# Why is the no-slip condition not applicable for rarefied gases?

It is written in Wikipedia that at very low pressures the no-slip condition does not hold and there we are given a model for applications though there is no explanation given for the reason this is the case.

Specifically, adhesion and cohesion are touched upon as the governing principles for the no-slip phenomenon (though the site lacks the citation).

However, this means cohesion (if cohesion is the principle keeping like molecules together) is stronger when the fluid is rarefied and I have difficulty understanding that since in my mind less molecules mean a less attractive intermolecular force.

How can the gas molecules far away from the wall successfully attract those that are close to the wall when they are rarefied and fail to do it when there are a lot of them?

Is there any concise physical intuition by which we can justify this phenomenon to ourselves?

• The point is rather, that cohesion is much weaker and therefore the molecules adhering to the walls can not influence the rest of the gas as much that you can model it as a no slip condition. Jun 17, 2018 at 18:13
• Thanks for the response but it is still unclear. Does that mean cohesion strengthens when the gas is rarefied? If it does, it does not seem sensible from the number of molecules point of view. Jun 17, 2018 at 19:07

From a more heuristic, physical perspective, interactions between a molecule and the boundary will be "messy" enough that the particle won't have a mean tangential direction of movement while it is in the immediate vicinity of the wall. If the mean free path of such a molecule is very tiny, then any interaction that may "bounce" it out of the range of the wall will cause it to quickly hit a particle and bounce back, keeping it in range of the boundary and therefore causing its tangential velocity to be $$0$$.
For dilute gases, particle that hit the boundary may escape it, meaning that its tangential velocity can be quite far from $$0$$; these arguments (that particle-particle interactions suppress tangential velocity near the boundary) are the ones I've seen justify slip/Navier boundary conditions (which you can also find discussed in the book above).