ansumali S., and Karlin I.V. Stabilization of the lattice Boltzmann method by the H theorem: a numerical test. Phys. Rev. E 62 6 (2000) 7999
3. Ansumali S., and Karlin I.V. Entropy function approach to the lattice Boltzmann method. J. Statist. Phys. 107 (2002) 291-308
4. Ansumali S., and Karlin I.V. Single relaxation time model for entropic lattice Boltzmann methods. Phys. Rev. E 65 (2002) 056312
5. Ansumali S., Karlin I.V., and Öttinger H.C. Minimal entropic kinetic models for simulating hydrodynamics. Europhys. Lett. 63 (2003) 798-804
6. Bhatnagar P.L., Gross E.P., and Krook M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94 3 (1954) 511
7. Brownlee R., Gorban A., and Levesley J. Nonequilibrium entropy limiters in lattice Boltzmann methods. Phys. A Statist. Mech. Appl. 387 2-3 (2007) 385-406
8. Chen H., Chen S., and Matthaeus W. Recovery of the Navier-Stokes equation using a lattice-gas Boltzmann method. Phys. Rev. A 45 (1992) R5339-R5342
9. Chen H., Kandasamy S., Orszag S., Shock R., Succi S., and Yakhot V. Extended Boltzmann kinetic equation for turbulent flows. Science 301 5633 (2003) 633-636
10. Chen S., and Doolen G.D. Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30 1 (1998) 329-364
11. Freund H., Zeiser T., Huber F., Klemm E., Brenner G., Durst F., and Emig G. Numerical simulations of single phase reacting flows in randomly packed fixed-bed reactors and experimental validation. Chem. Eng. Sci. 58 3-6 (2003) 903-910
12. Frisch U., Hasslacher B., and Pomeau Y. Lattice-gas automata for the Navier-Stokes equation. Phys. Rev. Lett. 56 (1986) 1505
13. Gunawan R., Fusman I., and Braatz R.D. High resolution algorithms for multidimensional population balance equations. A.I.Ch.E. J. 50 11 (2004) 2738-2749
14. Gunawan R., Fusman I., and Braatz R.D. Parallel high-resolution finite volume simulation of particulate processes. A.I.Ch.E. J 54 6 (2008) 1449-1458
15. Higuera F., Succi S., and Benzi R. Lattice gas-dynamics with enhanced collisions. Europhys. Lett. 9 (1989) 345-349
16. Hulburt H.M., and Katz S. Some problems in particle technology: a statistical mechanical formulation. Chem. Eng. Sci. 19 8 (1964) 555-574
17. Immanuel C.D., and Doyle F.J. Computationally efficient solution of population balance models incorporating nucleation, growth and coagulation: application to emulsion polymerization. Chem. Eng. Sci. 58 16 (2003) 3681-3698
18. Karlin I.V., Ansumali S., Frouzakis C.E., and Chikatamarla S.S. Elements of the lattice Boltzmann method. I: linear advection equation. Commun. Comput. Phys. 1 4 (2006) 616-655
19. Karlin I.V., Ferrante A., and Öttinger H.C. Perfect entropy functions of the lattice Boltzmann method. Europhys. Lett. 47 (1999) 182-188
20. Karlin I.V., and Gorban A. Maximum entropy principle for lattice kinetic equations. Phys. Rev. Lett. 81 (1998) 6-9
21. Kulikov V., Briesen H., and Marquardt W. A framework for the simulation of mass crystallization considering the effect of fluid dynamics. Chem. Eng. Process. 45 10 (2006) 886-899
22. Kullback S. Information Theory and Statistics (1997), Dover Publications, New York
23. Kumar J., Peglow M., Warnecke G., and Heinrich S. The cell average technique for solving multi-dimensional aggregation population balance equations. Comput. Chem. Eng. 32 8 (2008) 1810-1830
24. Kumar S., and Ramkrishna D. On the solution of population balance equations by discretization-I. A fixed pivot technique. Chem. Eng. Sci. 51 8 (1996) 1311-1332
25. Kumar S., and Ramkrishna D. On the solution of population balance equations by discretization-III. Nucleation, growth and aggregation of particles. Chem. Eng. Sci. 52 24 (1997) 4659-4679
26. LeVeque R.J. Numerical Methods for Conservation Laws (1992), Birkhäuser, Berlin, Germany
27. Lim Y., Le Lann J.-M., Meyer X.M., Joulia X., Lee G., and Yoon E.S. On the solution of population balance equations (pbe) with accurate front tracking methods in practical crystallization processes. Chem. Eng. Sci. 57 17 (2002) 3715-3732
28. Ma D.L., Tafti D.K., and Braatz R.D. High-resolution simulation of multidimensional crystal growth. Ind. Eng. Chem. Res. 41 25 (2002) 6217-6223
29. Mantle M., Sederman A., and Gladden L. Single-and two-phase flow in fixed-bed reactors: MRI flow visualisation and lattice-Boltzmann simulations. Chem. Eng. Sci. 56 2 (2001) 523-529
30. Matsoukas T., and Lin Y. Fokker-Planck equation for particle growth by monomer attachment. Phys. Rev. E 74 3 (2006) 031122
31. Mahoney A.W., and Ramkrishna D. Efficient solution of population balance equations with discontinuities by finite elements. Chem. Eng. Sci. 57 7 (2002) 1107-1119
32. Marchisio D.L., and Fox R.O. Solution of population balance equations using the direct quadrature method of moments. J. Aerosol Sci. 36 1 (2005) 43-73
33. McGraw R. Description of aerosol dynamics by the quadrature method of moments. Aerosol Sci. Technol. 27 2 (1997) 255-265
34. Motz S., Mitrović A., and Gilles E.D. Comparison of numerical methods for the simulation of dispersed phase systems. Chem. Eng. Sci. 57 20 (2002) 4329-4344
35. Qamar S., Ashfaq A., Angelov I., Elsner M.P., Warnecke G., and Seidel-Morgenstern A. Numerical solutions of population balance models in preferential crystallization. Chem. Eng. Sci. 63 5 (2008) 1342-1352
36. Qamar S., Elsner M.P., Angelov I.A., Warnecke G., and Seidel-Morgenstern A. A comparative study of high resolution schemes for solving population balances in crystallization. Comput. Chem. Eng. 30 6-7 (2006) 1119-1131
37. Qian Y.H., d'Humieres D., and Lallemand P. Lattice BGK models for Navier-Stokes equation. Europhys. Lett. 17 (1992) 479-484
38. Ramkrishna D. Population Balances: Theory and Applications to Particulate Systems in Engineering (2000), Acadamic Press, San Diego, CA
39. Randolph A., and Larson M.A. Theory of Particulate Processes. second ed. (1988), Academic Press, San Diego, CA
40. Rasin I., Succi S., and Miller W. A multi-relaxation lattice kinetic method for passive scalar diffusion. J. Comput. Phys. 206 2 (2005) 453-462
41. Succi S. Lattice Boltzmann Equation for Fluid Dynamics and Beyond (2001), Oxford University Press, New York
42. Sullivan S., Sani F., Johns M., and Gladden L. Simulation of packed bed reactors using lattice Boltzmann methods. Chem. Eng. Sci. 60 12 (2005) 3405-3418
43. Theodoropoulos C., Sankaranarayanan K., Sundaresan S., and Kevrekidis I. Coarse bifurcation studies of bubble flow lattice Boltzmann simulations. Chem. Eng. Sci. 59 12 (2004) 2357-2362
44. Wolf-Gladrow D. Lattice-gas Cellular Automata and Lattice Boltzmann Models (2000), Birkhäuser Verlag, Berlin, Germany
45. Woo X.Y., Tan R.B.H., Chow P.S., and Braatz R.D. Simulation of mixing effects in antisolvent crystallization using a coupled cfd-pdf-pbe approach. Cryst. Growth Des. 6 6 (2006) 1291-1303