Casson Yield Stress Calculator

Model non‑Newtonian fluids with Casson rheology tools online. Solve yield stress, viscosity, or shear stress. Get clear unit conversions, checks, and downloadable reports fast.

Casson relation uses square-root linearization, so careful data selection improves stability.
Use apparent stress at the selected shear rate.
Set to zero for no yield threshold.
Often called Casson viscosity parameter.
Must be greater than zero.

Reset

Formula used

The Casson model is commonly written in a square‑root form:

√τ = √τy + √(ηc · γ̇)

From this, the calculator uses these rearrangements:

How to use this calculator

  1. Select a calculation mode that matches your known variables.
  2. Choose units for stress, viscosity, and shear rate.
  3. Enter your values carefully; keep γ̇ greater than zero.
  4. Press Submit to view results above the form.
  5. Use Download CSV or Download PDF for records.

Tip: If your inputs imply non‑physical results, the calculator clamps to zero and shows a warning.

Example data table

Sample values (illustrative only). Keep units consistent with your selections.
Mode Inputs Output
Solve τy τ = 12 Pa, ηc = 0.010 Pa·s, γ̇ = 80 1/s τy ≈ 3.456 Pa
Compute τ τy = 2 Pa, ηc = 0.015 Pa·s, γ̇ = 50 1/s τ ≈ 5.465 Pa
Two‑point fit (τ1,γ̇1)=(9 Pa,20 1/s), (τ2,γ̇2)=(16 Pa,80 1/s) τy ≈ 4.000 Pa, ηc ≈ 0.010 Pa·s

Casson yield stress: practical guide

1) What the model represents

The Casson model describes materials that resist motion until a threshold stress is exceeded. Below that threshold, the structure behaves like a weak solid; above it, the material flows and the stress rises with shear rate.

2) Core linearization used in labs

Many rheology workflows plot √τ against √γ̇. If the relationship is close to a straight line, the intercept corresponds to √τy, while the slope corresponds to √ηc. This calculator uses the same idea for two‑point fitting.

3) Typical magnitudes to sanity‑check

Yield stress varies widely across materials and conditions. Blood is often reported in the milli‑pascal range (for example around 0.01–0.03 Pa under normal conditions). Many molten chocolates are reported in the tens of pascals, with values sometimes cited around 4–32 Pa for dark coatings and ~14–29 Pa for milk versus dark samples in comparative tests.

4) Choosing shear‑rate points

For reliable yield estimates, select shear‑rate points that avoid instrument noise at extremely low rates and avoid heating or slip at very high rates. A practical approach is to keep measurements within a controlled ramp window and use repeat runs to confirm stability.

When possible, apply a short pre‑shear, then allow a fixed rest time before the ramp. Reporting temperature, geometry, and gap settings alongside τ–γ̇ data makes your Casson parameters easier to compare across batches and instruments.

5) Unit discipline and conversions

This tool converts stress (Pa, kPa, MPa, psi), viscosity (Pa·s, mPa·s, cP), and shear rate (1/s, 1/min). Convert first, then compute, so the square‑root operations remain consistent. If you paste mixed units, results can appear plausible but be wrong.

6) Understanding non‑physical warnings

When τ < ηc·γ̇, the rearranged yield‑stress equation would produce a negative square‑root difference. That indicates an inconsistent parameter set for Casson behavior at that shear rate. The calculator clamps the yield value to zero and shows a note.

7) Interpreting τy versus process behavior

A larger τy generally means more force to start flow, higher pump start‑up load, and stronger plug‑like regions in pipes. In coating and printing, yield stress affects leveling, sag resistance, and edge definition, so τy is often a quality‑control target.

8) When to use two‑point fitting

Two‑point fitting is helpful when you only have two reliable stress measurements at different shear rates. For better confidence, use multiple points and a regression on the Casson plot. If the two points are close in shear rate, uncertainty increases.

FAQs

1) What is Casson yield stress?

Casson yield stress is the stress threshold below which the material shows no steady flow. It reflects how strongly the microstructure resists deformation before it yields and starts moving.

2) Which mode should I use for experiments?

If you measured shear stress at a known shear rate and you have a viscosity estimate, use “Solve yield stress.” If you already know yield stress and viscosity, use “Compute shear stress” to predict stresses at new rates.

3) Why does the calculator return τy = 0 sometimes?

If inputs imply τ < ηc·γ̇, the Casson rearrangement would require a negative term under the square root. That combination is inconsistent for Casson flow at that point, so the tool clamps τy to zero and warns you.

4) Can I use viscosity in cP?

Yes. Enter viscosity in cP or mPa·s and the tool converts internally to Pa·s. Remember that 1 cP = 1 mPa·s = 0.001 Pa·s.

5) Is two‑point fitting accurate?

It can be a quick estimate, but accuracy depends on your two measurements and how linear your Casson plot is. Using points far apart in shear rate usually helps, but a multi‑point regression is better when available.

6) What shear‑rate range is reasonable?

Use a range where your instrument is stable and the sample is not slipping or heating. Many protocols use ramps spanning roughly a few to a few tens of 1/s, but you should follow your material and rheometer guidance.

7) Does Casson work for all non‑Newtonian fluids?

No. It is best for yield‑stress materials that show Casson‑like square‑root behavior. Some fluids fit Herschel–Bulkley, Bingham, or Carreau models better, especially across wide shear‑rate windows or strong time‑dependence.

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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.