Use this procedure to compare the Power Law, Bingham Plastic, Herschel-Bulkley, and Casson models against tabulated shear rate–shear stress data, then select a model that matches both the curve fit and the measured behavior of the non-Newtonian fluid.
Use this when
Use this procedure when laboratory or supplier data provide paired shear rate and shear stress values and you need to create a non-Newtonian fluid entry in FluidFlow. Model selection is a curve-fitting exercise, but statistical fit is not the only criterion: the selected model must also represent whether the fluid has a measured yield stress and whether the post-yield relationship is linear or non-linear.
Before you start
Prepare:
Tabulated shear rate and shear stress data for the fluid.
The temperature at which the rheology data were measured. FluidFlow non-Newtonian viscosity definitions is based on a single temperature dataset; if temperature variation is significant, create separate fluid entries for the relevant temperatures.
A measured yield stress, in Pa, when available. FluidFlow can alternatively calculate yield stress by extrapolating the entered rheology data.
The other fluid properties required to complete the non-Newtonian fluid entry, including density.
Model selection basis
Candidate model | Relationship represented | Yield stress included? | Use as a candidate when |
Power Law | Non-linear shear rate–shear stress curve starting at the origin | No | The dataset shows no yield stress. |
Bingham Plastic | Linear relationship after the yield point | Yes | The fluid requires a yield stress to initiate flow and the post-yield data are approximately linear. |
Herschel-Bulkley | Yield stress plus non-linear power-law behavior | Yes | The fluid has yield stress and the post-yield relationship is non-linear. |
Casson | Yield pseudoplastic relationship | Yes | The Casson curve is consistent with the dataset and the application basis supports use of this empirical model. |
Steps
Open Database → Fluids, select Add, and assign a unique name to the new fluid entry.
Set Fluid Type to Non-Newtonian Liquid.
Define the available fluid properties, including density. Use property data corresponding to the same fluid condition represented by the rheology dataset.
Under Liquid Viscosity, select the tabulated shear rate–shear stress data option rather than entering rheology constants directly.
Enter the shear rate–shear stress pairs manually or import the available CSV file. Confirm that the plotted data points reproduce the supplied dataset before comparing models.
Set the yield stress basis:
Select User-Defined and enter the measured yield stress when viscometry provides it.
Select Calculated when no measured value is available and FluidFlow must extrapolate yield stress from the entered points.
Change Curve Fit Type through each plausible model: Power Law, Bingham Plastic, Herschel-Bulkley, and Casson. Record the displayed coefficient of determination, R², for each fit.
Inspect the fitted tracing line against the experimental points. A better fit passes through more of the supplied points, while an R² value approaching 1.0 indicates stronger agreement between the data and the fitted equation. Use both checks.
Reject any statistically strong fit that contradicts the measured behavior:
Do not select Power Law if the fluid has a measured yield stress, because Power Law starts at the origin and does not represent yield stress.
Use Bingham Plastic only when the post-yield relationship is linear.
Use Herschel-Bulkley when yield stress is present and the post-yield relationship remains non-linear.
Retain Casson only when its yield-pseudoplastic form is consistent with the data and application.
Select the candidate that provides the best combined agreement with the R² value, the plotted tracing line, and the known yield-stress behavior. Save the fluid entry.
If two models remain credible, create a separate FluidFlow fluid entry for each and run sensitivity cases in the hydraulic model. Compare how the selected rheology model changes the system results before fixing the design basis.
In Summary
Use the plotted fit, R-squared, and yield behavior together. If two candidates remain credible, compare their hydraulic results in sensitivity cases.
Where this goes wrong
Failure | What it produces | Correction |
Selecting Power Law for a fluid with yield stress | A curve constrained to start at the origin even though the fluid requires finite shear stress before flow | Use a yield-stress model and compare Bingham Plastic, Herschel-Bulkley, and Casson. |
Using visual fit alone | A subjective selection when two curves appear similar | Compare the displayed R² values as well as the tracing lines. |
Using one fluid entry across significant temperature variation | A rheology definition tied to one temperature dataset applied beyond that condition | Create separate entries for the relevant temperatures and compare the results. |
Treating two similarly good fits as interchangeable | Unquantified uncertainty in calculated friction loss because the models use different correlations | Create separate entries and run sensitivity cases. |
Try It With Your Own Fluid Data
Enter your shear rate–shear stress dataset in FluidFlow and compare all four models side by side before you fix the design basis.