Dust-laden gas flows between two grounded collector plates past a thin high-voltage wire down the centreline. The corona around the wire ionises the gas; ions attach to every particle that drifts past until it reaches (for a conductive sphere) the saturation charge
q_sat = 3πε0 d_p² E
The same field then pushes that charge sideways against Stokes drag (with the Cunningham slip correction C_c for sub-micron particles, since the mean free path of air, λ ≈ 66 nm, is no longer negligible next to d_p). Combining charging and drag gives the classic migration (drift) velocity:
w = ε0 · d_p · E² · C_c / μ
C_c = 1 + (2λ/d_p)·[1.257 + 0.4·exp(-0.55 d_p/λ)]
E = V / s (applied voltage / plate half-spacing)
Collection efficiency over a plate of area A with volumetric gas flow Q follows the Deutsch–Anderson equation, derived by assuming the drift velocity instantly mixes each particle across the duct cross-section:
η = 1 - exp(-w·A / Q)
A = 2 · L · H (both plates, fixed L=3 m, H=1 m)
Q = (2s · H) · v_gas
- Voltage / spacing — set the field E = V/s that both charges and collects the particles; a bigger field or narrower duct raises w.
- Gas velocity — raises Q, cutting residence time and lowering η for the same plate.
- Particle diameter — bigger particles hold more charge (d_p²) but drag scales linearly with d_p, so w still grows with size; very fine (sub-micron) particles instead get a Cunningham-correction boost.
- Each dot is tracked individually — the measured η readout is the running fraction of particles the live particle tracker actually collects before it reaches the outlet, so you can watch it converge on the closed-form theory value above.
Real-world relevance: this is the working principle behind full-scale electrostatic precipitators on coal-fired power plants, cement kilns and smelters, typically removing >99% of fly ash by mass.