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Measuring Viscosity

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Measuring Viscosity with a Zahn Cup?
Use Centistokes, not just Seconds!

By: Frank Burgos

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We all know that flexo ink has a property called “viscosity” and that it’s important to keep it under control. In basic terms, viscosity is that property that makes molasses and water flow differently when poured; they have different viscosities.

I’ve worked with folks that control viscosity exclusively “by eye” or “by the way the ink flows” and do a good job of it. I’ve done it myself. However, at some point, most of us probably use this thing we call a “Zahn cup.” There are other instruments for measuring viscosity, some automatic, but I suspect that by a large measure, the Zahn Cup is the predominant tool for measuring viscosity in a flexo pressroom. If you use automated viscosity control, and you calibrate it with Zahn cups, this applies to you, as well.

In this article I am writing specifically, and only, about Zahn Cups, which are manufactured exclusively by Paul N. Gardner Company. I’ve narrowed it to this brand because I suspect it’s what the vast majority of us use. All of the numbers and diagrams shown here are generated with formulas that GARDCO has derived and published in their instruction manuals for Zahn cups.

Measuring viscosity is usually associated with either water-based or solvent-based flexo ink, and my experience is that there is little difference in viscosity among brands for each type. This relatively narrow range of viscosities can largely be covered by just two Zahn cup numbers: the #2 or #3. The #2 tends to be used for solvent-based ink, and the #3 of tends to be used for water-based ink. A rule of thumb that I apply is that water-based ink is “thicker” than solvent-based ink, so water-based is the one with the higher number. This is not absolute, so always refer to your ink manufacturer’s recommendations.

There are two series of GARDCO Zahn cup; the S90/Zahn Signature Dip cup, and the EZ™ Zahn (ASTM) Dip cup, and within each of these series, there are #2 and #3 cups. The EZ is an improvement over the Signature, but there are folks out there that have established their procedures with the Signature series. According to GARDCO’s manual, they make both series of Zahn cups “in order to meet with past and present specification requirements.” Therefore, it makes sense to look closely at the differences, with respect to viscosity measurements, between four types of Zahn Cup: Signature Series #2, Signature Series #3, EZ Series #2, and EZ Series #3.

Before we compare the different cups, I should introduce two units of measure that we don’t encounter in everyday conversation; the poise and the stoke. I’ll paraphrase GARDCO’s literature:

    The poise is the unit of measure for a fluid’s resistance
    to flow. The poise does not consider the influence of
    gravity.

    Zahn cups employ gravity to measure viscosity. Math
    is applied to factor in gravity and the density of the fluid producing a unit of measure called the stoke. This is
    divided by 100 to provide a more useful unit of measure
    called the “centistokes”.

(I’d like to note that temperature is an important variable in the measurement of viscosity, but we will totally disregard it in this discussion. We will assume that the ink has stabilized and is at normal operating temperature.)

The centistoke is a more objective way to describe viscosity than number of seconds efflux time (the time for the ink to drain from the cup) alone. Thankfully, because the efflux time for any cup can be correlated to a viscosity value in centistokes, and vice-versa, we can use centistokes as a bridge to convert efflux times between the various cups.

Let’s say your ink manufacturer tells you to keep the viscosity at “22-28 seconds with a Signature Series #2 Zahn Cup.” I won’t go into the formulas, but incorporating them in a spreadsheet, we can convert the seconds efflux time for Zahn cups to centistokes viscosity for any cup. When I did it for this range and cup, I came up with this: Table 1

22 seconds efflux time, or the time the ink takes to drip out of the hole, using a #2 Signature Cup corresponds to a viscosity of 57.4 centistokes. 28 seconds using a #2 Signature Cup corresponds to a viscosity of 89.9 centistokes. Therefore, your ink supplier is actually suggesting you keep the viscosity between 57.4 and 89.9 centistokes no matter how you measure the viscosity! He just gave you a shortcut, because if he gives you the centistoke range, the question that follows is, “What do I measure it with, and how many seconds?”

Now, to illustrate the difference between two cups of the same number, but different series, let’s also consider the corresponding centistoke range for the EZ #2. (See Table 1b) 22 seconds efflux time using an EZ #2 cup corresponds to a viscosity of 27.6 centistokes. 28 seconds using an EZ #2 cup corresponds to a viscosity of 51.7 centistokes. Therefore, even if you keep the ink viscosity at the 28 second mark using the EZ #2, your viscosity will actually be lower (51.7 centistokes) than the minimum recommended by your supplier (57.4)! This is a serious implication.

Fortunately for the water-based folks, the differences are not as dramatic between the Signature #3 and the EZ #3. (See Table 2) For example, 12 seconds with a Signature #3 corresponds to 75 centistokes, and 72 centistokes with an EZ #3. 20 seconds with a Signature #3 corresponds to 176 centistokes, and 172 centistokes with an EZ #3. These differences are practically negligible, but technically, it’s the same problem, and I wouldn’t ignore it.

The good news is that you can, as I indicated earlier, use formulas or charts to convert efflux times between different cup types, which brings up a question I’ve heard many times: “Can I use a #2 in place of a #3, and vice-versa?”

To find out, let’s focus only on two cups in the same series; the EZ #2 and EZ #3, henceforth just #2 or #3:

For each Zahn cup, GARDCO publishes permissible operating ranges for efflux time and centistokes. It is not valid to operate outside of these ranges. (See Table 3) The lowest permissible centistoke value common to both #2 and #3 is 72, limited by the lowest permitted efflux time for the #3 of 20 seconds. The highest centistoke value common to both is 157, limited by the highest permitted efflux time for the #2 of 60 seconds. Therefore, we are bound by the range 72-157 centistokes. For the #2, this corresponds to a time range of 34-60 seconds. For the #3, it corresponds to 12-19 seconds.

Because the #3 can only substitute for the range of 34-60 seconds on the #2, the #3 is not a valid substitute for someone who operates in the 22-28 seconds range with the #2, as in the example cited earlier.

Another consequence when using a #3 in place of a #2 is the loss of precision. Note that the range of 72-155.6 is covered by a narrower range of seconds using the #3 (8 seconds) than the #2 (27 seconds).

Going the other way, (See Table 4) let’s say an average range of viscosity for water-based ink using a Signature #3 cup is 12-16 seconds. This is according to the recommendations I recall when I printed with water-based ink. The corresponding range of 75–128 correlates to 25-36 seconds for the #2, which falls completely within its valid range of 19 to 60 seconds. It does seem valid to use a #2 in place of a #3, folks! I’ve always heard that there was no correlation, so this may come as news to some of you, as well.

While the consequence of going up from a #2 to a #3 resulted in a loss in precision, dropping from a #3 to a #2 seems to actually result in a gain in precision. The range 75-128 centistokes corresponds to a range in efflux time of 25-36 seconds, or a range of 11 seconds with the #2, rather than just 5 seconds with the #3. One downside seems to be that it takes about twice the amount of time to measure with the #2.

We could play with the numbers more, but by now I think it’s clear that the implications of the slight differences between cups can be significant. I personally do not recall ever seeing viscosity referred to in terms of centistokes in our industry. I always see it referred to as “number of seconds with a Zahn cup”, and I don’t even recall mention of the type of cup. Having had a closer look, going forward I would express viscosity in centistokes, and I would document the type and number of the cup. I might go even further and begin a controlled transition toward using the EZ series, which as I indicated, is an improvement over the Signature series.

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