Towards monomer-resolved Discrete Element Models to predict soot fractal-like agglomerate thermal restructuring

Our understanding of inter-particle forces and how they determine the morphology of flame-made nanoparticles, such as soot agglomerates, is currently limited. Therefore, most simulation approaches, including discrete element models (DEM), assume a rigid-body morphology in diffusion and premixed flames (Liu et al., 2025). However, this hypothesis may not hold under other conditions, including high-concentration nanoparticle synthesis, post-flame thermal treatment, and atmospheric aging, where agglomerates may experience restructuring. As a result, current work discusses different models to abandon the rigid-body assumption and predict the thermal restructuring of soot agglomerates.

Individual diffusion-limited cluster–cluster aggregation (DLCA) soot fractal-like agglomerates (fractal dimension, 1.78; prefactor, 1.3) consisting of 50 to 500 spherical, monodisperse monomers were generated using FracVAL (Morán et al., 2019) and their restructuring was simulated using ESPResSo (Weik et al., 2019). A simplified model of Johnson-Kendall-Roberts (JKR) contact forces (modeled as breakable harmonic bonds) as well as Van der Waals forces were considered in Langevin dynamics simulations of individual monomers (modeled as deformable spheres) belonging to an agglomerate in the ballistic, transition, and diffusive regimes.

The results revealed a two-stage restructuring process across all regimes and agglomerate sizes. While the first stage involved rapid and local rearrangement of monomers, the second and slower stage was characterized by global restructuring of external branches around the backbone structure (which stays almost intact), eventually reaching an asymptotic morphology characterized by high local compactness of monomers. Considering the van der Waals forces and breakage of bonds between monomers results in faster restructuring, more locally compact, and less globally compact morphologies. Restructuring timescales, defined as the parameter of a time exponential fit, were shown to be linearly correlated with agglomerate size in all regimes. The monomer-resolved DEM model incorporated here can be used in agglomeration simulations, leading to a better understanding of detailed morphological evolutions during agglomeration.

References
Liu, F., Yon, J., Morán, J., Kelesidis, G. A., Escudero, F., & Fuentes, A. (2025). Progress in multi-scale modeling of soot particle aggregation in laminar sooting flames. Progress in Energy and Combustion Science, 110, 101234. https://doi.org/10.1016/j.pecs.2025.101234

Morán, J., Fuentes, A., Liu, F., & Yon, J. (2019). FracVAL: An improved tunable algorithm of cluster–cluster aggregation for generation of fractal structures formed by polydisperse primary particles. Computer Physics Communications, 239, 225–237. https://doi.org/10.1016/j.cpc.2019.01.015

Weik, F., Weeber, R., Szuttor, K., Breitsprecher, K., de Graaf, J., Kuron, M., Landsgesell, J., Menke, H., Sean, D., & Holm, C. (2019). ESPResSo 4.0 – an extensible software package for simulating soft matter systems. The European Physical Journal Special Topics, 227(14), 1789–1816. https://doi.org/10.1140/epjst/e2019-800186-9