## Monday, June 20, 2011

### Viscosity

Viscosity is something that everyone is familiar with, but only in the most qualitative of senses. Consider these examples:
• While people can tell which liquid is more viscous than another one, no one is able to quantify it just by looking at a liquid. For instance, water has a viscosity of 1 cPs (0.001 Pa s). So name a fluid that has a viscosity twice that of water. Or looking at it differently, how much more viscous is honey than water? 2 times? 10 times? 100 times? Or even 1000 times? (Answers below).

• When the viscosity of a fluid is measured, typically only one or two significant figures are used. For instance, in some recent work for a client, they had a thick water solution with a viscosity of 350,000 cPs. There is no way that I or anyone else could measure this to 351,000 cPs or 349,000 cPs or...

• Given this, it's almost as if viscosity should be expressed after taking it's log. It's not as if any information would be lost that couldn't be recovered, but it would also make it clearer how insignificant small differences in the numbers are. Taking the numbers from the last example, log(350,000) = 5.544, while log(351,000) = 5.545 and log (349,000) = 5.543. Now instead of seeing a slight change in the third significant figure, the changes are in the fourth. Granted, I've seen people who would think a change in the eighth significant figure are significant, but most people would see the point I am making here.

• I would double down on this argument not only because of the lack of significant figures, but also because of the wide range of viscosities that are observed. We've already seen 1 cPs, but the numbers can also go up into the billions of cPs or more for viscous polymers. As is is now, it is very rare that I ever prepare a plot or see another's plot with viscosity data that isn't logarithmic on at least one axis.
Answers to the qualitative viscosity questions: A liquid with viscosity twice that of water? I don't know of any right off hand. The closest I can think of is blood, which is at about 4 cPs in normal conditions. Olive oil is about 100 times thicker, while castor oil is about 1000 times thicker. And as for honey, Wikipedia lists it as between 2000 and 10,000 times thicker than viscosity.

So now that you have these numbers, does that help calibrate your internal scale, or are you still just as lost as before? I would be shocked if things are much better. Despite working with viscosity measurements on and off for the past 21 years, it's still just a number to me.