A simple semi-empirical model for effective density measurements of fractal aggregates

Abstract

Effective density measurements are used extensively to convert submicron particle sizes based on a particle׳s mobility diameter into mass. Measurements of the effective density also provide information concerning the particle morphology. For example, the effective density curves of fractal aggregates reveal a scaling factor that seems to correlate with the fractal dimension of the particles. The present paper proposes a simple semi-empirical model that permits the quantitative interpretation of these measurements to determine parameters such as the fractal dimension, the primary particle size, and the bulk density of an aggregate particle. The proposed model is based on the assumption that the hydrodynamic drag force of an aggregate is proportional to the drag force applied to isolated primary spheres and to the number of primary spheres in the aggregate at power α. The model was applied to soot particles produced by either a spark discharge (PALAS GFG1000) or by combustion (miniCAST 5206)—both mechanisms enable the generation of aggregates or agglomerates with very different primary sphere diameters. The proposed model showed a good fit for all of the effective density measurements obtained in this study; the α parameter was driven by the aggregate fractal dimension and by the Knudsen number that was determined based on the primary particle diameter. Finally, for a known primary particle diameter, the fractal dimension and the bulk density were determined successfully with the proposed model.