Suppose we are considering some fluid. As I currently understand, viscosity exists because of the following: supposing we draw one infinitesimal surface on the fluid, then the fluid parcels on either side have different momentum.

Since a fluid parcel is made up of a large number of molecules and its velocity is the average velocity of those molecules if some molecules cross the surface into the other fluid parcel they will change the average velocity of the fluid parcel they migrated into.

In that case, this will change the momentum of the fluid parcels and since change of momentum is related to force this will give rise to one kind of force which will be the viscosity force.

Is that understanding right? I thought at first there was something to do with the collisions of molecules but what I said above is what I understood when I read about it on the book. If it's not like that, how we should think about viscosity qualitatively?


1 Answer 1


What you said is a correct way to look at it. If you take an imaginary surface you will get molecules of the fluid crossing that surface. This crossing is due to the random thermal motion of the molecules, which on average, will even out (meaning for every molecule that moves "up" into a faster stream, a molecule will move "down" into the slower stream). This gives things like boundary layers their shape and thickness.

This process is enhanced on the macro-scale when the flow is turbulent. Now you have large-scale eddies moving molecules from the faster to slower streams and vice-versa. This is why a turbulent boundary layer is thinner -- there is more momentum transfer resulting in a more rapid (in space) mixing of momenta.

Now, the only point that you are confused about is the collisions. If there were no collisions, there would be no viscosity. As a slower molecule moves into the faster stream, it is "ignored" in a collisionless system. So it neither speeds up nor slows down. And in this system, you will end up with total mixing eventually of all different velocity levels and you'll get flow that has a single, uniform velocity with non-equilibrium velocity distributions because there is no way to reach equilibrium. This would also be a frozen flow because it cannot leave this state.

So the collisions matter very much. As a slower molecule moves into a faster stream, it collides with the faster molecules. This slows down the faster ones, speeds up the slower one, but the net speed is lower. There is an attempt to reach equilibrium in the streams. In this sense, a viscous flow is a non-equilibrium flow where the translational modes are not in equilibrium.


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