There is this famous experiment to demonstrate the Bernoulli effect, where you try to very rapidly inflate a loose air balloon of sorts, like shown for example in this video. Here's a still image so you know what I'm talking about:
The point being that if you have a fast air stream from a nozzle (like your mouth), it will pull a lot more air with it compared to just the air in the stream itself. Fine. That's just Bernoulli at work.
Now, let's travel (preferably somewhere nice ;) ), and in buses or airplanes you have seen these vents in the ceiling above your seat:
Let's assume that the air coming from the vent is perfectly clean (an excellent approximation, at least in airplanes given their filtration systems), whereas there is some contamination in the surrounding air. Most relevantly, that could be viruses and bacteria, or more easily to experiment with, imagine some odor (and I'm sure you have an easy time imagining that...).
Now, my experience (with the latter scenario) seems to indicate that opening the air vent fully indeed does more quickly reduce the unwanted pollutants to low levels. However, it is not clear to me why that needs to be the case, given the Bernoulli effect, and I lack a solid intuition. Thus my question:
Given the Bernoulli effect, how do ceiling vents in airplanes and buses help to quickly reduce unwanted contaminants in the air? Are there limiting cases in which either the direct air stream dominates, or the air pulled in via Bernoulli, or the overall turbulence caused by the air stream?
Edit: to clarify, is there a general way to estimate the amount of air that comes directly from the air vent, versus the amount of air that is additionally pulled in through the Bernoulli effect?