The air ionizers charge air particles( be they dust, smoke, pollen,) in the air via an electrical charge. These charges particles will cling to walls, desks, floors whatever and not float around the air. It's just that simple. Some of the units are now designed to give off a substantial greater amount of ozone, in addition to the ionizing action. These new air cleaners health effects are questionable. Units that say they can clean the air in the next room or at great distances are cleaning the air, not by charging the particles (ionization), but via the ozone they produce.
what this has to do with tubs, I don't know.