# Why does a viscous fluid tends to cling to a solid in contact with it?

My textbook says that a viscous fluid tends to cling to a solid in contact with it, and also gives a consequence of the same: "Dust particles cling to blades of a fan even when it is rotating rapidly."

I gave it lots of thought but couldn't come up with any satisfactory reason.

• I thought the dust example was due to no-slip boundary conditions? But maybe that is the same thing – BioPhysicist Nov 14 '18 at 23:51

## 2 Answers

Perhaps what you are referring to is the no-slip condition, in which fluid at a solid boundary will have a macroscopic velocity relative to the boundary of $$\mathbf{0}$$.

I've seen two arguments for it:

1. Adhesion beats cohesion near the boundary, and the particles near the boundary will be adhesively joined to the boundary.
2. Particle collisions against the non-specular boundary and neighboring particles will probabilistically trap particles near the boundary.

This second argument provides a nice explanation for why this condition fails in rarefied gas flows, namely that particle-particle collisions are not frequent enough to continually push particles at the boundary back if they try to escape.

The oil vapors (viscous fluid) are the first to adhere to the fan blade because of the molecular atraction between the two. Dust particles do not stick to a clean surface (unles it has electrostatic charge) because they are solid, thus not "flexible" enough to touch the said surface through a large enough area. Because of the imperfections of the two surfaces (that of the dust and of the blade) large percentage of the surface molecules of a dust particle will never get close enough to the surface of the blade to be atracted by it. Oil on the other hand, takes the shape of the blade surface and that of the dust clinging onto them both forming a bond between the two

• Ok but how does this explain that a viscous fluid tends to adhere to a solid, you explained it via molecular attraction, can it be explained at a more macromolecular level? – Arnav Upadhyay Nov 15 '18 at 5:52
• There is a Wikipedia article that explains the mechanisms involved in different types of adhesion (I'm not sure if you've seen it) - en.wikipedia.org/wiki/Adhesion – Alex Doe Nov 15 '18 at 10:56