There is a bit more to the operation of the oil bath air cleaner. In addition to what Stuart posted, there also is a "misting" action that is happeneing, caused by the way the air flows throhg the housing. Thsi oil mist also traps dirt, namely the fine particles that do not end up in the pool of oil in the bottom of the housing. Thsi mist is collected on a fine wire mesh located in the housing, then returned to the reservoir, along with the trapped dirt.
A modern dry filter may be more efficient at trapping dirt, but an oil bath will not clog up, and properly maintained, are as efficient if not more overall. If you look at them, almost all big rigs still use the oil bath type air cleaner (the big chrome tank located next to the front of the cab) because of the low restriction of that type.