Two approaches to the simulation of silica particle synthesis

Simulation of coalescence and breakage: an assessment of two stochastic methods suitable for simulating liquid–liquid extraction

“…Alternatively, an assumed shape can be imposed on the distribution to fit with a limited number of the moments. This can include monodisperse, log-normal (Grosschmidt et al, 2003) or Rosin-Rammler (Angeli and Hewitt, 2000).…”

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

“…There exist three main ways to simulate such systems: the method of moments [1], the sectional method [2] and stochastic particle methods [3,4]. The method of moments constructs moment evolution equations for the system, which then progresses through time so giving various moments of the particle system.…”

“…More recently, Eibeck and Wagner applied these ideas to coagulation and fragmentation, deriving both the direct simulation algorithm (DSA) and mass-flow algorithm (MFA) with accompanying convergence proofs and introducing fictitious jumps for the reduction of the complexity of the algorithm [7,8,9]. 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].…”

“…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]. 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.…”

Modelling nanoparticle dynamics: coagulation, sintering, particle inception and surface growth

“…Stochastic methods have been used previously to study univariate nanoparticle dynamics with a source term [2,3] and bivariate dynamics that include coagulation and sintering [13,15]. The purpose of this paper is to extend the model to include surface growth as well as particle inception, coagulation and sintering, and introduce a new mass-flow stochastic algorithm.…”