Deposition of aerosol flowing past a cylindrical fiber in a uniform electric field

The deposition of aerosol particles from an air stream of velocity V₀ upon a circular cylindrical fiber perpendicular to the stream in a homogeneous electrical field E₀, has been investigated theoretically. The dielectric constant ϵ_c of the fiber controls by means of the parameter $\text{a =}\text{(ϵ}{}_{\mathrm{c}}\text{− 1)}\text{(ϵ}{}_{\mathrm{c}}\text{+ 1)}$ the additive inhomogeneous field of the fiber, which effectuates the deposition of the particles. When computing the trajectories, both inertia and image forces for charged particles have been neglected. The computations have been made for frictionless potential flow and for viscous flow according to Lamb.

For uncharged particles, the dimensionless parameter F ∼ r₈³E₀²B/r_cV₀ (where r_s, B = radius and mobility of the particle; r_c = radius of the fiber) determines the value of the deposition coefficient. Exact solutions for the limiting case a = 0 as well as some approximate solutions for a ≠ 0, obtained by the Runge-Kutta method, are given.

For particles carrying an electrical charge q, the dimensionless parameter G = E₀qB/V₀ is decisive. From the exact solutions the deposition coefficient is given by $\text{ζ =}\text{G(a + 1)}\text{(G + 1)}\text{,}\text{if}\text{G > 0}$, for ideal and viscous flow. With negative G, the fiber may be surrounded by a “dust-free space.”