In this work, a ID steady state model to study the dynamics along with trapping of dust grains in a plasma sheath over the lower electrode in a plasma reactor, is proposed. Electron and negative ions density distributions are taken Boltzmannian whereas positive ions are described by a cold fluid model. Numerous forces acting on dust grains are taken into account, viz, electric force, gravity force, ion drag force, neutral drag force, etc. It is found that trapping is grain size dependent, and it affects only negatively charged grains. The trapping position is determined and the physical parameters controlling the later are discussed.