Modeling simultaneous coagulation and charging of nanoparticles at high temperatures using the method of moments

Abstract

A large number of chemically and thermally ionized species are produced in flames. During flame synthesis of nanoparticles, these ions collide with the particles as do the particles amongst themselves. Both charging and particle-particle collisions decide the particle size distribution, but existing models in flame synthesis often do not consider the coupling of these two effects. In this work, a model simulating simultaneous charging and coagulation is developed using the method of moments (MoM), with the help of asymptotic methods and perturbation theory. This model considers different charged states, as well as the particle size distribution in each charged state and their interactions. To achieve this, first, a simplified polynomial expression for the charging coefficient is derived from Fuchs’ theory. This expression is found to be in good agreement with the complete Fuchs theory expression at high temperatures in the free molecular regime. Next, this expression is used in the general dynamic equation for simultaneous charging and coagulation to derive population balance equations of volume moments. A simplified modeling method, named the monodisperse model (MdM), was used to compare the simulation results. Both the MoM and MdM showed good agreement in different simulated cases. It was found that for constant bipolar ion environment, the collisional growth increases as the ion concentration increases, and flattens out for high ion concentration (>108 #/cm3). Simulated results also showed that for a unipolar ion environment, MoM predicted that the particle growth by collisions would be more suppressed, resulting in particles with a lower polydispersity index. The simplified expressions for the ion-attachment coefficient used in the MoM works well at high temperatures in the free molecular regime, and that MdM is able to capture the physics of the system well.