Flow Curves of a Herschel-Bulkley Fluid

​
fluid properties
yield stress
τ
0
(Pa)
5.
consistency
k (Pa
n
s
​)
2.
flow index
n
0.7
shear rate

γ
​
-1
s
​
50.
axes maxima
τ
60.
η
app
4.

γ
(
-1
s
) = 50.00 τ (Pa) = 35.92
η
app
(Pa s) = 0.72
This Demonstration lets you generate and plot flow curves of Newtonian, Bingham, and shear-thinning (pseudoplastic) fluids using the Herschel–Bulkley model. It provides visualization of the differences between Newtonian and non-Newtonian fluids and how they are affected by the yield stress, consistency, and flow index. It also shows how the apparent viscosity of non-Newtonian fluids, unlike that of Newtonian fluids, changes with the shear rate.

Details

This Demonstration plots shear stress
τ
versus shear rate

γ
and apparent viscosity
η
app
versus shear rate using the Herschel–Bulkley model,
τ=
τ
0
+k
n

γ
, where
τ
0
is the yield stress (in Pa),
k
the consistency (in
Pa
n
s
), and
n
the flow index (dimensionless). (
τ
is in Pa and
η
app
is in Pa s.) The apparent viscosity is calculated as
η
app
=τ/

γ
. When
τ
0
=0
and
n=1
, the model describes a Newtonian fluid; when
τ
0
>1
and
n=1
, the model describes a Bingham fluid, and when
τ
0
=0
and
n<1
, the model describes a pseudoplastic fluid.
The user can enter the fluid's rheological parameters,
τ
0
,
k
, and
n
, a chosen value of

γ
, and maximum values of the plots' ordinates with sliders. The panel displays the numeric values of the shear stress and apparent viscosity at the chosen shear rate and plots the corresponding
τ
versus

γ
and
η
app
versus

γ
for the chosen fluid's parameters. The points
(

γ
,τ)
and
(

γ
,
η
app
)
, whose numerical values are displayed, are also shown as movable dots on the corresponding plots.
Snapshot 1: pseudoplastic fluid (no yield stress)
Snapshot 2: pseudoplastic fluid having a high yield stress
Snapshot 3: Newtonian fluid
Snapshot 4: Bingham fluid

Permanent Citation

Mark D. Normand, Micha Peleg
​
​"Flow Curves of a Herschel-Bulkley Fluid"​
​http://demonstrations.wolfram.com/FlowCurvesOfAHerschelBulkleyFluid/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011