Calculator inputs
Use consistent units for viscosity, shear rate, and time constant.
Plotly graph
The curve shows how viscosity changes across the selected shear rate range. The red marker highlights the target shear rate calculation.
Formula used
η(γ) = η∞ + (η₀ − η∞) / [1 + (kγ)m]
Parameter meaning
η(γ) is the apparent viscosity at shear rate γ.
η₀ is the zero shear viscosity at very low shear.
η∞ is the infinite shear viscosity at very high shear.
Model behavior
k controls where thinning becomes significant.
m controls how sharply viscosity drops with shear rate.
The characteristic transition rate is often estimated as 1 / k.
This model is commonly used for polymer melts, suspensions, emulsions, inks, coatings, and other shear thinning fluids where viscosity decreases as shear rate increases.
How to use this calculator
- Enter the fluid name for reference.
- Input zero shear viscosity, infinite shear viscosity, time constant, and exponent.
- Choose the target shear rate where you want the viscosity estimate.
- Define the minimum and maximum shear rate for the chart and table.
- Select log spacing for wide rheology ranges or linear spacing for narrow studies.
- Press Calculate viscosity to view the result above the form.
- Review the metrics, chart, and generated table.
- Use the CSV or PDF buttons to download the data.
Example data table
Example inputs: η₀ = 12 Pa·s, η∞ = 0.8 Pa·s, k = 0.45 s, m = 1.4
| Shear rate (s⁻¹) | Predicted viscosity (Pa·s) |
|---|---|
| 0.5 | 10.7653 |
| 1 | 9.2403 |
| 5 | 3.5237 |
| 10 | 2.0157 |
| 50 | 0.9415 |
FAQs
1. What does the Cross viscosity model describe?
It describes how a fluid’s viscosity decreases with increasing shear rate. The model connects low shear viscosity, high shear viscosity, and the transition region using a compact rheological equation.
2. When should I use this model?
Use it for shear thinning materials such as polymer solutions, melts, slurries, coatings, food products, and biological fluids when experimental data show viscosity falling smoothly as shear rate rises.
3. What is zero shear viscosity?
Zero shear viscosity, η₀, is the viscosity measured under extremely low shear conditions. It represents the fluid’s resistance to flow before strong shear thinning starts.
4. What is infinite shear viscosity?
Infinite shear viscosity, η∞, is the limiting viscosity at very high shear rates. It shows the lowest asymptotic viscosity predicted by the model when the structure is highly aligned or disrupted.
5. What does the parameter k do?
The parameter k sets the shear rate scale for the transition zone. A larger k shifts thinning behavior toward lower effective transition rates because the term kγ reaches unity sooner.
6. What does the exponent m control?
The exponent m controls how steeply viscosity drops. Higher values usually create a sharper transition between the low shear plateau and the high shear plateau.
7. Should I use linear or log spacing?
Use log spacing when your shear rate covers several decades, which is common in rheology. Use linear spacing when your study covers a narrow band and evenly spaced values are easier to interpret.
8. Can I export the results?
Yes. The page includes CSV export for spreadsheet work and PDF export for reports or sharing. Both downloads use the currently generated calculated table.