Brookfield Engineering Labs., Inc.
Page 80
Manual No. M13-167-A0415
VII. MATH MODELS
VII.1 The Power Law (Ostwald) Model
(
τ
= shear stress,
k
= consistency index,
= shear rate, and
n
= 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
n
describes the degree of non-Newtonian flow, the flow index essentially indicates how “non-
linear” a material is.
Figure VII-1
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.
