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6.1 The Power Law (Ostwald) model
τ
τ
=����̇ �� (
= shear stress, �� = consistency index, ��̇ = shear rate, and �� = flow index)
What does it tell you?
The Power Law model provides a consistency index, k, which is a product's viscosity at one reciprocal second.
(Reciprocal seconds are the units of measurement for shear rate). It also provides a flow index, n, which indicates
the degree with which a material exhibits non-Newtonian flow behavior. Since Newtonian materials have linear shear
stress vs. shear rate behavior and v describes the degree of non-Newtonian flow, the flow index essentially indicates
how "non-linear" a material is.
When n < 1 the product is shear-thinning or Pseudoplastic. This means the apparent viscosity decreases as shear
rate increases. The closer n is to 0, the more shear thinning the material is.
When n > 1 the product is shear-thickening or Dilatant. Their apparent viscosity increases as shear rate increases.
When should you use it?
This model should be used with non-Newtonian, time-independent fluids that do not have a yield stress. These fluids
will begin to flow under any amount of shear stress. Graphs of such material generally intersect the y-axis at 0.
An Example of the Power Law Model at Work
Formulators at a personal care company would
like to use a substitute ingredient to decrease
cost. They use the Power Law model to evaluate
the effect the new ingredient will have on the
behavior of their shampoo. They need to know
how it will behave during processing and how it
will behave when it is being used by the customer.
M19-2101 REVISION 2.0
Figure 6-1
D V N E X T R H E O M E T E R - O P E R AT I O N A L M A N U A L
Shampoo
Flow Index (n) = 0.081
Consistency Index (k) = 89,188 cP
80
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