When a DU projectile hits a target, up to 70% of the DU combusts, bursting into dense black clouds of uranium-oxide particles - effectively creating a ceramic DU aerosol. Most of the particles are of respirable size (less than 10 microns), ie. they're small enough to be ingested via inhalation (as well as via open wounds of course, and they're even small enough to penetrate some gas masks), and can be carried long distances (25 miles or more) by the wind, before settling. They can then be resuspended again by wind or movement, and dispersed yet further again. They can also migrate long distances via the ground water table.
This ceramic formulation is significant, because it is highly insoluble in lung fluids, unlike the traditional uranium dust encountered by miners, which is rapidly excreted from the body. Once deposited in the lungs, kidneys or bone, DU particles generally remain in the body for many years. Indeed, veterans of the 1991 Gulf War are still passing DU in their urine to this day.