Particle size scaling of non-Gaussian granular charge distributions

Dielectric particles of the same material exchange electrical charge during collisions or sliding contacts, yet the underlying charge-exchange mechanism is still not understood. The fact that particles can become highly charged as a result of this effect has significant consequences for many settings, both in nature and industry, such as thunderstorms, volcanic eruptions, particle aggregation during meteorite and planet formation, and the clogging of industrial granular systems. Toward understanding these systems, great efforts have been made to develop precise in situ measurements for particle charge, e.g., to determine ensemble charge distributions or measure exchange during individual contacts. Here, we present experimental results concerning the particle size scaling of the stationary-state charge distributions of oxide particles in the sub-millimeter range. We measure the charge distributions for large ensembles of monodisperse ZrO2:SiO2 composite spheres, ranging from 172 to 545µ⁢m in diameter. These distributions are non-Gaussian and collapse to a single master curve when plotted as functions of the surface charge density Σ=𝑞/4⁢𝜋⁢𝑅2. X-ray fluorescence and atomic force microscopy measurements show that the differences in the measured charge distributions are not due to variations in chemical composition or surface roughness, but rather to size alone. Our findings provide constraints on microscopic models for charge exchange, namely that they should lead to steady-state distributions that are non-Gaussian and scale in a specific way with particle size.