Calculator inputs
Example data table
| η∞ (Pa·s) | K | n | γ̇ (s-1) | Predicted η (Pa·s) | Comment |
|---|---|---|---|---|---|
| 0.020 | 1.250 | 0.62 | 1 | 1.270 | Near low-shear region. |
| 0.020 | 1.250 | 0.62 | 10 | 0.541 | Viscosity drops as shear rises. |
| 0.020 | 1.250 | 0.62 | 50 | 0.304 | Strong shear-thinning zone. |
| 0.020 | 1.250 | 0.62 | 100 | 0.247 | Approaching high-shear trend. |
| 0.020 | 1.250 | 0.62 | 1000 | 0.110 | Closer to η∞ limit. |
Formula used
Sisko model: η = η∞ + Kγ̇n−1
Shear stress: τ = ηγ̇
Kinematic viscosity: ν = η / ρ
Here, η is apparent viscosity, η∞ is the infinite-shear viscosity, K is the Sisko coefficient, γ̇ is shear rate, n is the flow behavior index, τ is shear stress, and ρ is density.
How to use this calculator
- Enter the Sisko model constants η∞, K, and n.
- Type the target shear rate for the main result.
- Add density if you also need kinematic viscosity.
- Choose a graph range and the number of plot points.
- Click Calculate viscosity to show the result above the form.
- Review the graph and generated table.
- Use CSV or PDF export for reporting.
Frequently asked questions
1) What does the Sisko model describe?
It describes non-Newtonian fluids whose apparent viscosity changes with shear rate and tends toward a limiting high-shear viscosity. It is useful for polymer melts, suspensions, and many shear-thinning materials.
2) What happens when n is less than 1?
When n is below 1, the power term decreases with rising shear rate. That means the fluid shows shear-thinning behavior, so apparent viscosity falls as deformation rate increases.
3) Why must shear rate stay above zero?
The formula includes γ̇ raised to the power n−1. For many practical Sisko fits, especially with n below 1, a zero shear rate can create undefined or nonphysical values.
4) What is η∞ in practical terms?
η∞ is the viscosity limit reached at very large shear rates. It represents the residual viscosity after the shear-dependent contribution becomes much smaller.
5) Why is density optional here?
Density is only needed if you want kinematic viscosity. Dynamic viscosity comes directly from the Sisko equation, but converting to m²/s or cSt requires dividing by density.
6) What units should I use for K?
Use a value consistent with your fitted Sisko equation and the chosen SI input framework. Because K is linked to the exponent n, its dimensional form depends on the model fit.
7) What does the graph help me see?
The graph shows how viscosity changes over the chosen shear-rate range. It helps you compare operating regions, detect strong shear-thinning, and report behavior more clearly.
8) When should I export CSV or PDF?
CSV works well for spreadsheet analysis and curve fitting checks. PDF is better for lab notes, technical reports, and quick sharing with clients or teammates.