  Insulating particles can become highly electrified during powder handling,
volcanic eruptions, and the wind-blown transport of dust, sand, and snow.
Measurements in these granular systems have found that smaller particles
generally charge negatively, while larger particles charge positively. These
observations are puzzling, since particles in these systems are generally
chemically identical, and thus have no contact potential difference. We show
here that simple geometry leads to a net transfer of electrons from larger to
smaller particles, in agreement with these observations. We integrate this
charging mechanism into the first quantitative charging scheme for a granular
system of identical insulators, and show that its predictions are in agreement
with measurements. Our theory thus seems to provide an explanation for the
hitherto puzzling phenomenon of the size-dependent charging of granular systems
of identical insulators.
