How does the viscosity of a fluid change with temperature in a rotating system?

[pyroknife]

I was reading an example problem in my fluid mechanics textbook that talks about the difference between liquids and gases. I am not sure why this is the case, if someone can explain that'd be great.

So the problem is about two coaxial cylinders that rotate. There is a fluid in the gap between these 2 cylinders. The cylinders rotate and a constant shear stress is maintained, which warms up the fluid. One of the walls (it does not mention which) of the fluid is insulated thermally. The other is at room temp. In the problem, it states that for a LIQUID, the temperature increases, viscosity decreases and velocity increases as time increases for the insulated wall. So here I don't understand why the viscosity decreases. Can someone explain? Since it's constant shear, velocity has to increase because velocity and viscosity are inversely proportional.

The example then goes on to say that for a GAS, everything is backwards (i.e., visocisty increases, velocity decreases), except the temperature of the insulation wall still increases.
Why the difference? Does it have something to do with the way molecules are arranged in the 2 fluids?

 

[olivermsun]

It's kind of an interesting reason. Gases don't have much interaction between molecules, except for momentum transfer via collisions. Higher temps mean more particle velocity, hence more frequent collisions and greater interaction. On the other hand, liquids have significant intermolecular forces. Higher temps and more particle velocity mean shorter "encounters" (when the forces are significant) between molecules, hence lesser interaction.

 

[pyroknife]

Interesting but why does higher temp mean more particle velocity?

 

[olivermsun]

See: Kinetic theory of gases.

 

[Chestermiller]

I don't think they are talking about particle velocities. I think they are talking about the velocity of the natural convection currents that develop in the system, as hot fluid rises near the insulated wall and cold fluid descends near the colder constant temperature wall. I'm guessing you are learning about natural convection heat transfer in your course.

 

[olivermsun]

I was responding to the OP's questions about the temperature dependence of viscosity in liquids vs. in gases, which is dependent AFAIK on particle interactions.

As for the fluid velocities, I don't think convection needs to be invoked; usually this setup is posed as a straight viscosity-shear stress problem.

 

[Chestermiller]

I was responding to the OP's questions about the temperature dependence of viscosity in liquids vs. in gases, which is dependent AFAIK on particle interactions.

As for the fluid velocities, I don't think convection needs to be invoked; usually this setup is posed as a straight viscosity-shear stress problem.

You probably interpreted it correctly. I was just guessing at some possibly underlying questions. After all, he did say that the fluid was heating viscously and that one wall was maintained at the initial cool temperature, while the fluid near the other insulated wall was presumably hotter.

 

[olivermsun]

There are definitely some intriguing possibilities if the temperature differences or the cylinder speed differential become large!