Stochastic solution of population balance equations for reactor networks

Global sensitivity analysis of a model for silicon nanoparticle synthesis

“…The gas-phase expansion factor is given by symbol ψ and the gas-phase species concentrations are given by vector c. Each of the operators contains a set of processes which may create, destroy and transform particles. For example, operator Rðc; n; P q Þ would contain a surface growth process describing the transformation P q -P r by adding a gas-phase component from c. Further definition of these quantities is given in Celnik et al (2007) and Menz et al (2014). A stochastic numerical method is employed to solve the population balance model.…”

“…Coupling with the gas-phase is accomplished using the technique of operator splitting (Celnik et al, 2007;Shekar et al, 2012). Performance of the model and its numerical convergence behaviour have been addressed in Celnik et al (2007), Shekar et al (2012), and Menz et al (2013Menz et al ( , 2014.…”

Adiabatic reactor network synthesis using coupled genetic algorithm with quasi linear programming method

“…Among the important works done in recent years for modeling of RNs are: microwave plasma thermal decomposition of H2S (Sassi and Amira, 2012), application of RN in integrated modeling of an SOFC system (Vourliotakis et al, 2011(Vourliotakis et al, , 2012, and application of population balance modeling along with stochastic methods to solve RN problem (Menz et al, 2014).…”

A New Analytical Solution for Solving the Smoluchowski Equation Due to Nanoparticle Brownian Coagulation for Non-Self-Preserving System

“…Brownian coagulation is regarded as the most important inter-particle mechanism modifying the size distribution of particles in processes involving nanoparticle synthesis, polymerization, aerosol, emulsification and flocculation (Fox, 2008;Anand et al, 2012;Buesser and Pratsinis, 2012;Menz et al, 2014). Because of Brownian coagulation, the particle systems are always unstable, even in the absence of turbulence (Friedlander, 2000;Crowe et al, 2011;Sitarski, 2012;Wei, 2013).…”

“…Although the numerical solution is better than the analytical solution in precision (Wang et al, 2007;Yuan and Fox, 2011;Zhao and Zheng, 2009;Wei and Kruis, 2013;Menz et al, 2014), it consumes much more computational expenses and thus may not be suited for the quick determination of particle properties (Claudotte et al, 2010;Rigopoulos, 2010).…”