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Brookfield Engineering

Rheology School

Neil Cunningham, Rheology School
www.rheologyschool.com

Looking for a quick and easy way to benchmark your products and compare them to those of your competitors? Well a single point viscosity test is a start but for a shear-thinning fluid it doesn't give you the whole picture, i.e. how the viscosities of products compare over a range of spindle speeds or shear rates.

Often two products that give similar single-point viscosity readings - say 1200 mPa.s (1200 cP) with spindle 3 at 10 rpm - will exhibit differing flow properties in the "real world". If you've ever over-ruled the results of a viscosity test because the appearance of the sample contradicted what the viscometer was telling you then you'll know what I mean; the visual assessment - what it's "really" like when you swirl, pour or spoon it, for example - may impose completely different degrees of shear to the sample than those applied in the viscometer test spec. A multi-point flow curve, over a range of speeds or shear rates, will often reveal any rheological differences between products that are not immediately apparent in a single-point test.

Once we can do this we can then quantify those differences with a simple rheological model. One such is the Power Law (or Ostwald) Model. This will fit a typical viscosity vs shear rate or stress vs shear rate curve within the range of about one to a few hundred reciprocal seconds. The Power Law model takes the form of:

So what does it tell us? Well, the Power Law model gives us two parameters:

Power Law Index (or Flow Index) h: This is, in essence, a measure of non-Newtonian-ness. For a Newtonian fluid Power Law Index = 1; for a shear-thinning fluid it is between 0 and 1 and for a shear thickening fluid it is greater than 1.

Consistency K: This is no more than the viscosity (or stress) at a shear rate of 1s-1. I like to think of it as the point the viscosity/shear rate curve "hangs from".

Graph 1 illustrates how Power Law Index and Consistency values relate to flow curve shape:

Here's a typical example of the usage of this method:

Three samples of moisturising lotions were evaluated: a premium market leading brand, a mid-market brand and an economy brand. The following test method was employed:

  • Instrument: Brookfield RVDVIII Ultra rheometer fitted with a Small Sample Adaptor and spindle/chamber SC4-15/7R (the small sample adaptor enables us to apply a defined shear rate to the sample)
  • Temperature: 25° C
  • RPM down-ramp: 50, 40, 30, 20, 10, 5, 2.5, 1.5. 1 min hold at each speed before recording viscosity value
  • Plot Viscosity vs Shear Rate.
  • If using RheoCalc software, click on Analysis Tab and fit Power Law Model.

By plotting on logarithmic axes it is much easier to compare highly shear-thinning products:

The model provided the following outputs:

Sample Consistency (Pa·s) Power Law (Flow) Index
Premium 63.9 0.16
Mid-Market 34.1 0.27
Economy 24.7 0.15

It is particularly interesting to note that, while the Premium brand has a higher viscosity than the Mid-Market brand over the measured range of shear rates it is also significantly more shear-thinning (lower Power Law Index) so the flow curves would be expected to cross over at higher shear rates. As processes such as filling, pumping and spreading on the skin are all generally high shear rate processes it is then evident that we cannot simply predict those flows from the viscosity at, say, 5 s-1 (about 10 rpm in this case).

In summary the use of viscosity profiling methods in conjunction with quantification of the curves using a rheological model is very important for understanding and controlling how a fluid product will perform in the "real world" of usage.