Population balance models for

Gertlauer, A., Mitrovic, A., Motz, S. and Gilles, E.-D., 2001. A population balance model for crystallization processes using two independent particles properties. Chemical Engineering Science, 56(7), 2553-2565. 

Leblanc and Fogler developed a population balance model for the dissolution of polydisperse solids that included both reaction controlled and diffusion-controlled dissolution. This model allows for the handling of continuous particle size distributions. The following population balance was used to develop this model. 

Staggs, J. E. J. Population balance models for the thermal degradation of PMMA. Polymer 2007 48 3868. 

Haseltine, E. L. Systems Analysis of Stochastic and Population Balance Models for Chemical Reactions . Department of Chemical Engineering, Madison, University of Wisconsin (2005). Haseltine, E. L., and Rawlings, J. B. J. Chem. Phys. 117(15), 6959 (2002). 

Wang T, Wang J, Jin Y (2005) Population Balance Model for Gas-Liquid Flows Influence of Bubble Coalescence and Breakup Models. Ind Eng Chem Res 44 7540-7549... 

Therefore, the approximate integral method is not widely used solving the population balance model for bubbly flows as the kernels involved for these systems are rather complex, thus it is very difficult to eliminate the higher order moments developing closures with sufficient accuracy. 

Aamir, E., Nagy, Z. K., Rielly, C. D., Kleinert, T. Judat, B. 2009 Combined quadrature method of moments and method of characteristics approach for efficient solution of population balance models for dynamic modeling and crystal size distribution control of crystallization processes. Industrial Engineering Chemistry Research 48, 8575-8584. 

Braumann, a., Kraft, M. Wagner, W. 2010 Numerical study of a stochastic particle algorithm solving a multidimensional population balance model for high shear granulation. Journal of Computational Physics 229, 7672-7691. 

Buffo, A., Marchisio, D. L. Vanni, M. 2012 Multidimensional population balance model for the simulation of turbulent gas-liquid systems in stirred tank reactors. Chemical Engineering Science 74, 31 14. 

Sanyal, j., MARCfflsio, D. L., Fox, R. O. Dhanasekharan, K. 2005 On the comparison between population balance models for CFD simulation of bubble columns. Industrial Engineering Chemistry Research 44, 5063-5072. 

Example I2j6-I Population Balance Model for Micromixing... 

M. Mezhericher, M. Naumann, M. Peglow, A. Levy, E. Tsotsas, 1. Borde, Continuous species transport and population balance models for first drying stage of nanosuspension droplets. Chemical Engineering Journal, 210 (2012) 120-135. 

A. Buck, M. Peglow, M. Naumann, E. Tsotsas, Population balance model for drying of droplets containing aggregating nanoparticles, AIChE Journal, 58 (2012) 3318-3328. 

B. J. McCoy, A New Population Balance Model for Crystal Size Distributions, Journal of Colloid and Interface Science, 240, 139 (2001). 

Sood, A. and Awasthi, S.K. (2004) Population balance model for miniemulsion polymerization, 2 - model solution and validation. Macromol. Theory Simul., 13, 615. 

Kotoulas, C., Kiparissides, C., 2006. A generalized population balance model for the prediction of particle size distribution in suspension polymerization reactors. Chem. Eng. Sci. 61, 332-346. 

The heart of the population balance model for breakage processes lies in the breakage functions described in Section 3.2.1. The breakage functions must be obtained either directly from experiments or by modeling considerations related to the processes causing the breakage. This is the subject of the next section. 

Shah, B. H. and D. Ramkrishna, A Population Balance Model for Mass Transfer in Lean Liquid-Liquid Dispersions, Chem. Eng. Sci. 28, 389-399 (1973). 

The foregoing condition may be used to determine t) in (7.4.5). Equations (7.4.5) and (7.4.6) then consist of the population balance model for aggregating systems with a local volume of mixing as defined in this section. It is our objective next to compare the prediction of this population balance model with Monte Carlo simulations using the interval of quiescence in Section 4.6 as well as with predictions made from the product density equations using various closure approximations. The Monte Carlo approach provides one... 

One-dimensional population balance models for both batch and continuous systems are described in this section as special cases of the generalized population balance model stated in General Population Balance Equations. ... 

Runkana V, Somasundaran P, Kapur P (2006) A population balance model for flocculation of colloidal suspensions by polymer bridging. Chem Eng Sci 61 182-191... 

Example 12.6. LA Population Balance Model for Micro-Mixing in a Perfectly Macro-Mixed Reactor PDF Moment Method... 

POPULATION BALANCE MODEL FOR MICRO-MIXING IN A PERFECTLY MACRO-MIXED REACTOR PDF MOMENT METHOD... 

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