Developing comparable test methods using dissimilar equipment

This article applies to: All Brookfield laboratory viscometers

Occasionally, you may need to compare viscosity results taken on your viscometer to other viscosity results from a different Brookfield device, a different test method, or potentially even a different manufacturer’s device entirely. This article covers the basic process for determining if you are able to quantitatively compare results from differing instruments and methods, and how to design test methods to give equivalent results to existing data.

This article will reference tables and figures in Appendix A of More Solutions to Sticky Problems.

Newtonian fluids versus non-Newtonian fluids

Newtonian fluids are fluids whos viscosity is independent of the shear rate of the test. Comparing measurements from differing test methods or instruments is quite easy if the fluid is known to be perfectly or very closely Newtonian, since the viscosity should be the same in both test cases no matter the measurement method.

Non-Newtonian fluids are fluids whos apparent viscosity is dependent on the shear rate of the test. Some fluids can be very minorly non-Newtonian and only undergo very small viscosity changes, and others can undergo extreme changes in viscosity over a relatively small range of shear rates. When comparing viscosity results between dissimilar test methods carried out on non-Newtonian fluids, extra care must be taken to properly compare or equate the results. The rest of this article assumes that the test or tests are being carried out on non-Newtonian fluids.

Shear rate as a method of comparison

The easiest way to quantitatively compare viscosity readings taken with dissimilar instruments or measurement methods would be to look at the shear rate of the measurement. The basic unit of “test force” is measured by the shear rate, which is dependent on the geometry and test speed of any measurement, which is constant for any given spindle and speed combination.

For non-Newtonian fluids, the apparent viscosity changes as a function of shear rate, so using this variable to compare dissimilar measurement methods is the most convenient.

Brookfield spindles with known shear rate constants

Some, but not all, of Brookfield’s spindles or accessories have known well-defined shear rate constants that can be used to determine the shear rate of a test. Most notably, standard spindles in the shape of a disk that are supplied with Brookfield laboratory viscometers (s01 through s06, s62, s63) do not have a known well-defined shear rate constant. These disk shaped spindles cannot be used if the results need to be compared with results from a dissimilar test method.

Spindles that are cylindrical in shape, or are part of a concentric-cylinder geometry such as small-sample adapter kits or the ULA do have a known well-defined shear rate constant. Standard cylindrical spindles s61, s64, and s07 (and optional spindles LV-2C s66 and LV-3C s67) should only have their shear rate calculated when used without the guard leg. All of these spindles can be used to generate results that can be quantitatively compared with results from dissimilar test methods, given certain conditions.

Shear rate constants in More Solutions to Sticky Problems are given as a function of spindle RPM. For example, the LV-1 spindle s61 has a defined shear constant of 0.220N, where N is the spindle RPM. Solving this simple equation gives you the shear rate of the current test in units of reciprocal seconds (1/s).

For a comprehensive list of spindles and accessories that have or do not have shear rate constants known, as well as a listing of said constants, see Appendix A of the document More Solutions to Sticky Problems.

Developing comparable measurement methods

Determining the target shear rate

When making comparisons between measurements taken using different test methods, the first step will always be to determine the shear rate of the original test you are trying to replicate. In some cases where viscosity reporting best practices are followed, the shear rate will be given. In other cases, you may have to calculate the shear rate on your own given other information. Let’s pretend you are trying to measure some incoming material, and the supplier gives the information below:

Resin batch 174a, 5340cP at 50°C, spindle LV-4 at 60RPM on LVDV1M

From the above information, we can see that the spindle s64 is used at a spindle speed of 60RPM. This is all we need to calculate the shear rate of this test. Taking the shear rate constant for the s64 spindle and substituting 60RPM for N, we get a shear rate of 0.209*60RPM = 12.54 1/s.

Determining required spindle RPM

Once you know the shear rate of the test you are trying to replicate, you can determine if you have the required units or spindles to perform a comparable test. Let’s pretend you have only an RV torque DV2T instrument, the set of standard RV spindles, and a small sample adapter kit with 2 common spindles, s18 and s27. Immediately, you can disregard spindles s01 through s06 in the standard spindle set, as these do not have defined shear rate constants, as discussed above. This leaves only s07, s18, and s27 as options for developing your comparable method. (Spindle s18 and s27 must be used with the matching SC4-13R sample chamber for the remainder of this analysis to remain true. The spindles are referenced as simply their spindle number for simplicity)

Using the shear rate of the test to replicate as well as the shear rate coefficients of the above 3 spindles, you can determine the spindle RPM’s required to match the desired shear rate by dividing the desired shear rate by the new spindle numerical shear constant (as a number, disregarding the “N”) For example, we can look at the s18 spindle, which has a shear rate constant of 1.32N. The equation would be (12.54 1/s)/1.32 = 9.5 RPM.

Determining measurement ranges from required RPM

Once you know the required spindle speed to replicate the shear rate of the test you are replicating, you can use what you’ve learned in the knowledge base article Calculating Measurement Ranges and Tolerances to calculate the minimum and maximum viscosity you would be able to measure with that spindle and speed combination. If any of those ranges encompass the expected viscosity of the sample, then congratulations, you’ve found an equivalent test method! Let’s look at the table below to see the possible test methods for the 3 spindles on the RV torque DV2T in our example:

Given the above information, the small-sample adapter spindle s27 with the small sample adapter kit would be a good candidate for performing a comparable test to the one performed at the supplier’s facility. The expected viscosity of 5340cP falls in range of the measurement at a moderate torque. One would expect to measure similar viscosities to the ones found on the viscosity report if the temperature is also controlled accordingly.

Regarding exact shear rate matching

Since the DV2T instrument is only able to control at whole-number RPM’s above 10RPM, you need to round the required RPM’s from 36.9RPM to 37, but that represents an insignificant change in the overall shear rate of the measurement. The supplier’s test has a shear rate of 12.54 1/s, and this comparable test with an s27 spindle would have a shear rate of 12.58 1/s. There is not one single guideline for how close is “close enough” when it comes to matching shear rates like this, though. The acceptable range of “close” matched shear rates would depend heavily on the specific sample properties, and would need to be determined experimentally if a rigorous proof is required.

Important notes

Following this method does not guarantee an exact match between dissimilar test methods. This is simply a framework to develop approximately equivalent test methodologies for basic comparison. There are several factors that could result in discrepancies when measuring materials using dissimilar methods, none of which are easily explained or accounted for in this format. Feel free to reach out to technical support with additional questions.