Extension of discrete tribocharging models to continuous size distributions.

Triboelectric charging, the phenomenon by which electrical charge is exchanged during contact between two surfaces, has been known to cause significant charge separation in granular mixtures, even between chemically identical grains. This charging is a stochastic size-dependent process resulting from random collisions between grains. The prevailing models and experimental results suggest that, in most cases, larger grains in a mixture of dielectric grains acquire a positive charge, while smaller grains charge negatively. These models are typically restricted to mixtures of two discrete grain sizes, which are not representative of most naturally occurring granular mixtures, and neglect the effect of grain size on individual charging events. We have developed a model that predicts the average charge distribution in a granular mixture, for any continuous size distribution of dielectric grains of a single material. Expanding to continuous size distributions enables the prediction of charge separation in many natural granular phenomena, including terrestrial dust storms and industrial powder handling operations. The expanded model makes predictions about the charge distribution, including specific conditions under which the usual size-dependent polarity is reversed such that larger grains charge negatively.