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Why Can’t I Get a Reliable Viscosity Measurement on My Thixotropic Fluid with a Zahn Cup? – Part III

Posted by Mike Bonner

Aug 13, 2019 4:14:00 PM

In Part II of this series, we continued our discussion on viscosity by tackling the topic of thixotropy.  With this defined, we can now circle back to bring it all together and show how different measurement methods produce different results and how our measurement choices can actually work against us.

The Cup Measurement Process

The fundamental cup measurement process is straightforward.  The cup is fully submerged in the fluid and pulled straight up and out.  The time that it takes for the fluid to drain from the cup defines the viscosity in “cup seconds”.

Seems simple enough, right?  But as we noted in Part I of this series, there are a host of problems associated with this simple process.

When do I start timing?  When the top of the cup breaks the surface?  When the bottom of the cup clears the surface? 

And when do I stop?  When the stream first breaks?  When it breaks into droplets?  When the cup is empty?

And, if the cup is not pulled straight up, it affects the flow through the orifice by diverting the pressure on the orifice to the wall of the cup. So, how straight is straight?

It’s east to see why different operators get different readings.

So, let’s look at what’s really happening behind the scenes…

The Physics Behind Cup Measurements

When the cup is drawn out of the fluid it is full.  The volume of liquid in the cup exerts a force on the fluid at the hole due to gravity.  Given our discussion in Part I of this series, this is the basic definition of Kinematic Viscosity.  There is also the weight of the atmosphere pressing on the surface of the fluid, but that is a constant for any given location (mostly due to elevation) and cup variety (volume, diameter, hole size, etc.), so we can ignore that in our discussion.

As gravity pulls downward on the fluid it is “forced” through the hole.  As a result, some shear is introduced into the fluid.  But this “force” is determined by the volume in the cup – and that is decreasing over time, which means that the force on the fluid passing through the hole is also decreasing over time.  As a result, the shear on the fluid also decreases.

figure 2The next really important question is, “Is there enough force/shear to fully shear-thin the material?”  Referencing Figure 2 in Part II of this series, this means moving it through the First Newtonian Range, through the transition range (in the middle), and into the Second Newtonian Range far enough to reach a stable viscosity.  If you’re thinking about the volume of fluid in the cup, the size of the orifice, the time it takes to pass the fluid through that orifice and thinking that it’s pretty unlikely that we are going to get out of that First Newtonian Range, much less reach the Second Newtonian Range, you have got a pretty good grasp of our discussion so far!

So, what if the shear does make it through the First Newtonian Range, only to fall somewhere in the middle transition range?  If you said that the measurement results will be unstable and unreliable because of the interaction between shear and viscosity, you would be correct.  And this is another reason that cup measurement results vary – through absolutely no fault of the operator.

Why Doesn’t My Cup Measurement Match My Automated Viscometer

This is a common question posed to virtually all viscometer manufacturers (no, we are not alone – and yes, we do talk!)  But, after this discussion, it is probably easier to understand that automated viscometers measure viscosity by measuring the force required to introduce shear into the fluid – much in the way that Newton defined viscosity in the first place.  It is much easier for a mechanical viscometer to introduce shear into the fluid than it is for gravity.

Another interesting fact is that most viscometers are calibrated with Newtonian fluids – calibration standards designed to be very consistent and predictable in their performance (read: viscosity) over both shear and temperature.  If you measure a Newtonian fluid with both a mechanical viscometer and a cup, the measurements will be very close – because shear is not a factor.  But Non-Newtonian fluids are a very different story.

When is a Viscosity Measurement Useless?

Given the known impact of viscosity on the outcome of our fluid dispensing processes, this may seem like a silly question.  But practically speaking, a great many of the viscosity measurements that we take are useless.

So, when is a viscosity measurement useless?

When the viscosity of the fluid is measured under conditions that are not the same, or even remotely similar to those the fluid will encounter in our process!  And given our discussion of Newtonian and Non-Newtonian fluids and the effect of shear – both on our measurements and on our process outcome, it is fairly easy to conclude that a cup measurement rarely replicates modern process conditions.

Then Why Cup Measurements?

By now you’re probably back to where we started, asking yourself, “If all this is true, why are cup measurements what everyone depends on to manage their process?”

And it’s a fair question.

Cup measurements have been around for a long time – far longer than the complex fluids that most of us use in our processes today.  And, when compared to sophisticated measurement systems, cups are cheap.  And cup readings don’t take more than a minute or two to take, so the measurements are cheap.

Which brings us to the age-old rule that “You get what you pay for!”

The fact is that we need to identify the measurement that accurately predicts how our fluid will perform in our process.  Implement it.  And stick to it.


1 – Graphs courtesy of Sofraser

Topics: Zahn cups, Efflux Cups, fluid process control, viscometers, viscometry, non-newtonian fluids

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