Suppose we put a bowl containing loose powder into a vacuum chamber. The powder is very fine, and very light, and can be blown away easily by small air currents when not in the vacuum chamber. If we turn on the pump to suck air out of the chamber, what would happen to the powder?
Would some of the powder be sucked out of the chamber into the pump? How would loose powder inside a vacuum chamber behave when the pump is activated?
There are two regimes of operation for vacuum chambers, separated roughly by whether the “mean free path” for air molecules is short or long relative to the size of the chamber.
In the high-pressure limit, the mean free path is very short, and so the next thing any particular air molecule collides with is overwhelmingly likely to be another air molecule. I have in my head that a typical mean free path in air at atmospheric pressure is about sixty nanometers, but I haven’t taken the moment to confirm. In this high-pressure limit, air acts like a fluid: it makes sense to talk about high- and low-pressure regions, and introducing a low-pressure region at the inlet of your vacuum pump will cause bulk airflow in the vacuum chamber. Information about pressure changes propagates through the fluid at roughly the speed of sound.
In the low-pressure limit, the mean free path is very long. Once the mean free path is much larger than your vacuum chamber, you no longer have pressure-driven bulk fluid flow: each air molecule is more likely to collide with the wall of the chamber than with another air molecule. In this regime, your pump no longer provides a pressure gradient. Instead, the pump inlet is a region of the vacuum chamber wall where an air molecule is more likely to be removed from the vacuum volume than to scatter back in. This pressure-free density regime has a sensible name which I will suddenly remember in the shower tomorrow.
Airborne fine dust is a high-pressure phenomenon. The terminal velocity of a falling object is given by $$ v_t= \sqrt\frac{2 m g}{\rho A C_d} $$ for an object with weight $mg$, cross-section $A$, and drag coefficient $C_d$, falling in a fluid with density $\rho$. An “airborne” object is one whose terminal velocity is smaller than a typical air-current speed, so that random air currents may carry the object away from the ground. In the low-density $\rho\to 0$ limit, the terminal velocity is unbounded, because the drag responsible for the terminal-velocity approach becomes negligible.
As a commenter points out: if you like your vacuum chamber and your vacuum pumps, you should not put fine dust in them. Even if the dust is well-confined when you introduce it, accumulating in a neat pile because there are no air currents to blow it around: once you reintroduce air into the chamber, the dust will get everywhere.
I can speak from experience - specifically the experience of many hours spent cleaning the vacuum chamber after this happened to me as a new PhD student.
The problem is that your fine powder contains air trapped in the interstices between the powder grains, and as the pressure is reduced this air flows out of the powder and can carry fine grains with it.
How much of a problem this is depends on how rapidly your pump can lower the pressure in the chamber. Provided the pressure decreases slowly enough the air flow out of the powder will be too slow to disperse the powder. There isn't any easy way to tell how much of a problem this is going to be. All I can suggest is that you lower the pressure very slowly when you first try it. You can easily see if it's going to be a problem because you can see the powder "bubbling".
Not to be glib, but the answer the title question is that the entire function of the (mechanical) pump is to move the air inside the chamber to the outside of the chamber, so ... yes, the air inside will move.
With respect to your dust particles, yes, some of them will be pulled out of the chamber along with the air. Once the air is mostly gone, this effect will stop, and the dust grains will simply cover the bottom and interior walls of the chamber.
Ever wondered how a powder fire extinguisher works?
In fact, exactly like you describe in your question.
You push the lever and you connect the inside of the container to the much lower pressure outside (just like the vacuum pump in your question).
Guess what - almost all of the powder gets out.
The mechanism is reliable enough to be used in a fire extinguisher.
In different businesses, the same method is used to move cement, flour and other powdery substances between containers (and in some unfortunate events, out of the container).
Of course, the less gas is in the container and the less the speed at which you pump it out, the less force will the particles experience when the gas blows them around.
If you evacuate your container at low enough rate, you may as well have the gravity holding your loose particles in their place.
