Year: 2026
Type: article
Abstract: In iron combustion, the formation of nanoparticles and their subsequent deposition onto fuel particle surfaces have been observed. Deposition is strongly influenced by heterogeneous surface reactions, which induce coupled thermophoretic and Stefan flow-driven nanoparticle transport. In this work, an analytical expression for thermophoretically-dominated nanoparticle collection on spherical fuel particles is derived and combined with existing formulations for Brownian diffusion and Stefan flow using a superposition approach. The resulting model provides a comprehensive description valid across Brownian diffusion-dominated, drift-dominated (thermophoretic and/or Stefan flow-driven), and dust-free regimes. The framework is validated using both Euler–Euler and Euler–Lagrange simulations over a wide range of temperature differences, Stefan flow velocities, and Knudsen numbers relevant to iron combustion. The results demonstrate smooth transitions between regimes and accurate recovery of the corresponding limiting solutions. The proposed model offers a consistent and computationally efficient prediction of nanoparticle collection based solely on far-field and surface conditions, enabling its application in simulations of complete burner configurations. Novelty and significance statement: The classical concept of a spherical collector is extended to reactive fuel particles in iron combustion. Based on analytical considerations, a criterion is identified to correctly capture the dominance of either thermophoretic or Stefan flow effects. This enables a more comprehensive description of nanoparticle collection that consistently accounts for Brownian diffusion, thermophoresis, and Stefan flow within a single framework. The proposed model is validated using detailed Euler–Lagrange simulations, demonstrating its robustness under large temperature gradients, strong Stefan flows, and varying Knudsen numbers.
Authors: Nils Hartmann, Andreas Kronenburg, Thorsten Zirwes, David Märker, Tien Duc Luu, Oliver T. Stein
Institutions: University of Stuttgart, Karlsruhe Institute of Technology
Language: English
Subfield: Ocean Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,570
OpenAlex ID: W7214202380