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Making Use Of Models: The Power Law (or Ostwald) Model

Making Use Of Models

I’m a big fan of rheological models for benchmarking and profiling products; they allow you get numbers from graphs – great for QC – and they make competitor-comparisons and market-benchmarking a whole lot easier.

The Power Law model (sometimes known as the Ostwald model) is an easy-to-use model that is ideal for shear-thinning, relatively mobile fluids such as weak gels and low-viscosity dispersions. The model is nothing more than the Newtonian model, with an added exponent on the shear rate term:

Rehology models

 

K is often known as the consistency coefficient. This describes the overall range of viscosities across the part of the flow curve that is being modelled.  Also, if the Power Law region includes 1s-1 shear rate then K is the viscosity or stress at that point. The exponent n is known as the Power Law Index (or sometimes the Rate Index). For a shear thinning fluid: 0<n<1. The more shear-thinning the product, the closer n is to zero.
Examples of Power law Model fits on viscosity/shear rate profiles of two cosmetic emulsions are shown below:



Power Law Model fits for two cosmetic emulsions

Try it for yourself. Run a shear rate sweep (say 0 to 100s-1 over three minutes) on a sample and fit the Power Law model. Now compare the numbers you get to another formulation or a competitor.
If you are getting a poor fit then you may not be obtaining “equilibrium” results. Try extending the time period of the test or running the profile in reverse.
If you need to obtain Power Law data for your products and you don't have your own rheometer then my rheology analysis service may be for you.

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