I already asked the same question and got great answers but im also confused.
One of the answers said that I can imagine that, because air over the wing has a higher pressure than the air right above the wing it gets pushed down which is why the air follows the wing instead of just going in a straight line.
But as far as I understood another answer said that viscosity makes air stick to the surface of the wing which makes it follow the wings shape.
So what is correct?
It’s pressure equalization that determines the final amount of gas in the space, but it’s the high particle energy/speed and small size that can make it happen fast enough to fill the backside of a wing even though momentum doesn’t seem to be pushing any air in that direction. Viscosity does not make things stick together. No-slip means surface and gas velocities are equal.
The best way to think of a gas is an enormously large number of molecules filling every portion of space, even in a very tiny space, with high particle speeds in every direction, responding almost instantly and able to achieve equilibrium pressures and densities immediately. Anything happening macroscopically is minor comparatively and is merely an average of what the particles are doing.
Also, despite what you may have heard the ubiquitous “no-slip” boundary condition, there are not more molecules concentrated right on the wing than there are just off of it. There is nothing attracting the molecules to the surface. The only point of no-slip is that, at the surface, we can assume the average velocity of the gas matches that of the surface.
The motion of a jet of air is just the average net velocity of the particles.
The particles are full of energy: Temperature is actually the kinetic energy of the molecules. For example, in an ideal gas model, the relationship between pressure and temperature is determined by modeling it as many tiny particles. Pressure comes from the particles colliding with a wall at the point we are determining pressure, in a perfectly elastic collision, transferring an impulse to the wall. Many particles do that in a given time $t$: $F= \sum \tfrac{m \cdot \Delta v_{rms} }{t}$. And this aspect of the model (particularly velocity) matches perfectly with the temperature model of the same particles: a temperature model where internal energy in the gas comes from its kinetic energy $\sum \tfrac{1}{2}mv_{rms}^2$, where $m$ is the mass of a single molecule.
And a good guesstimate is $$v_{rms} = \sqrt { \tfrac{3RT}{M_m}} \approx \sqrt { \tfrac{3 \cdot 10 \cdot 300}{0.03}} \approx 500 m/s$$
We would have to be around mach-1.5 for the air’s net velocity to match the average particle speed of room air. But this needs to be considered in conjunction with how many particles we’re talking about as pressure waves up to the speed of sound can briefly increase the local average. Also remember that this does not yet include pressure-driven net flows, which can be a significant addition at near-sonic speeds.
One thing to realize about a gas is the number of molecules. Avogadro’s number is huge (23$^{rd}$ order).
For example, as air is 0.0013 $g/cc$ at room pressure and temperature, and 30 $g/mol$, then even assuming a low pressure of 0.1 $atm$, which reduces density ten-fold, we have...
In a billionth of a cubic centimeter there will be 800 trillion molecules, each one moving on its own, with the average speed as given. So if a space opens up, the time to fill it is minuscule and not based on net, pressure-driven flows that only determine final equilibrium of average speeds (as $p$ and $T$).
