Saturday, August 21, 2010

Do all liquids have a turbulent regime?

This chapter insists that there is no intrinsic length scale for liquid. Thus liquid can appear extremely viscous to objects on the nano scale. But I think we still need to be careful about the generalisation that a liquid can appear to have whatever viscosity we want just by changing the forces acting on the objects moving in the liquid. My hesitation comes from the fact that there are certain other limitations on the behaviour of liquids.

Imagine a liquid with an exceptionally high viscosity, where the critical force is a few kilonewtons. For particles moving under forces slightly lower than this, in the regime dominated by friction, motion will cease very shortly after the force applied to them ceases. All the kinetic energy of the particle would heat up the environment, as the energy is being lost to friction. Now, what if this heat was enough to cause the liquid around the particle to begin to boil? This liquid would never have a regime dominated by inertia.

This hypothetical liquid would have viscosity orders of magnitude higher than corn syrup, and I don’t think it reflects any liquid found in nature*. This example is not a situation that would come up very often, but it illustrates the flaw in thinking that any liquid can be made to appear to have any viscosity just by changing the forces acting on the particles in it.

*Pitch has a viscosity of about 200MPas, 40 million times more viscous than corn syrup. If pitch counts as a liquid, then this may be an example of a liquid with no turbulent regime. Pitch shatters when it is hit with a hammer, which may indicate what happens to a liquid without a turbulent regime if it encounters forces that would be in its turbulent regime.


  1. Would the boiling of a very viscous liquid be possible in that way?

    I would assume that viscosity relates to the strength of bonding within the liquid. Wouldn't this increase the boiling point of the liquid? Thus making it very hard to generate enough energy which would boil the liquid as a whole.

    Also with the pitch and hammer. Would the surface tension of the pitch play a role in it's shattering?

  2. I dont think the claim is that any liquid can have any viscosity.

    For most fluids the viscosity is the same but may vary slightly with temperature and pressure.

    The point is that the Reynolds number (equation 5.11) can vary significantly by varying the fluid velocity and/or the length scale.
    As long as v is less than the speed of light and R is less than the size of the universe we are o.k!

    On the other hand finding more than a few km of tar may be a problem...

  3. You made mention to the fact that any liquid can appear viscous in the nanoworld.
    Let's first look at the macroscopic world. If a liquid is viscous, such as glycerine, we find that it follows laminar flow, and is hard to mix (it can undergo time-reversal if not left unattended for long after an initial mix has occured), and if it is nonviscous, it's easy to mix and time-reversal isn't a readily available option.
    Now, let's go to the nanoscale world. Thanks to the properties of nanoparticles, we see that the non-viscous liquids start to portray viscous effects, and start to follow laminar fellow. What I found to be especially interesting about this, was the fact that water (which is less viscous than corn syrup in the macroscopic world) was observed to be more viscous than the corn syrup in the nanoworld. This lead to the statement that the nature of a of fluid has dependancy upon the scale of the process under consideration.
    I admit that I'm still finding this a bit hard to conceive, because despite knowing that particles can have different properties to the bulk, the idea of the type of flowing changing seems a fair bit out there.
    Though, as one last point to this, there is the viscous force which is equal to -viscosity times by the velocity times by the area of exposure of sliding plates to the fluid divided by the fluid thickness.

  4. I understand that the viscosity of the liquid is changing, but the viscosity appears to change depending on the lenght scale we use, like the example Matt gives above.

    I understand my example is a quite far-fetched. But I'm just trying to test the limits of a claim I percieved the book to make. I suppose I was taking the limits a bit too far though.