A stochastic model for nanoparticle deposits growth

Natural events and human activities are responsible for the generation and transport of large amounts of micro-sized particles, which could contaminate several engineering devices like solar panels, wind turbines, and aero-engines. In industrial processes, systems as heat exchangers, fans, and dust collectors are continuously affected by nanoparticles' interaction. For several applications, the adhesion of such nanoparticles is detrimental, generating safety and performance issues. Particleto-particle and particle-To-surface interactions are well known, even if a general explanation of nanoparticle deposit growth is still unknown. In the present paper, an interpretation of deposit growth due to nanoparticle deposition can predict particle adhesion, and layer accretion is proposed. A statistical model and a set of coefficients are used to generalize nanoparticle deposits' growth by an S-shaped function. In particular, the nanoparticle deposits grow analogously to a typical autonomous population settlement in a virgin area following statistical rule, which includes the initial growth, the successive stable condition (development), and catastrophic events able to destroy the layer. This approach generalizes nanoparticle adhesion/deposition behavior, overpassing the constraints reported in common deposition models, mainly focused on the mechanical aspect of the nanoparticle impact event. The catastrophic events, such as layer detachment, are modeled with a Poisson s distribution, related to material characteristics and impact conditions. This innovative approach, analogies, and coefficients applied to common engineering applications may be the starting point for improving the prediction capability of nanoparticle deposition.