We use DC voltages in an electrostatic precipitator (ESP) because it is necessary to induce a charge on the particulates, and then attract them to a plate by the use of an opposite charge. An AC source would be changing constantly. That would leave our particulates picking up "different charges" at different times as they pass the plates. Further, these particulates wouldn't be attracted to the plates because the plates would be changing polarity as well.
ESP's use a DC source to apply a charge of a given polarity to the particulates in the air stream, and use a plate of the opposite charge to attract and "hold" the particulates. AC sources can't do that.
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