Brookfield DV-I Prime - Manual (Page 34)

Brookfield Engineering Laboratories, Inc. Page 34 Manual No. M/07-022-D0613
II.12.3 The Bingham Model
€
t =
€
t
o
+ hD (
€
t
= shear stress,
€
t
o
= yield stress, h = plastic viscosity, and D = shear rate)
What does it tell you?
The Bingham model indicates a product’s yield stress,
€
t
o
, which is the amount of shear stress
required to initiate flow. It also provides the plastic viscosity,
h
, which is the viscosity after a
product yields.
Figure II-45
When should you use it?
This model should be used with non-Newtonian materials that have a yield stress and then behave
in a Newtonian fashion once they begin to flow. As a result, the shear stress-shear rate plot forms
a straight line after yielding. (Products that have a yield stress only begin to flow after a certain
amount of shear stress is applied. They are also called “viscoplastic”. Their shear stress vs. shear
rate graphs intersect the y-axis at a point greater than 0.)
An Example of the Bingham Model at Work
A manufacturer of drilling fluid applies the
Bingham Model to ensure the quality of their
product. Results from a recent batch, shown
in Figure II-45, showed that the yield stress
and plastic viscosity were both below the
pass/fail criteria, which would cause the fluid
to insufficiently hold-up the cuttings. The
shipment was cancelled and the root-cause
of the problem was identified.
Drilling Fluid
Plastic Viscosity (
h
) = 6621 cP
Yield Stress (
€
t
o
) = 166.4 dynes/cm 2