Gelation dynamics of aerosol agglomerates from the free molecular to the continuum regime

Coagulation of aerosols at high concentrations plays a key role in determining the morphology of nanoparticle agglomerates in gas-phase synthesis reactors, as well as in natural and industrial combustion environments, such as wildfires and pool fires. Here, coagulation of aerosol agglomerates at solid volume fractions, f _v = 0.05–0.3 is investigated from the continuum to the free molecular regime by discrete element modelling (DEM). The DEM-derived coagulation rates, gelation times, t _g , radii of gyration and fractal dimensions, D _f , are validated in detail against Monte Carlo, Brownian and Langevin dynamics literature. At the high concentrations elucidated here, aerosols rapidly form a space-spanning, gel-like network of polydisperse, compact agglomerates with D _f ≥ 2. Increasing f _v from 0.05 to 0.3 results in smaller, less polydisperse and more compact agglomerates. The transport regime controls gelation dynamics, as well as the agglomerate gel size distribution. In the continuum and lower transition regimes, agglomerates remain smaller and less polydisperse with t _g ∼ f _v ^-1.95. In contrast, larger and more polydisperse agglomerate gels form in the upper transition and free molecular regimes with t _g ∼ f _v ^-1.2. In this regard, simple power laws are derived here to estimate accurately the collision frequency and gelation time of aerosol agglomerates and assist reactor design for gas-phase nanomaterial synthesis.