A realistic generalized model for the electric field in containers: Evaluation at the powder-air interface

Models for estimating electric field strength in silos and containers typically focus on the maximum field value occurring along the container wall (Glor (2023) and Nugel, Scotton and Suter (Nugel et al., 2025) [8], often located within the bulk powder. While this approach ensures conservative estimations, it does not align with the physical location where ignition is most likely to occur. According to TRGS 727 [10], the relevant field for assessing cone discharge hazards is that at the powder-air interface, where an explosive atmosphere may simultaneously occur with a cone discharge during filling of containers or silos. This study extends and prolongs the analytical model previously developed by Nugel, Scotton, and Suter (Nugel et al., 2025) [8], by specifically targeting the electric field at the upper surface of the powder bed, where ignition is most likely to occur, and by integrating the influence of bulk heap geometry, in line with the findings of Zhou and al. (Zhou et al., 2019) [11], who demonstrated that conical heap shape is the most constraining parameter governing the magnitude of the electric field along the silo walls. By combining both approaches, a refined methodology is proposed that evaluates the electric field directly above the powder bed while explicitly accounting for the geometrical influence of conical heap configurations. Unlike the model by Nugel, Scotton and Suter (Nugel et al., 2025) [8], which evaluates the electric field assuming a flat bulk surface and therefore results in less conservative estimates, and which identifies the maximum electric field within the powder volume without assessing whether an explosive atmosphere is present at that location, the present approach offers a conservative analytical formulation that remains valid for any cone angle formed by the bulk heap. It explicitly focuses on the powder–air interface, which represents the physically relevant zone for cone discharge hazards. Although the study by Zhou and al. (Zhou et al., 2019) [9] highlights the influence of bulk heap geometry, it does not offer a generalized expression that can be directly implemented in industrial risk assessment, as it remains confined to specific conical shapes and fixed angles. To characterize the field at this interface, newly defined dimensionless correction factors are introduced. These allow a more realistic estimation of the electric field strength at the powder-air interface, without requiring full numerical integration for each specific container geometry or filling condition. • Continuous modeling of the electric field at the powder–air interface. • New equations estimate the field with and without charge relaxation. • Practical formula to assess the risk of cone discharges. • Refined version of the model proposed by Nugel, Scotton, and Suter [ 8 ].