Brookfield DV-I Prime Uživatelský manuál stáhnout pdf (Strana 32)

Brookeld Engineering Laboratories, Inc. Page 32 Manual No. M/07-022-D0613

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 uids that do not have a yield

stress. These uids will begin to ow 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 eect 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 ow index (n) of 0.08. This indicates that the

shampoo is shear-thinning enough to ow properly during processing and that it will ow

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 lling

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

II.12.2 The Herschel-Bulkley Model

(

€

= shear stress,

€

= yield stress, k = consistency index, = shear rate, and n = ow index)

What does it tell you?

The Herschel-Bulkley model is simply the Power Law model with the addition of

€

for yield

stress. Yield stress,

€

, denotes how much shear stress is required to initiate ow. This model also

provides a consistency index, k, which is a product’s viscosity at 1 reciprocal second, and a ow

index, n, which indicates the degree with which a material exhibits non-Newtonian ow behavior.

Since Newtonian materials have linear shear stress vs. shear rate behavior and n describes the

degree of non-Newtonian ow, the ow index essentially indicates how “non-linear” a material

is. For Herschel-Bulkley uids, 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.

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