Parallel and Turbulent Flow Precipitator Efficiencies for Distributions of Particle Mobilities

Regimes of parallel and turbulent flow in a parallel plate precipitator are discussed as theoretical idealizations. Particle trajectories and resultant efficiency of an ideal parallel flow device are described and compared with the Deutsch equation analysis, based upon complete mixing in turbulent flow, for a single mobility species. A relationship is developed between particle size and mobility which incorporates field and diffusion charging and the Cunningham correction to Stoke´s drag. Log normal distributions of particle size are transformed into mobility distribution functions. Efficiencies based upon parallel flow and turbulent mixing are expressed for the particle mobility distributions by finding incremental efficiencies for each segment of a given distribution and weighting each segment by its relative proportion of the whole. These efficiencies are compared with each other and with the result obtained by inserting the mean mobility into the Deutsch equation. It is shown that, for relatively high standard deviation, use of an average mobility value in the Deutsch equation can result in device efficiency characteristics quite similar to those resulting from collection of the various mobility species in parallel flow. A much lower efficiency results from incremental analysis of the same distribution under the assumption of turbulent mixing.