Estimates of Non-Ideal Effects on the Friction Coefficient of Agglomerates

There are several characteristics of silver agglomerates that are not incorporated in existing models for agglomerate dynamics. These characteristics include particle alignment in the electric field, necking between particles, polydispersity of the primary particles, and variable primary sphere size. Estimates of these features on the agglomerate dynamics were computed as perturbations to the Chan-Dahneke agglomerate model. The variable primary sphere size effect results in the largest change from the idealized model with about a 10% increase in scaling exponents for both friction coefficient – number of primary particles (η) and mass-mobility diameter (Dfm). The second largest change is a 4% decrease in the exponent η and a 4% increase in the exponent (Dfm) from the alignment in the electric field. The effects of necking between particles and polydispersity of the primary particles are negligible for the two exponents. The combined effect, excluding the variable primary particle size, results in a 17.5% decrease in the dynamic shape factor for agglomerates with a 300 nm mobility diameter. Adjusting the model by this amount provides a significant improvement in the agreement between the model and silver agglomerate measurements for the dynamic shape factor. Experimentally the number of primary spheres is determined from the mass of the agglomerate assuming a constant primary sphere diameter. The predicted apparent exponent η based on a 10% variability in the primary sphere size is about a 5% less than the apparent exponent assuming a constant primary sphere size. This is a significant effect relative to the observed 15% decrease in η (Shin et al., 2009a) as the agglomerate size increases from the free molecular regime into the transition regime.