10th International Aerosol Conference September 2 - September 7, 2018 America's Center Convention Complex St. Louis, Missouri, USA
Abstract View
Towards a Coarse-Grained Model of Nano-Particle Agglomeration
MILENA SMILJANIC, Andreas Kronenburg, Rudolf Weeber, Christian Holm, University of Stuttgart
Abstract Number: 498 Working Group: Aerosol Modeling
Abstract The agglomeration of nano-particles plays an important role in many industrial applications, such as particle flame synthesis and spray-drying, where the structure of the agglomerates strongly affects final product characteristics. The process itself consists of two steps: (1) nano-particles collide due to their relative velocities caused by Brownian motion and/or turbulent flow, and (2) they adhere and form aggregates. Detailed models use Langevin Dynamics to track the movement of each particle and compute particle collisions and particle-particle interactions individually, as it is reported in the literature. More recent work investigates the influence of turbulent motion on aggregates’ growth and the resulting aggregate morphology. Numerical simulations were, however, limited to rather low numbers of particles (up to 4 million particles) and rather dense particle loadings. This limited the statistics and prevented long simulation times.
The simulation of larger systems will require some simplifications of the modeling process. Here, we develop a coarse-graining approach for the agglomeration of nano-particles and clusters, covering both primary particles of the size of few nanometers to agglomerates that are several orders of magnitude larger. Coarse-graining involves the replacement of parts of the clusters by “representative” particles of (representative) spherical shape. Due to the sparse nature of agglomerates, two spheres that envelop their respective agglomerates could intersect, but the agglomerates that they represent would not necessarily touch and stick. This approach allows not only for collisions on the surface, but also for the particle-cluster or cluster-cluster penetration, based on the calculated collision probability as a function of compactness of the underlying aggregates and of the overlap of the two coarsened spherical particles.
For the calculation of collision probability functions, besides usual agglomerate’s morphology characteristics such as number of particles (N), radius of gyration (Rg) and fractal dimension (Df ), we additionally used agglomerate's maximum radius (Rmax). Assuming random aggregate orientation, we introduce a model of concentric spherical shells, placed at the aggregate's center of mass, with minimal shell radius and shell width equal to the single particle diameter and the maximum shell radius equal to the aggregates maximum radius, respectively. Identical clusters randomly rotated are then shot towards the aggregate, and collisions between their respective particles are saved as hits (nhit) for the corresponding cluster shells. On the contrary, penetration of the tested clusters through shells without detecting any collision are accounted for misses (nmiss). For each cluster there are conducted N=3000 simulations and averaged within several cluster groups, over 100 clusters for each cluster group. This study examines aggregates of following characteristics: Rg=(3,5,7) and Df=(1.6,2.0,2.4).
Distance dependent collision probabilities (Pcoll,i) have been calculated as
Pcoll,i=nhit,i/(nmiss,i+nhit,i) .
As results show, along the interaction radius collision probability function is strongly affected by the aggregate fractal dimension and radius of gyration, slightly varying within relatively confined parameter ranges. In addition to it, results on cluster-cluster collision probabilities are used in coarse-grained simulations as determining parameter for creating bonds between colliding coarsened particles and their further growth, as well as for modelling of cluster-cluster interactions.