This Demonstration plots shear stress

versus shear rate

and apparent viscosity

versus shear rate using the Herschel–Bulkley model,

, where

is the yield stress (in Pa),

the

* *consistency (in

), and

the flow index (dimensionless). (

is in Pa and

is in Pa s.) The apparent viscosity is calculated as

. When

and

, the model describes a Newtonian fluid; when

and

, the model describes a Bingham fluid, and when

and

, the model describes a pseudoplastic fluid.

The user can enter the fluid's rheological parameters,

,

, and

, a chosen value of

, 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

versus

and

versus

for the chosen fluid's parameters. The points

and

, 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