Brookfield DV2+Pro Viscometer - Manual (Page 58)

Brookfield Engineering Labs., Inc. Page 58 Manual No. M03-165-F0612
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 be the consumer
With the new ingredient the shampoo has a flow index (n) of 0.08. This indicates that
the shampoo is shear-thinning enough to flow properly during processing and that it
will flow properly for the end-user. The consistency index, k, indicates how the shampoo
behaves when it experiences low shear rates. The power law values show that the shampoo
becomes quite thin at process shear rates and therefore it can be easily pumped into filling
equipment, hold tanks, etc. The consistency index of 91,071 cP shows that the shampoo
is very viscous at low shear rates, and as a result, it will appear to customers to be “rich
and creamy” while still being easy to apply.
Shampoo
Flow Index ( n) = 0.08
Consistency Index (k) = 91071cP
V1.3.2 The Herschel-Bulkley Model
(τ
°
= shear stress,
τ
°
= yield stress, k = consistency index, = shear rate, and n = flow index)
What does it tell you?
The Herschel-Bulkley model is simply the Power Law model with the addition of
€
t
o
for yield
stress. Yield stress, τ
° , denotes how much shear stress is required to initiate flow. This model also
provides a consistency index, k, which is a product’s viscosity at 1 reciprocal second, and 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. For Herschel-Bulkley fluids, n will always be greater than or less than 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. It’s apparent viscosity increases as shear
rate increases.