An analysis is presented of the suspensions of small, electrified particles in a gas. Two limits of interest for the electrodynamic particulate suspension technique are considered, corresponding to large and small values of the ratio t₂₎₋₋/tₛ of the mean time between particle collisions to the viscous adaptation time required for the particles to reach their terminal velocities. The effect of the particle inertia can be neglected when this ratio is large, and only the distribution of particle charges at each point of the suspension needs to be computed. The way this distribution approaches an equilibrium form, determined elsewhere in the continuum regime when the mean free path of the particles is small compared with the suspension size, is described, as well as the connection between continuum regime and quasi-neutrality of the suspension. In the opposite case when t₂₎₋₋/tₛ is small, the inertia of the particles plays an important role, and the joint distribution of particle charges and velocities is required. A Boltzmann equation is proposed for this distribution function, taking advantage of the fact that the charges of the particles have little effect on the redistribution of momentum and energy in the collisions. The equilibrium distribution function in the continuum regime is computed approximately, and hydrodynamic equations for the particle phase analogous to the Euler equations for a monoatomic gas are derived. The simplification of these equations when the particle inertia is negligible at the scale of the suspension is worked out.
F.J. Higuera (2025) studied this question.