This thesis contains work of a computational and theoretical nature. The floating
potential of dust grains immersed in plasma is investigated via particle-in-cell
simulation for a range of parameters. In particular, work is focused on the charging
of grains large with respect to the electron Debye length. Numerical fits are given for
the floating potential of large grains in stationary and flowing plasma. A modified
version of the well known orbit-motion-limited (OML) theory is developed for large
dust grains. The modified OML theory is shown to be in good agreement with
simulation. This modified theory is then adapted for use with flowing plasmas. In
the case of flowing plasma, for low ion temperatures and flow speeds upwards of
Mach 1, interesting and unexpected effects are seen in the potential and density
distribution around dust grains, these are investigated and discussed. Finally, the
application of this work is outlined with particular focus on dust grains in a
tokamak plasma environment.