A stochastic approach for the numerical simulation of the general dynamics equation for aerosols

A new numerical approach for the simulation of the growth of inorganic nanoparticles

“…These methods have since been applied to chemical engineering by Goodson and Kraft who studied the convergence properties of the algorithm [10] and by Grosschmidt et al [4] who applied the algorithm to the production of silica. A similar extension to the model, subsequently solved by a stochastic MFA has been performed by Debry et al in [11]. However, there are a number of differences between their algorithm and the one used in [4].…”

“…However, there are a number of differences between their algorithm and the one used in [4]. In [11] they make use of a deterministic time step equal to the maximum value of a majorized coagulation kernel, but do not discuss the introduction of fictitious jumps. They also use operator splitting methods to simulate processes other than coagulation and make use of a bin method for particle storage and selection.…”

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

“…The theory for Brownian coagulation was originally devised for liquids by Smoluchowski (1917) and was subsequently applied in other chemical process and environmental fields. The governing equation for Brownian coagulation has been established for nearly a century in its integral-differential form (Müller, 1928), which is usually called the Smoluchowski equation (SE), but the solution for it remains a challenging issue due to its nonlinear integral-differential property (Debry et al, 2003;Wang et al, 2007;Wei and Kruis, 2013). Currently, the process of Brownian coagulation receives much more attention in the newly emerging fields of aerosol science, cloud science, supercritical fluid processes and nanoparticle synthesis engineering (Garrick, 2011;Yu and Lin, 2010a;Buesser and Pratsinis, 2012), where the quick and reliable predication of the size distribution of particles has become a critical issue (Seipenbusch et al, 2008).…”

The moments method for multi‐modal multi‐component aerosols as applied to the coagulation‐type equation

“…In recent years, more mathematically advanced numerical methods have been introduced. Sandu and Borden (2003) proposed a highly efficient method of discretization of the aerosol dynamic equation based on the projection methods, like the collocation and Galerkin techniques, whereas Debry et al (2003) explored the statistical approach based on the Monte Carlo method to solve the general dynamic equation for aerosol. All these methods, being successful in their own rights, have one problem: calculations are time intensive because of the necessity of high-resolution discretization.…”