# Shear viscosity and Capillary Rheometer

1. Feb 15, 2015

### fog37

Hello Forum,

I have some conceptual doubts about shear viscosity and would like some help if possible. In general, viscosity depends both on temperature and on shear forces (more strongly on shear forces).

"Shear viscosity" is the viscosity that a molten plastic assumes when the molten fluid is subjected to shear forces that put it in motion, make the fluid layers slide one over the other. This happens when the molten plastic is pushed through a channel/pipe or mixed it. For most fluids, the shear viscosity decreases with shear (thinning).

That said, a capillary rheometer is the device used to measure shear viscosity versus shear strain rate (1/s). This device pushes the molten plastic through a small orifice once a certain pressure is applied at the top. Based on the molten plastic output flow rate, the shear viscosity is calculated. Inside a cylindrical pipe the molten plastic assumes a parabolic profile (more or less). This velocity profile represent the velocity gradient. The v gradient is related to the shear rate of deformation of the plastic. The smaller v gradient the less the fluid layers interact with each other. By knowing the shear strain rate of deformation and the shear forces we can determine the viscosity (slope of the graph).

How does the capillary rheometer calculate the shear stresses? Indirectly, by knowing the pressure applied at the top of the molten plastic?

How does the output flow rate from the rheometer orifice relate to the v gradient and to the shear strain rate of deformation? The larger the output flow rate the larger the strain rate?

thanks!
fog37

2. Feb 15, 2015

### Staff: Mentor

Hi fo37,

What is the context of your questions? Is this for schoolwork, or for measurements in your company's lab?

3. Feb 15, 2015

### Staff: Mentor

In the capillary rheometer, you are trying to determine the shear stress at the wall as a function of the shear rate at the wall. The shear stress at the wall is related to the pressure drop by (neglecting the exit effect):

$$\tau = \frac{DΔP}{4L}$$
Determining the shear rate at the wall from measurements of the flow rate and wall shear stress is done by well-established techniques. As a first approximation, the shear rate at the wall is just the Newtonian result, 8V/D. However, this is usually not accurate enough. The techniques for determining the shear rate at the wall are discussed in any book on rheology. Google Rabinowitch equation.

If you have a commercial viscometer, it should come with a users manual. You can also probably Google Capillary Viscometer or Capillary Rheometer and get the gory details.

Chet

4. Feb 16, 2015

### fog37

Thank you Chet.

So, to calculate the shear viscosity we need data for the shear stress and shear strain which are indirectly obtained. It makes sense that the normal compressive pressure at the top will induce shear, tangential forces at the wall of the channel. But exactly at the wall the molten polymer should adhere to the wall (non slip condition) no matter the type of viscosity, correct?

The melt index (or MFI or MFR) is a parameter calculated at a single shear stress condition and serves to compare polymers of the same family (the lower MFI the more viscous). Comparing the MFI of different polymers can be misleading, correct?

Some polymers are not rated using MFI but using IV (intrinsic viscosity of solution viscosity). Do you know why?

best,
fog37

5. Feb 17, 2015

### Staff: Mentor

No. Shear rate, not shear strain.
Yes. So?
Yes, sometimes. It's a quick and dirty method.
You need to get yourself a textbook on Polymer Science. Otherwise, you are wasting your time speculating about these things.

IV is a measure of the molecular weight of the polymer. It is related to the zero shear viscosity of the polymer, but doesn't relate to either shear thinning behavior of the polymer or to polymer viscoelasticity.

Chet