Air purifier placement

I've recently started investigating air purifiers due to lingering cooking odors. My apartment doesn't have good circulation and these odors can last sometimes even until the next morning.

One particular difficulty is that my apartment is also a large open space, with especially high ceilings (13ft/4m). For this reason I am wondering whether an air purifier will be more effective on the ground or if i placed in on top of my kitchen cabinets? There is about 3ft/1m clearance from the top of my cabinets to the ceiling so i should be able to fit a sizeable unit there.