This thesis concerns the interaction of small, particulate, solid matter - 'dust' - with
plasmas, in the plasma edge region where such dust is commonly found. Dust in this
region can have a significant impact on a variety of industrial plasma applications, and
it is low-temperature industrial plasmas that form the focus of this work.
A novel model for the sheath region at the edge of a plasma is proposed, to account
for the loss of electrons at the plasma boundary. This is then compared to an existing
Boltzmann electron model; significant differences are noted in the sheath structure, and
consequently the charging and dynamics of dust in the plasma sheath.
The effect of sparse ion collisions in the vicinity of a dust grain near the plasma edge
is also investigated. The strong plasma flow in the edge region is found to significantly
increase collisional charging of dust grains. Somewhat counter-intuitively, it is found
that even sparse collisions can play a significant (and in fact dominant) role in the
charging and shielding of dust grains at the edge of a plasma. The length-scale over
which the charge on such grains is shielded by the plasma is found to be significantly less
than the Debye length. Together, the altered grain charging and shielding behaviour
have the potential to fundamentally alter how dust grains interact with edge-plasmas.