Model non‑Newtonian viscosity with Sisko parameters, shear rate, and units quickly clearly. Generate curves, verify assumptions, and download tables for your workflow today easily.
The Sisko constitutive relation for steady shear is: τ = K·γ̇n + μ∞·γ̇. The apparent viscosity is the ratio of shear stress to shear rate: μapp = τ/γ̇ = K·γ̇n−1 + μ∞.
Example uses K = 1.20 Pa·sn, n = 0.70, μ∞ = 0.02 Pa·s.
| Shear rate (1/s) | K (Pa·sn) | n | μ∞ (Pa·s) | μapp (Pa·s) |
|---|---|---|---|---|
| 1 | 1.2 | 0.7 | 0.02 | 1.22 |
| 10 | 1.2 | 0.7 | 0.02 | 0.62 |
| 100 | 1.2 | 0.7 | 0.02 | 0.33 |
Non‑Newtonian fluids rarely keep a constant viscosity when the shear rate changes. The Sisko model captures this by combining a power‑law term with a high‑shear viscosity limit, making it useful for wide operating ranges in process and research work.
The model uses the consistency index K, flow behavior index n, and the infinite‑shear viscosity μ∞. K carries units of Pa·s^n and is often fitted from rheometer curves. For many shear‑thinning fluids, n is between 0.2 and 0.9. μ∞ is often small but nonzero for concentrated suspensions and melts at high shear.
Apparent viscosity is μapp = K·γ̇^(n−1) + μ∞. When n < 1, the power‑law contribution decreases as shear rate increases, so viscosity drops and approaches μ∞ at very high γ̇. This asymptote helps prevent unrealistic vanishing viscosity in simulations.
Shear stress follows τ = K·γ̇^n + μ∞·γ̇. The first term represents structure‑dependent resistance; the second acts like a linear, Newtonian contribution at high shear. Reporting τ alongside μapp helps connect rheology to pressure drop, wall shear, and mixing power in equipment.
Use a single shear rate to evaluate one operating point, such as a target pump speed or process setpoint. Use a range table to generate a curve for validation, model comparison, or fitting against rheometer data across decades of γ̇. Include the same γ̇ values your process sees, and compare μapp to measured viscosity checkpoints when possible.
Rheology datasets frequently span 1/s to 10^3–10^5 1/s. Log spacing allocates more points at low shear where changes are steep and spreads points evenly by decade. Linear spacing is better when you only care about a narrow band.
Viscosity is commonly expressed in Pa·s, mPa·s, or cP. Converting μ∞ and exporting results prevents transcription errors. CSV supports spreadsheets and plotting; the PDF summary is convenient for lab notebooks and design packages used by reviewers.
The Sisko form assumes steady shear and does not model yield stress, time dependence, or viscoelastic effects. Validate parameters against the temperature, composition, and shear regime you will use. Small changes in n can shift predictions substantially, so document fit quality and measurement uncertainty.
μ∞ is the viscosity approached at very high shear rates. It adds a linear stress term and prevents the apparent viscosity from dropping unrealistically toward zero.
K has units of Pa·s^n so that K·γ̇^n produces shear stress in pascals. Keep γ̇ in 1/s for consistency and reliable exports.
Use range mode when you need a viscosity curve, want to compare against rheometer data, or must export multiple operating points for a report or simulation input.
Because μapp depends on γ̇^(n−1), small shifts in n change the slope on a log plot. This effect is strongest across wide shear‑rate ranges.
No. The Sisko form does not include a yield stress. If your material exhibits a yield point, consider a Herschel–Bulkley or Bingham‑type approach.
Log spacing is best for ranges spanning multiple decades, capturing low‑shear curvature efficiently. Linear spacing is fine for narrow ranges around a setpoint.
State K, n, μ∞, temperature, and the shear‑rate range. Include both μapp and τ, and attach the exported CSV or PDF for traceability.
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.