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With the new ingredient the shampoo has a flow index (n) of 0.081. 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 89,188 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.
6.2 The Herschel-Bulkley model
τ
τ
τ
=
+ ����̇ �� (
= shear stress,
0
The Herschel-Bulkley model is simply the Power Law model with the addition of
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
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.
The Herschel-Bulkley model should be used with non-Newtonian, time-dependent materials that have
a yield stress. Products with a yield stress only begin to flow after a certain amount of shear stress
M19-2101 REVISION 2.0
τ
0 = yield stress, �� = consistency index, ��̇ = shear rate, and �� = flow index)
0
flow behavior. Since Newtonian materials have linear shear stress vs. shear rate behavior
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
Figure 6-2
τ
for yield stress. Yield stress,
0
τ
0,
81
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