Dynamics of unipolar charged particles flowing through a cylindrical tube at high number concentrations

This work provides a theoretical and non -dimensional numerical analysis of the dynamics of gasborne unipolar charged particles flowing through a cylindrical tube at high number concentrations. It is discovered that above a threshold input particle number concentration, the concentration at the exit of the tube is nearly constant and independent of further increase in the input. Based on a maximum of 2% sensitivity of the system, the threshold input number concentration is quantified for a tube of any length more than 40 x the radius. The theoretical analysis developed in this work is used to derive correlations for the threshold input concentration and the exit concentration, as well as show that the exit particle concentration is lower than the threshold input value by a factor of 20/P-D, where P-D is the well-known diffusive particle penetration. The analysis demonstrates that a constant concentration can occur if and only if the ratio of nondimensional electric particle mobility to the Gormley -Kennedy diffusion parameter is above 74, which is a hitherto unexplored regime of charged aerosol flow dynamics. It is shown that the constant concentration can occur in compact tube designs (L/R<100) as long as the mass Peclet number of the particles is high and reducing the mass Peclet number to around 10 or below makes it impossible to obtain an input -independent number concentration. It is also shown that the Reynolds number of the flow has very little effect on the charged transport dynamics, where the order of magnitude of the input -independent number concentration is not highly sensitive to the Reynolds number, provided the system remains laminar. Finally, practical examples for designing instrumentation to generate a constant concentration of charged particles are discussed.