Particle transport in electrostatic precipitators

We discuss the transport of particles in a precipitator due to the combined effects of mobility and eddy diffusion in the gas flow. For an idealized model of a duct precipitator, the convective diffusion equation is solved analytically for the monodisperse particle concentration n(x, z) as a sum of normal modes which can represent any entrance profile n(x = 0,z). These modes decay exponentially in the flow direction, x, with the lowest (dominant) mode having the slowest decay and, therefore, controlling the efficiency in long ducts. The dominant mode yields the fractional efficiency formula η = 1 − exp − (wELud)F = 1 − exp − (wEAQ)F, which reduces to the Deutsch result when F = 1. The multiplier F which is a function of PE = (wEdD) (a measure of the relative effects of migration velocity wE and diffusivity D) is evaluated for different assumed boundary conditions. It appears that F values significantly greater than unity are possible, particularly for PE ⪢ 1. Numerical solutions of the convective diffusion equation have also been computed for a uniform entrance profile (n(x = 0,z) = n0, which agree with the analytic results and show the entrance profile decaying to the self-similar dominant mode profile for (wEAQ) ⪸ 1. The implications of the results to precipitator performance and design are discussed. In particular, it is argued that the efficiency can be significantly higher than the Deutsch value, and that by improving gas flow quality to minimize turbulence, significant reductions of precipitator length could be achieved.