Introduction
Non-Newtonian fluids have viscosities that change with shear rate, unlike Newtonian fluids whose viscosity is constant. In FluidFlow, you can model this behavior using established rheological models that relate shear stress (τ) to shear rate (γ̇). Selecting the right model ensures accurate predictions of pressure drop, flow rate, and head loss across your network.
Key Concepts
Shear stress (τ): The tangential force per unit area applied to the fluid.
Shear rate (γ̇): The rate at which adjacent fluid layers move relative to each other.
Apparent viscosity (μₐₚₚ): The effective viscosity at a given shear rate.
μₐₚₚ = τ / γ̇
Supported Rheological Models
1) Bingham Plastic
Definition:
τ = τᵧ + μₚ γ̇
Parameters:
τᵧ: Yield stress required to initiate flow
μₚ: Plastic viscosity or coefficient of rigidity
Characteristics:
Does not flow until τ > τᵧ
Linear τ–γ̇ relationship after yield
Typical applications:
Drilling muds, toothpaste, slurries with distinct yield behavior
2) Herschel–Bulkley
Definition:
τ = τᵧ + K γ̇^n
Parameters:
τᵧ: Yield stress
K: Consistency index
n: Flow behavior index
Characteristics:
Generalizes Bingham (if n = 1) and Power Law (if τᵧ = 0)
Captures yield plus shear-thinning or -thickening
Typical applications:
Cement slurries, pastes, complex suspensions
3) Casson
Definition:
√τ = √τᵧ + η꜀√γ̇
Parameters:
τᵧ: Yield stress
η꜀: Casson viscosity
Characteristics:
Yield-stress behavior
Empirical fit for structured or particulate fluids
Typical applications:
Blood, chocolate, inks, pigment suspensions, emulsions
4) Power Law
Definition:
τ = K γ̇^n
Parameters:
K: Consistency index
n: Flow behavior index
Characteristics:
n < 1: shear-thinning (Pseudoplastic)
n = 1: Newtonian
n > 1: shear-thickening (Dilatant)
No yield stress
Typical applications:
Polymer solutions, paints, slurries without a clear yield point
Choosing and Configuring a Viscosity Model in FluidFlow
Option A: Directly Define Constants
Use when you already know the rheological constants from literature or lab data.
Add a new fluid and select Non Newtonian Liquid as the fluid type.
Click the three-dot button beside the Liquid Viscosity Definition field.
In the Viscosity Definition, select Directly Define Constants.
Enter constants:
Bingham Plastic: τᵧ, μₚ
Herschel–Bulkley: τᵧ, K, n
Casson: τᵧ, η꜀
Power Law: K, n
Review the generated curve to confirm behavior across your operating γ̇ range.
Option B: Curve Fit from Experimental Data
Use when you have shear stress vs. shear rate data.
In the Viscosity Definition tab, select Shear Stress-Shear Rate.
Click the three-dot button beside [Table Data].
Enter paired data points for shear rate (γ̇, s^-1) and shear stress (τ, Pa).
Select the Curve Fit Type: Bingham Plastic, Herschel–Bulkley, Casson, or Power Law.
Review generated γ̇-τ and μₐₚₚ–γ̇ curves. Adjust model choice if the fit is poor or non-physical in your operating range.
Model Selection Guide
Model | Yield Stress? | Flow Relationship | Typical Fluids | When to Use |
Bingham Plastic | Yes | Linear after yield | Drilling muds, slurries | Distinct yield point with near-linear post-yield behavior |
Herschel–Bulkley | Yes | Non-linear | Pastes, cement slurries | Yield plus shear-thinning or -thickening |
Casson | Yes | Square-root relation | Blood, chocolate, inks | Empirical fit for structured or particulate fluids |
Power Law | No | Non-linear | Polymer solutions, paints | No yield stress but viscosity varies with γ̇ |
FAQs
Q: Which model should I try first?
A: If yield stress is present, start with Herschel–Bulkley for flexibility. If not, start with Power Law.
Q: What if my data fits two models equally well?
A: You may create multiple fluid entries in the database for the different models that accurately represent the liquid. These additional entries allow you to conduct sensitivity analysis and evaluate how different viscosity models affect your system.
Q: How do I handle different temperatures when modeling non-Newtonian fluids?
A: Non-Newtonian fluid viscosity definitions rely on a single temperature point. For systems with significant temperature variations that affect viscosity, you should define multiple fluid entries in the database to account for these changes.
Q: My n > 1. Is that valid?
A: Yes. This indicates shear-thickening behavior, which is valid for both Power Law and Herschel-Bulkley models. Make sure to verify that this behavior is consistent with your material's known properties and expected operating conditions.
Conclusion
FluidFlow supports industry-standard rheological models to capture non-Newtonian behavior. Choosing an appropriate model, entering consistent parameters, and validating against realistic shear-rate ranges are essential to accurate network predictions.
Selecting and validating the right non-Newtonian model in FluidFlow leads to trustworthy pressure-drop and flow predictions, enabling safer designs, lower energy use, and fewer commissioning surprises.