1932

Abstract

Population balance modeling is undergoing phenomenal growth in its applications, and this growth is accompanied by multifarious reviews. This review aims to fortify the model's fundamental base, as well as point to a variety of new applications, including modeling of crystal morphology, cell growth and differentiation, gene regulatory processes, and transfer of drug resistance. This is accomplished by presenting the many faces of population balance equations that arise in the foregoing applications.

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2014-06-07
2024-04-25
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Literature Cited

  1. Naimi LJ, Sokhansanj S, Womac AR, Bi X, Lim CJ. 1.  et al. 2011. Development of a population balance model to simulate fractionation of ground switchgrass. Trans. ASABE 54:219–27 [Google Scholar]
  2. Hosseini SA, Shah N. 2.  2011. Modelling enzymatic hydrolysis of cellulose part I: population balance modelling of hydrolysis by endoglucanase. Biomass Bioenergy 35:3841–48 [Google Scholar]
  3. Hosseini SA, Shah N. 3.  2011. Enzymatic hydrolysis of cellulose part II: population balance modelling of hydrolysis by exoglucanase and universal kinetic model. Biomass Bioenergy 35:3830–40 [Google Scholar]
  4. Liao CM, Feddes JJR. 4.  1991. Modeling and analysis of airborne dust removal from a ventilated airspace. Can. Agric. Eng. 33:355–61 [Google Scholar]
  5. Lipovka AA. 5.  1995. Solution of the set of population balance-equations for atomic and molecular quantum levels in some particular cases. Astron. Zh. 72:392–96 [Google Scholar]
  6. Rovenskaya NI. 6.  2008. The highly excited hydrogen bn-factors calculated. Astrophys. Space Sci. 314:25–33 [Google Scholar]
  7. Stamatakis M. 7.  2013. Cell population balance and hybrid modeling of population dynamics for a single gene with feedback. Comput. Chem. Eng. 53:25–34 [Google Scholar]
  8. Shu CC, Chatterjee A, Dunny G, Hu WS, Ramkrishna D. 8.  2011. Bistability versus bimodal distributions in gene regulatory processes from population balance. PLoS Comput. Biol. 7:e1002140 [Google Scholar]
  9. Shu CC, Chatterjee A, Hu WS, Ramkrishna D. 9.  2012. Modeling of gene regulatory processes by population-mediated signaling: new applications of population balances. Chem. Eng. Sci. 70:188–99 [Google Scholar]
  10. Henson MA. 10.  2003. Dynamic modeling of microbial cell populations. Curr. Opin. Biotechnol. 14:460–67 [Google Scholar]
  11. Kromenaker SJ, Srienc F. 11.  1994. Cell-cycle kinetics of the accumulation of heavy and light chain immunoglobulin proteins in a mouse hybridoma cell line. Cytotechnology 14:205–18 [Google Scholar]
  12. Mantzaris NV. 12.  2007. From single-cell genetic architecture to cell population dynamics: quantitatively decomposing the effects of different population heterogeneity sources for a genetic network with positive feedback architecture. Biophys. J. 92:4271–88 [Google Scholar]
  13. Rounseville KJ, Chau PC. 13.  2005. Three-dimensional cell cycle model with distributed transcription and translation. Med. Biol. Eng. Comput. 43:155–61 [Google Scholar]
  14. Borissova A, Goltz GE, Kavanagh JP, Wilkins TA. 14.  2010. Reverse engineering the kidney: modelling calcium oxalate monohydrate crystallization in the nephron. Med. Biol. Eng. Comput. 48:649–59 [Google Scholar]
  15. Sherer E, Hannemann RE, Rundell A, Ramkrishna D. 15.  2007. Estimation of likely cancer cure using first- and second-order product densities of population balance models. Ann. Biomed. Eng. 35:903–15 [Google Scholar]
  16. Fernandes RL, Carlquist M, Lundin L, Heins AL, Dutta A. 16.  et al. 2013. Cell mass and cell cycle dynamics of an asynchronous budding yeast population: experimental observations, flow cytometry data analysis, and multi-scale modeling. Biotechnol. Bioeng. 110:812–26 [Google Scholar]
  17. Bannari R, Bannari A, Vermette P, Proulx P. 17.  2012. A model for cellulase production from Trichoderma reesei in an airlift reactor. Biotechnol. Bioeng. 109:2025–38 [Google Scholar]
  18. Rathore AS, Sharma C, Persad A. 18.  2012. Use of computational fluid dynamics as a tool for establishing process design space for mixing in a bioreactor. Biotechnol. Prog. 28:382–91 [Google Scholar]
  19. Fadda S, Cincotti A, Cao G. 19.  2012. A novel population balance model to investigate the kinetics of in vitro cell proliferation: part I. Model development. Biotechnol. Bioeng. 109:772–81 [Google Scholar]
  20. Zhang H, Zhang K, Fan SD. 20.  2009. CFD simulation coupled with population balance equations for aerated stirred bioreactors. Eng. Life Sci. 9:421–30 [Google Scholar]
  21. Sherer E, Tocce E, Hannemann RE, Rundell AE, Ramkrishna D. 21.  2008. Identification of age-structured models: cell cycle phase transitions. Biotechnol. Bioeng. 99:960–74 [Google Scholar]
  22. Cipollina C, Vai M, Porro D, Hatzis C. 22.  2007. Towards understanding of the complex structure of growing yeast populations. J. Biotechnol. 128:393–402 [Google Scholar]
  23. Hatzis C, Porro D. 23.  2006. Morphologically-structured models of growing budding yeast populations. J. Biotechnol. 124:420–38 [Google Scholar]
  24. Martin PJ, Chin NL, Campbell GM. 24.  2004. Aeration during bread dough mixing II. A population balance model of aeration. Food Bioprod. Process. 82:268–81 [Google Scholar]
  25. Han BB, Linden JC, Gujarathi NP, Wickramasinghe SR. 25.  2004. Population balance approach to modeling hairy root growth. Biotechnol. Prog. 20:872–79 [Google Scholar]
  26. Mhaskar P, Hjortso MA, Henson MA. 26.  2002. Cell population modeling and parameter estimation for continuous cultures of Saccharomyces cerevisiae. Biotechnol. Prog. 18:1010–26 [Google Scholar]
  27. Hunter JB, Asenjo JA. 27.  1990. A population balance model of enzymatic lysis of microbial-cells. Biotechnol. Bioeng. 35:31–42 [Google Scholar]
  28. Fu CL, Tong CF, Dong C, Long M. 28.  2011. Modeling of cell aggregation dynamics governed by receptor-ligand binding under shear flow. Cell. Mol. Bioeng. 4:427–41 [Google Scholar]
  29. Fadda S, Briesen H, Cincotti A. 29.  2011. The effect of EIF dynamics on the cryopreservation process of a size distributed cell population. Cryobiology 62:218–31 [Google Scholar]
  30. Luni C, Doyle FJ, Elvassore N. 30.  2011. Cell population modelling describes intrinsic heterogeneity: a case study for hematopoietic stem cells. IET Syst. Biol. 5:164–73 [Google Scholar]
  31. Ma YP, Wang JK, Liang SL, Dong C, Du Q. 31.  2010. Application of population dynamics to study heterotypic cell aggregations in the near-wall region of a shear flow. Cell. Mol. Bioeng. 3:3–19 [Google Scholar]
  32. Mancuso L, Liuzzo MI, Fadda S, Pisu M, Cincotti A. 32.  et al. 2009. Experimental analysis and modelling of in vitro proliferation of mesenchymal stem cells. Cell Prolif. 42:602–16 [Google Scholar]
  33. Pisu M, Concas A, Fadda S, Cincotti A, Cao G. 33.  2008. A simulation model for stem cells differentiation into specialized cells of non-connective tissues. Comput. Biol. Chem. 32:338–44 [Google Scholar]
  34. Sidoli FR, Mantalaris A, Asprey SP. 34.  2004. Modelling of mammalian cells and cell culture processes. Cytotechnology 44:27–46 [Google Scholar]
  35. Nielsen LK, Bender JG, Miller WM, Papoutsakis ET. 35.  1998. Population balance model of in vivo neutrophil formation following bone marrow rescue therapy. Cytotechnology 28:157–62 [Google Scholar]
  36. Huang PY, Hellums JD. 36.  1993. Aggregation and disaggregation kinetics of human blood platelets: part 1. Development and validation of a population balance method. Biophys. J. 65:334–43 [Google Scholar]
  37. Nason JA, Lawler DF. 37.  2010. Modeling particle-size distribution dynamics during precipitative softening. J. Environ. Eng. 136:12–21 [Google Scholar]
  38. Bandara UC, Yapa PD. 38.  2011. Bubble sizes, breakup, and coalescence in deepwater gas/oil plumes. J. Hydraul. Eng. 137:729–38 [Google Scholar]
  39. Matsui Y, Fukushi K, Tambo N. 39.  1998. Modeling, simulation and operational parameters of dissolved air flotation. Aqua 47:9–20 [Google Scholar]
  40. Hanhoun M, Montastruc L, Azzaro-Pantel C, Biscans B, Frèche M, Pibouleau L. 40.  2013. Simultaneous determination of nucleation and crystal growth kinetics of struvite using a thermodynamic modeling approach. Chem. Eng. J. 215:903–12 [Google Scholar]
  41. Nopens I, Nere N, Vanrolleghem PA, Ramkrishna D. 41.  2007. Solving the inverse problem for aggregation in activated sludge flocculation using a population balance framework. Water Sci. Technol. 56:95–103 [Google Scholar]
  42. Mohanarangam K, Cheung SCP, Tu JY, Chen L. 42.  2009. Numerical simulation of micro-bubble drag reduction using population balance model. Ocean Eng. 36:863–72 [Google Scholar]
  43. Bryson AW, Hofman DL. 43.  1989. A population balance approach to the study of bubble behavior at gas-evolving electrodes. J. Appl. Electrochem. 19:116–19 [Google Scholar]
  44. White CM, Zeininger G, Ege P, Ydstie BE. 44.  2007. Multi-scale modeling and constrained sensitivity analysis of particulate CVD systems. Chem. Vapor Depos. 13:507–12 [Google Scholar]
  45. Zhao HB, Zheng CG. 45.  2008. A stochastic simulation for the collection process of fly ashes in single-stage electrostatic precipitators. Fuel 87:2082–89 [Google Scholar]
  46. Qi NN, Zhang K, Xu G, Yang YP, Zhang H. 46.  2013. CFD-PBE simulation of gas-phase hydrodynamics in a gas-liquid-solid combined loop reactor. Pet. Sci. 10:251–61 [Google Scholar]
  47. Balaji S, Du J, White CM, Ydstie BE. 47.  2010. Multi-scale modeling and control of fluidized beds for the production of solar grade silicon. Powder Technol. 199:23–31 [Google Scholar]
  48. Pedel J, Thornock JN, Smith PJ. 48.  2013. Ignition of co-axial turbulent diffusion oxy-coal jet flames: experiments and simulations collaboration. Combust. Flame 160:1112–28 [Google Scholar]
  49. Fan W, Hao X, Xu YY, Li YW. 49.  2011. Simulation of catalyst on-line replacement for Fischer-Tropsch synthesis in slurry bubble column reactor. Chem. Technol. Fuels Oils 47:116–33 [Google Scholar]
  50. Khoshandam A, Alamdari A. 50.  2010. Kinetics of asphaltene precipitation in a heptane-toluene mixture. Energy Fuels 24:1917–24 [Google Scholar]
  51. Barta HJ, Drumm C, Attarakih MM. 51.  2008. Process intensification with reactive extraction columns. Chem. Eng. Process. 47:745–54 [Google Scholar]
  52. Klose W, Schinkel A. 52.  2002. Measurement and modelling of the development of pore size distribution of wood during pyrolysis. Fuel Process. Technol. 77:459–66 [Google Scholar]
  53. Junk KW, Brown RC. 53.  1993. A model of coal combustion dynamics in a fluidized-bed combustor. Combust. Flame 95:219–28 [Google Scholar]
  54. Zitha PLJ, Du DX. 54.  2010. A new stochastic bubble population model for foam flow in porous media. Transp. Porous Media 83:603–21 [Google Scholar]
  55. Sow M, Crase E, Rajot JL, Sankaran RM, Lacks DJ. 55.  2011. Electrification of particles in dust storms: field measurements during the monsoon period in Niger. Atmos. Res. 102:343–50 [Google Scholar]
  56. Furukawa Y, Watkins JL. 56.  2012. Effect of organic matter on the flocculation of colloidal montmorillonite: a modeling approach. J. Coast. Res. 28:726–37 [Google Scholar]
  57. Vokou D, Chalkos D, Karamanlidou G, Yiangou M. 57.  2002. Activation of soil respiration and shift of the microbial population balance in soil as a response to Lavandula stoechas essential oil. J. Chem. Ecol. 28:755–68 [Google Scholar]
  58. Sherer E, Hannemann RE, Rundell A, Ramkrishna D. 58.  2006. Analysis of resonance chemotherapy in leukemia treatment via multi-staged population balance models. J. Theor. Biol. 240:648–61 [Google Scholar]
  59. Wen JZ, Celnik M, Richter H, Treska M, Vander Sande JB, Kraft M. 59.  2008. Modelling study of single walled carbon nanotube formation in a premixed flame. J. Mater. Chem. 18:1582–91 [Google Scholar]
  60. Kwok LS, Coroneo MT. 60.  1994. A model for pterygium formation. Cornea 13:219–24 [Google Scholar]
  61. Sharma A, Coles WH. 61.  1989. Kinetics of corneal epithelial maintenance and graft loss—a population balance model. Investig. Ophthalmol. Vis. Sci. 30:1962–71 [Google Scholar]
  62. Flood AE, Wantha L. 62.  2013. Population balance modeling of the solution mediated transformation of polymorphs: limitations and future trends. J. Cryst. Growth 373:7–12 [Google Scholar]
  63. Singh MR, Ramkrishna D. 63.  2013. A comprehensive approach to predicting crystal morphology distributions with population balances. Cryst. Growth Des. 13:1397–411 [Google Scholar]
  64. Chakraborty J, Singh MR, Ramkrishna D, Borchert C, Sundmacher K. 64.  2010. Modeling of crystal morphology distributions. Towards crystals with preferred asymmetry. Chem. Eng. Sci. 65:5676–86 [Google Scholar]
  65. Mahoney AW, Doyle FJ, Ramkrishna D. 65.  2002. Inverse problems in population balances: growth and nucleation from dynamic data. AIChE J. 48:981–90 [Google Scholar]
  66. Iggland M, Mazzotti M. 66.  2012. Population balance modeling with size-dependent solubility: Ostwald ripening. Cryst. Growth Des. 12:1489–500 [Google Scholar]
  67. Zhang HT, Quon J, Alvarez AJ, Evans J, Myerson AS, Trout B. 67.  2012. Development of continuous anti-solvent/cooling crystallization process using cascaded mixed suspension, mixed product removal crystallizers. Org. Process Res. Dev. 16:915–24 [Google Scholar]
  68. Mangin D, Garcia E, Gerard S, Hoff C, Klein JP, Veesler S. 68.  2006. Modeling of the dissolution of a pharmaceutical compound. J. Cryst. Growth 286:121–25 [Google Scholar]
  69. Chakraborty J, Ramkrishna D. 69.  2011. Population balance modeling of environment dependent breakage: role of granular viscosity, density and compaction. Model formulation and similarity analysis. Ind. Eng. Chem. Res. 50:13116–28 [Google Scholar]
  70. Ramkrishna D. 70.  2004. On aggregating populations. Ind. Eng. Chem. Res. 43:441–48 [Google Scholar]
  71. Kayrak-Talay D, Dale S, Wassgren C, Litster J. 71.  2013. Quality by design for wet granulation in pharmaceutical processing: assessing models for a priori design and scaling. Powder Technol. 240:7–18 [Google Scholar]
  72. Boukouvala F, Niotis V, Ramachandran R, Muzzio FJ, Ierapetritou MG. 72.  2012. An integrated approach for dynamic flowsheet modeling and sensitivity analysis of a continuous tablet manufacturing process. Comput. Chem. Eng. 42:30–47 [Google Scholar]
  73. Gradon L, Podgórski A. 73.  1996. Deposition of inhaled particles: discussion of present modeling techniques. J. Aerosol Med. 9:343–55 [Google Scholar]
  74. Yamasue E, Numata T, Okumura H, Ishihara KN. 74.  2009. Impact evaluation of rare metals in waste mobile phone and personal computer. J. Jpn. Inst. Met. 73:198–204 [Google Scholar]
  75. Lee J, Sung NW, Huh KY. 75.  2011. Prediction of soot particle size distribution for turbulent reacting flow in a diesel engine. Int. J. Eng. Res. 12:181–89 [Google Scholar]
  76. Mosbach S, Celnik MS, Raj A, Kraft M, Zhang HR. 76.  et al. 2009. Towards a detailed soot model for internal combustion engines. Combust. Flame 156:1156–65 [Google Scholar]
  77. Kakudate K, Kajikawa Y, Adachi Y, Suzuki T. 77.  2002. Calculation model of CO2 emissions for Japanese passenger cars. Int. J. Life Cycle Assess. 7:85–93 [Google Scholar]
  78. Hulburt H, Katz S. 78.  1964. Some problems in particle technology: a statistical mechanical formulation. Chem. Eng. Sci. 19:555–74 [Google Scholar]
  79. Randolph AD. 79.  1964. A population balance for countable entities. Can. J. Chem. Eng. 42:280–81 [Google Scholar]
  80. Fredrickson A, Ramkrishna D, Tsuchiya H. 80.  1967. Statistics and dynamics of procaryotic cell populations. Math. Biosci. 1:327–74 [Google Scholar]
  81. Ramkrishna D. 81.  2000. Population Balances: Theory and Applications to Particulate Systems in Engineering New York: Academic
  82. Jakobsen HA. 82.  2008. Chemical Reactor Modeling: Multiphase Reactive Flows Berlin: Springer-Verlag
  83. Ramkrishna D. 83.  1985. The status of population balances. Rev. Chem. Eng. 3:49–95 [Google Scholar]
  84. Ramkrishna D, Mahoney AW. 84.  2002. Population balance modeling. Promise for the future. Chem. Eng. Sci. 57:595–606 [Google Scholar]
  85. Ramkrishna D. 85.  1979. Statistical models of cell populations. Adv. Biochem. Eng. 11:1–47 [Google Scholar]
  86. Sporleder F, Borka Z, Solsvik J, Jakobsen HA. 86.  2012. On the population balance equation. Rev. Chem. Eng. 28:149–69 [Google Scholar]
  87. Randolph A. 87.  1971. Theory of Particulate Processes: Analysis and Techniques of Continuous Crystallization New York: Academic
  88. Hjortso M. 88.  2005. Population Balances in Biomedical Engineering New York: McGraw Hill Prof.
  89. Christofides PD. 89.  2002. Model-Based Control of Particulate Processes Dordrecht, Neth.: Kluwer Acad. Publ.
  90. Solsvik J, Jakobsen HA. 90.  2013. On the solution of the population balance equation for bubbly flows using the high-order least squares method: implementation issues. Rev. Chem. Eng. 29:63–98 [Google Scholar]
  91. Sajjadi B, Raman AAA, Ibrahim S, Shah R. 91.  2012. Review on gas-liquid mixing analysis in multiscale stirred vessel using CFD. Rev. Chem. Eng. 28:171–89 [Google Scholar]
  92. Mortier S, De Beer T, Gernaey KV, Remon JP, Vervaet C, Nopens I. 92.  2011. Mechanistic modelling of fluidized bed drying processes of wet porous granules: a review. Eur. J. Pharm. Biopharm. 79:205–25 [Google Scholar]
  93. Bajcinca N, Qamar S, Flockerzi D, Sundmacher K. 93.  2011. Integration and dynamic inversion of population balance equations with size-dependent growth rate. Chem. Eng. Sci. 66:3711–20 [Google Scholar]
  94. Kiparissides C, Krallis A, Meimaroglou D, Pladis P, Baltsas A. 94.  2010. From molecular to plant-scale modeling of polymerization processes: a digital high-pressure low-density polyethylene production paradigm. Chem. Eng. Technol. 33:1754–66 [Google Scholar]
  95. Sadiku O, Sadiku ER. 95.  2010. Numerical simulation for nanoparticle growth in flame reactor and control of nanoparticles. J. Comput. Theor. Nanosci. 7:2262–70 [Google Scholar]
  96. Rigopoulos S. 96.  2010. Population balance modelling of polydispersed particles in reactive flows. Prog. Energy Combust. Sci. 36:412–43 [Google Scholar]
  97. Liao YX, Lucas D. 97.  2010. A literature review on mechanisms and models for the coalescence process of fluid particles. Chem. Eng. Sci. 65:2851–64 [Google Scholar]
  98. Yu MZ, Lin JZ. 98.  2010. Nanoparticle-laden flows via moment method: a review. Int. J. Multiph. Flow 36:144–51 [Google Scholar]
  99. Liao YX, Lucas D. 99.  2009. A literature review of theoretical models for drop and bubble breakup in turbulent dispersions. Chem. Eng. Sci. 64:3389–406 [Google Scholar]
  100. Tindall MJ, Maini PK, Porter SL, Armitage JP. 100.  2008. Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations. Bull. Math. Biol. 70:1570–607 [Google Scholar]
  101. Ribeiro CP, Lage PLC. 101.  2008. Modelling of hydrate formation kinetics: state-of-the-art and future directions. Chem. Eng. Sci. 63:2007–34 [Google Scholar]
  102. Dukhin AS, Dukhin SS, Goetz PJ. 102.  2007. Gravity as a factor of aggregative stability and coagulation. Adv. Colloid Interface Sci. 134–35:35–71 [Google Scholar]
  103. Roth P. 103.  2007. Particle synthesis in flames. Proc. Combust. Inst. 31:1773–88 [Google Scholar]
  104. Maximova N, Dahl O. 104.  2006. Environmental implications of aggregation phenomena: current understanding. Curr. Opin. Colloid Interface Sci. 11:246–66 [Google Scholar]
  105. Taboada-Serrano P, Chin CJ, Yiacoumi S, Tsouris C. 105.  2005. Modeling aggregation of colloidal particles. Curr. Opin. Colloid Interface Sci. 10:123–32 [Google Scholar]
  106. Vale HM, McKenna TF. 106.  2005. Modeling particle size distribution in emulsion polymerization reactors. Prog. Polym. Sci. 30:1019–48 [Google Scholar]
  107. Cameron IT, Wang FY, Immanuel CD, Stepanek F. 107.  2005. Process systems modelling and applications in granulation: a review. Chem. Eng. Sci. 60:3723–50 [Google Scholar]
  108. Somasundaran P, Runkana V. 108.  2003. Modeling flocculation of colloidal mineral suspensions using population balances. Int. J. Miner. Process. 72:33–55 [Google Scholar]
  109. Braatz RD. 109.  2002. Advanced control of crystallization processes. Annu. Rev. Control 26:87–99 [Google Scholar]
  110. Mohanty S. 110.  2000. Modeling of liquid-liquid extraction column: a review. Rev. Chem. Eng. 16:199–248 [Google Scholar]
  111. Kovscek AR, Radke CJ. 111.  1994. Fundamentals of foam transport in porous media. Foams Fundam. Appl. Pet. Ind. 242:115–63 [Google Scholar]
  112. Rawlings JB, Miller SM, Witkowski WR. 112.  1993. Model identification and control of solution crystallization processes: a review. Ind. Eng. Chem. Res. 32:1275–96 [Google Scholar]
  113. Ramkrishna D, Borwanker J. 113.  1973. A puristic analysis of population balance—I. Chem. Eng. Sci. 28:1423–35 [Google Scholar]
  114. Gardiner CW. 114.  1985. Handbook of Stochastic Methods Berlin: Springer
  115. van Kampen NG. 115.  1992. Stochastic Processes in Physics and Chemistry Amsterdam: Elsevier
  116. Sherer E, Ramkrishna D. 116.  2008. Stochastic analysis of multistate systems. Ind. Eng. Chem. Res. 47:3430–37 [Google Scholar]
  117. Sherer E, Hannemann RE, Rundell AE, Ramkrishna D. 117.  2009. Application of stochastic equations of population balances to sterilization processes. Chem. Eng. Sci. 64:764–74 [Google Scholar]
  118. Froment GF, Bischoff KB, De Wilde J. 118.  1990. Chemical Reactor Analysis and Design New York: Wiley
  119. Gunawan R, Ma DL, Fujiwara M, Braatz RD. 119.  2002. Identification of kinetic parameters in multidimensional crystallization processes. Int. J. Mod. Phys. B 16:367–74 [Google Scholar]
  120. Bandyopadhyaya R, Kumar R, Gandhi K, Ramkrishna D. 120.  1997. Modeling of precipitation in reverse micellar systems. Langmuir 13:3610–20 [Google Scholar]
  121. Bandyopadhyaya R, Kumar R, Gandhi K. 121.  2000. Simulation of precipitation reactions in reverse micelles. Langmuir 16:7139–49 [Google Scholar]
  122. Bandyopadhyaya R, Kumar R, Gandhi K. 122.  2001. Modelling of CaCO3 nanoparticle formation during overbasing of lubricating oil additives. Langmuir 17:1015–29 [Google Scholar]
  123. Levenspiel O. 123.  1972. Chemical Reaction Engineering New York: Wiley
  124. White E, Wright P. 124.  1971. Magnitude of size dispersion effects in crystallization. AIChE Symp. Ser. 67:81–87 [Google Scholar]
  125. Ulrich J. 125.  1989. Growth rate dispersion—a review. Cryst. Res. Technol. 24:249–57 [Google Scholar]
  126. Larson M, White E, Ramanarayanan K, Berglund K. 126.  1985. Growth rate dispersion in MSMPR crystallizers. AIChE J. 31:90–94 [Google Scholar]
  127. Langevin P. 127.  1908. On the theory of Brownian motion. C. R. Acad. Sci. 146:530–33 [Google Scholar]
  128. Rao N, Borwanker J, Ramkrishna D. 128.  1974. Numerical solution of Ito integral equations. SIAM J. Control 12:124–39 [Google Scholar]
  129. Talay D. 129.  1995. Simulation of stochastic differential systems. Probabilistic Methods in Applied Physics P Krée, W Wedig 54–96 Berlin: Springer [Google Scholar]
  130. Gillespie DT. 130.  1977. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81:2340–61 [Google Scholar]
  131. Shah B, Ramkrishna D, Borwanker J. 131.  1977. Simulation of particulate systems using the concept of the interval of quiescence. AIChE J. 23:897–904 [Google Scholar]
  132. Cao Y, Gillespie DT, Petzold LR. 132.  2006. Efficient step size selection for the tau-leaping simulation method. J. Chem. Phys. 124:044109 [Google Scholar]
  133. Bilgili E, Scarlett B. 133.  2005. Population balance modeling of non-linear effects in milling processes. Powder Technol. 153:59–71 [Google Scholar]
  134. von Smoluchowski M. 134.  1917. Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen. Z. Phys. Chem. 92:129–68 [Google Scholar]
  135. Chandrasekhar S. 135.  1943. Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15:1 [Google Scholar]
  136. Spielman LA. 136.  1970. Viscous interactions in Brownian coagulation. J. Colloid Interface Sci. 33:562–71 [Google Scholar]
  137. Coulaloglou C, Tavlarides L. 137.  1977. Description of interaction processes in agitated liquid-liquid dispersions. Chem. Eng. Sci. 32:1289–97 [Google Scholar]
  138. Muralidhar R, Ramkrishna D. 138.  1986. Analysis of droplet coalescence in turbulent liquid-liquid dispersions. Ind. Eng. Chem. Fundam. 25:554–60 [Google Scholar]
  139. Tobin T, Muralidhar R, Wright H, Ramkrishna D. 139.  1990. Determination of coalescence frequencies in liquid-liquid dispersions: effect of drop size dependence. Chem. Eng. Sci. 45:3491–504 [Google Scholar]
  140. Tobin T, Ramkrishna D. 140.  1992. Coalescence of charged droplets in agitated liquid-liquid dispersions. AIChE J. 38:1199–205 [Google Scholar]
  141. Tobin T, Ramkrishna D. 141.  1999. Modeling the effect of drop charge on coalescence in turbulent liquid-liquid dispersions. Can. J. Chem. Eng. 77:1090–104 [Google Scholar]
  142. Simons S, Williams MMR, Cassell JS. 142.  1986. A kernel for combined Brownian and gravitational coagulation. J. Aerosol Sci. 17:789–93 [Google Scholar]
  143. Sathyagal A, Ramkrishna D, Narsimhan G. 143.  1995. Solution of inverse problems in population balances—II. Particle break-up. Comput. Chem. Eng. 19:437–51 [Google Scholar]
  144. Wright H, Ramkrishna D. 144.  1992. Solutions of inverse problems in population balances—I. Aggregation kinetics. Comput. Chem. Eng. 16:1019–38 [Google Scholar]
  145. Wright H, Muralidhar R, Ramkrishna D. 145.  1992. Aggregation frequencies of fractal aggregates. Phys. Rev. A 46:5072 [Google Scholar]
  146. Ramkrishna D. 146.  1994. Toward a self-similar theory of microbial populations. Biotechnol. Bioeng. 43:138–48 [Google Scholar]
  147. Williams M, Meloy T, Tarshan M. 147.  1994. Assessment of numerical solution approaches to the inverse problem for grinding systems: dynamic population balance model problems. Powder Technol. 78:257–61 [Google Scholar]
  148. Raikar NB, Bhatia SR, Malone MF, Henson MA. 148.  2006. Self-similar inverse population balance modeling for turbulently prepared batch emulsions: sensitivity to measurement errors. Chem. Eng. Sci. 61:7421–35 [Google Scholar]
  149. Braumann A, Man PL, Kraft M. 149.  2011. The inverse problem in granulation modeling—two different statistical approaches. AIChE J. 57:3105–21 [Google Scholar]
  150. Kostoglou M, Karabelas A. 150.  2005. On the self-similar solution of fragmentation equation: numerical evaluation with implications for the inverse problem. J. Colloid Interface Sci. 284:571–81 [Google Scholar]
  151. Marchisio DL, Fox RO. 151.  2005. Solution of population balance equations using the direct quadrature method of moments. J. Aerosol Sci. 36:43–73 [Google Scholar]
  152. Bhole M, Joshi J, Ramkrishna D. 152.  2008. CFD simulation of bubble columns incorporating population balance modeling. Chem. Eng. Sci. 63:2267–82 [Google Scholar]
  153. Kumar S, Ramkrishna D. 153.  1996. On the solution of population balance equations by discretization—I. A fixed pivot technique. Chem. Eng. Sci. 51:1311–32 [Google Scholar]
  154. Chen P, Sanyal J, Dudukovic M. 154.  2004. CFD modeling of bubble columns flows: implementation of population balance. Chem. Eng. Sci. 59:5201–7 [Google Scholar]
  155. Vikhansky A, Kraft M. 155.  2004. Modelling of a RDC using a combined CFD-population balance approach. Chem. Eng. Sci. 59:2597–606 [Google Scholar]
  156. Cardew P. 156.  1985. The growth shape of crystals. J. Cryst. Growth 73:385–91 [Google Scholar]
  157. Zhang Y, Doherty MF. 157.  2004. Simultaneous prediction of crystal shape and size for solution crystallization. AIChE J. 50:2101–12 [Google Scholar]
  158. Borchert C, Nere N, Ramkrishna D, Voigt A, Sundmacher K. 158.  2009. On the prediction of crystal shape distributions in a steady-state continuous crystallizer. Chem. Eng. Sci. 64:686–96 [Google Scholar]
  159. Briesen H. 159.  2006. Simulation of crystal size and shape by means of a reduced two-dimensional population balance model. Chem. Eng. Sci. 61:104–12 [Google Scholar]
  160. Ma CY, Wang XZ, Roberts KJ. 160.  2008. Morphological population balance for modeling crystal growth in face directions. AIChE J. 54:209–22 [Google Scholar]
  161. Wang XZ, Ma CY. 161.  2009. Morphological population balance model in principal component space. AIChE J. 55:2370–81 [Google Scholar]
  162. Wan J, Wang XZ, Ma CY. 162.  2009. Particle shape manipulation and optimization in cooling crystallization involving multiple crystal morphological forms. AIChE J. 55:2049–61 [Google Scholar]
  163. Wilson A, Trumpp A. 163.  2006. Bone-marrow haematopoietic-stem-cell niches. Nat. Rev. Immunol. 6:93–106 [Google Scholar]
  164. Adimy M, Crauste F, Ruan S. 164.  2005. A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. SIAM J. Appl. Math. 65:1328–52 [Google Scholar]
  165. Foley C, Mackey MC. 165.  2009. Dynamic hematological disease: a review. J. Math. Biol. 58:285–322 [Google Scholar]
  166. Shu C-C, Ramkrishna D, Chatterjee A, Hu W-S. 166.  2013. Role of intracellular stochasticity in biofilm growth. Insights from population balance modeling. PLoS ONE. In press. doi: 10.1371/journal.pone.0079196.
  167. Witte AS, Cornblath DR, Schatz NJ, Lisak RP. 167.  1986. Monitoring azathioprine therapy in myasthenia gravis. Neurology 36:1533–34 [Google Scholar]
  168. Sherer EA. 168.  2007. Age-structured cell models in the treatment of leukemia: identification, inversion, and stochastic methods for the evaluation and design of chemotherapy protocols PhD Thesis, Purdue Univ., West Lafayette, Indiana 274
  169. Nagy ZK, Fevotte G, Kramer H, Simon LL. 169.  2013. Recent advances in the monitoring, modelling and control of crystallization systems. Chem. Eng. Res. Des. 91:1903–22 [Google Scholar]
  170. Singh MR, Chakraborty J, Nere N, Tung H-H, Bordawekar S, Ramkrishna D. 170.  2012. Image-analysis-based method for 3D crystal morphology measurement and polymorph identification using confocal microscopy. Cryst. Growth Des. 12:3735–48 [Google Scholar]
  171. Kodera Y, McCoy BJ. 171.  2003. Distribution kinetics of plastics decomposition. J. Jpn. Pet. Inst. 46:155–65 [Google Scholar]
  172. Tavare NS. 172.  1991. Batch crystallizers. Rev. Chem. Eng. 7:211–355 [Google Scholar]
  173. Ma CY, Wang XZ. 173.  2012. Model identification of crystal facet growth kinetics in morphological population balance modeling of l-glutamic acid crystallization and experimental validation. Chem. Eng. Sci. 70:22–30 [Google Scholar]
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