83
4
5 Bingham Plastic Fluids—These fluids exhibit a yield stress that
must be exceeded before flow starts. Tooth paste, oil paints, etc.
show such behaviour.
5 Pseudoplastic Fluids—The viscosity of pseudoplastic fluids
decreases with an increase in shear rate. Molten polymers have
this characteristic. Pseudoplastic fluids are used to advantage
in injection moulding as the viscosity of the melt further
decreases when the material flows through small cross-sectional gates.
5 Dilatant Fluids—In these fluids, the apparent viscosity
increases with an increase in the shear rate. Dilatant fluids are
also referred to as shear-thickening fluids (STF). Cornstarch
mixed in water is an example of a dilatant fluid.
4.1.1.3 Viscometric Models
The following viscometric models for different type of fluids have
been developed:
5 Power Law Model—This model requires two parameters to
characterize any polymer. The power law model was developed
by Ostwald-de-Waele and is applied for shear-thinning and
shear-thickening fluids only. The equation governing this
model is
τ
γ
= m
n
(4.3)
where
5 m = Consistency index
5 n = Power law index
5 If n = 1, then m = η, then it is Newtonian fluid
5 If n > 1, then it is shear-thickening fluid
5 If n < 1, then it is shear-thinning fluid
5 Eighty to eighty-five percent of polymers have shear-thinning
behaviour upon melting, and the value of n for them varies
from 0.4 to 0.7.
5 Truncated Power Law—This model requires three parameters
to characterize any polymer. This law is written as
η η
= 0
(4.4)
for
γ ≤
γ 0
η η
γ
γ
=
−
0
0
1
n
(4.5)
for
γ ≥
γ 0
where
5 η = Viscosity
5 η 0 = Initial viscosity
5
γ = Shear rate
5
γ 0 = Initial shear rate
Point to Ponder…
Shear-thickening fluids have a
potential use in protective armour
against stabs and bullets due to
their property of thickening with
increased shear rate.
4.1 · Fundamentals of Rheology
4
5 Bingham Plastic Fluids—These fluids exhibit a yield stress that
must be exceeded before flow starts. Tooth paste, oil paints, etc.
show such behaviour.
5 Pseudoplastic Fluids—The viscosity of pseudoplastic fluids
decreases with an increase in shear rate. Molten polymers have
this characteristic. Pseudoplastic fluids are used to advantage
in injection moulding as the viscosity of the melt further
decreases when the material flows through small cross-sectional gates.
5 Dilatant Fluids—In these fluids, the apparent viscosity
increases with an increase in the shear rate. Dilatant fluids are
also referred to as shear-thickening fluids (STF). Cornstarch
mixed in water is an example of a dilatant fluid.
4.1.1.3 Viscometric Models
The following viscometric models for different type of fluids have
been developed:
5 Power Law Model—This model requires two parameters to
characterize any polymer. The power law model was developed
by Ostwald-de-Waele and is applied for shear-thinning and
shear-thickening fluids only. The equation governing this
model is
τ
γ
= m
n
(4.3)
where
5 m = Consistency index
5 n = Power law index
5 If n = 1, then m = η, then it is Newtonian fluid
5 If n > 1, then it is shear-thickening fluid
5 If n < 1, then it is shear-thinning fluid
5 Eighty to eighty-five percent of polymers have shear-thinning
behaviour upon melting, and the value of n for them varies
from 0.4 to 0.7.
5 Truncated Power Law—This model requires three parameters
to characterize any polymer. This law is written as
η η
= 0
(4.4)
for
γ ≤
γ 0
η η
γ
γ
=
−
0
0
1
n
(4.5)
for
γ ≥
γ 0
where
5 η = Viscosity
5 η 0 = Initial viscosity
5
γ = Shear rate
5
γ 0 = Initial shear rate
Point to Ponder…
Shear-thickening fluids have a
potential use in protective armour
against stabs and bullets due to
their property of thickening with
increased shear rate.
4.1 · Fundamentals of Rheology