Model shear thinning viscosity from measured fluid parameters. Explore high and low shear limits clearly. Export tables, document results, and share clean reports instantly.
The Cross model captures shear‑thinning by smoothly transitioning between two viscosity plateaus. It is commonly used for polymer melts, solutions, and structured fluids.
The values below are illustrative for a shear‑thinning fluid. Use your own rheometer data for accurate work.
| Case | η0 | η∞ | λ (s) | m | γ̇ (1/s) | η(γ̇) |
|---|---|---|---|---|---|---|
| A | 12.0 | 0.8 | 2.5 | 1.3 | 10 | ≈ 1.516 |
| B | 40 | 2 | 1.2 | 1.0 | 1 | ≈ 19.273 |
| C | 8 | 0.5 | 0.8 | 1.8 | 100 | ≈ 0.511 |
This tool computes shear‑dependent viscosity with the Cross model, linking viscosity to shear rate. Enter η0, η∞, λ, and m, then evaluate η at a chosen γ̇. You can also generate a curve table for plotting and documentation. Tables support 2 to 200 points for quick scans or detailed curves.
η0 is the low‑shear plateau where microstructure remains intact, while η∞ is the high‑shear plateau. The dimensionless group λγ̇ sets the transition location; larger λ shifts thinning to lower shear rates. The exponent m controls how sharp the drop is, often between 0.5 and 2.5 for shear‑thinning fluids.
For λγ̇ ≪ 1, the denominator approaches 1 and η stays close to η0. For λγ̇ ≫ 1, the Cross term dominates and η approaches η∞. A practical transition estimate is γ̇ ≈ 1/λ.
Many datasets span decades of shear rate, such as 0.01 to 1000 s⁻¹. Use log spacing to sample each decade evenly and reveal the full transition shape. Use linear spacing when your operating window is narrow, like 10 to 200 s⁻¹.
Estimate η0 from the lowest‑shear plateau and η∞ from the highest‑shear plateau. Adjust λ to match where the curve bends and tune m to match the slope. Least‑squares fitting in log‑space is useful when viscosity spans orders of magnitude. Start with m≈1 and λ≈1/γ̇ at the curve’s midpoint as initial guesses.
Enter η0 and η∞ in the same viscosity units (Pa·s, mPa·s, or cP). Provide γ̇ in s⁻¹ and λ in seconds so λγ̇ stays dimensionless. The output η uses the same viscosity units you supplied.
The curve is most sensitive to λ and m near the transition region, while η0 and η∞ dominate at the extremes. The ratio η/η∞ helps confirm high‑shear convergence. If η0 < η∞, the Cross shear‑thinning assumption is violated.
Export CSV for spreadsheets, plotting, or regression workflows. Export PDF for a shareable summary in lab notes or design reviews. Record your range, spacing type, and point count so the curve can be reproduced reliably. Include η0, η∞, λ, and m with units in your report footer.
It models shear‑thinning fluids by transitioning smoothly from a low‑shear viscosity η0 to a high‑shear viscosity η∞ as shear rate increases.
λ sets the shear‑rate scale of the transition. The onset of shear‑thinning often appears near γ̇ ≈ 1/λ, so larger λ shifts thinning to lower shear rates.
m controls how sharp the viscosity drop is. Start with 1.0, then increase m for a steeper transition or decrease it for a more gradual curve.
The Cross form represents shear‑thinning behavior. If η0 is smaller than η∞, the curve would imply shear thickening, and the model is not appropriate.
Use log spacing for ranges spanning decades (e.g., 0.01–1000 s⁻¹). Use linear spacing for a narrow operating window where uniform steps are meaningful.
Any consistent viscosity unit works (Pa·s, mPa·s, cP). Enter η0 and η∞ in the same units, and the calculator will output η in those units.
Yes. Export a dense table to visualize behavior, or export your measured dataset and fit η0, η∞, λ, and m using least‑squares methods in your preferred software.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.