A simplified closed-form solution is presented for the deposition flux of atmospheric particulate matter on electrical insulators. Due to the lack of deposition measurements on such solid bodies, the mathematical model was closed using a 4D regression procedure based on numerical data at the obstacle scale. These data were obtained using the stochastic Lagrangian model SPRAY-WEB (University of Eastern Piedmont et al., 2021). The code, already validated by reproducing particulate dispersion and deposition on solid obstacles in Amicarelli et al. (2021), is here applied to an XP-70 porcelain disc insulator. An associated tutorial has been published for this numerical database (SPRAY-WEB, 2021).

Validation metrics on the performance of the closed-form solution show that errors meet the reference thresholds for numerical simulations of air quality defined by Chang & Hanna (2004) and are limited to a maximum of 24% (external verification). Although not suitable for closing mathematical models or representing a specific event, deposition fluxes from Zhang et al. (2014), averaged over the long term, are associated with the same insulator in this study. Compared to the aforementioned 1:1 scale experiment, the closed-form solution provides a 13% overestimation.

This solution can be used for preliminary and instantaneous estimates or integrated into air quality computational codes for rapid assessments of contamination maps for electrical insulators. Such applications aim to quantify functional damage to insulators (e.g., due to electrical discharges, short circuits). This closed-form solution is adaptable to generalize with each new availability of data.