The differential charging of a nonconducting spacecraft is modeled numerically by following charged-particle trajectories in a self-consistent space-charge-less sheath. In the presence of a plasma flow but independent of any photoelectric or secondary emission a potential difference between the front and wake surfaces of the spacecraft is generated, resulting in an asymmetric sheath and in the creation of a potential barrier for electrons. Th potential difference canamount to volts in the ionosphere and kilovolts in the solar wind. As in the more familiar case of photoelectric charging, the asymmetric sheath and potential barrier produced by the plasma flow can lead to erroneous interpretations of experiments measuring space electric fields and low-energy particle spectra.