The Bohm criterion for the dusty plasma sheath

The Bohm criterion for the dusty plasma sheath is investigated with a fluid model. It is shown that the presence of dust particles near the interface between the bulk plasma and the sheath should have effects upon the ion Mach number. The dust particles charging and density variation are taken into account, and therefore the self-consistent relation between the dust surface potential and ion Mach number at the sheath edge is derived. The numerical results reveal that both the ion critical Mach number and the dust critical Mach number with variation of density ratio of dust-to-electron begin to decline after a maximum