It has variable viscosity dependent on stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid

For non-Newtonian fluids, the viscosity varies with the shear rate

τ = K d u d y n

with. n < 1 for pseudoplastic fluids (viscosity decreases with shear rate, shear‐thinning);

K=Contant

In Newtonian fluids, this value doesn't change, but with non-Newtonian fluids, apparent viscosity is directly affected by the shear rate. It can be calculated by dividing shear stress by shear rate.calculation both are diferent.

https://www.researchgate.net/post/How_to_measure_and_control_the_viscosity_of_non-Newtonian_fluid#:~:text=In%20Newtonian%20fluids%2C%20this%20value,shear%20stress%20by%20shear%20rate.

The chapter by Chhabra, R.P. 2010, "Non-Newtonian Fluids: An Introduction. In: Krishnan, J., Deshpande, A., Kumar, P. (eds) Rheology of Complex Fluids. Springer, New York, NY" provides theoretical and practical notions on non-Newtonian fluids encountered in both in nature and in technology. "Starting with the definition of a non-Newtonian fluid, different types of non-Newtonian characteristics are briefly described. Representative examples of materials (foams, suspensions, polymer solutions and melts), which, under appropriate circumstances, display shear-thinning, shear-thickening, visco-plastic, time-dependent and viscoelastic behaviour are presented. Each type of non-Newtonian fluid behaviour has been illustrated via experimental data on real materials. This is followed by a short discussion on how to engineer non-Newtonian flow characteristics of a product for its satisfactory end use by manipulating its microstructure by controlling physico-chemical aspects of the system. Finally, we touch upon the ultimate question about the role of non-Newtonian characteristics on the analysis and modelling of the processes of pragmatic engineering significance."

Chapter available on:

https://www.academia.edu/download/77655120/chhabra.pdf

Non Newtonian fluids haven't unique viscosity. Viscosities depend on shear rate. You can talk about apparent viscosity and several mathematical models can be used to relate shear stress and shear rate. Examples Power law model, Herschel Buckey, Casson, etc.

The viscosity of non-Newtonian fluids doesn't follow a single formula like Newtonian fluids. It varies depending on the specific type of non-Newtonian behavior, such as shear-thinning or shear-thickening.

There are many good papers out there, and some useful graphs that demonstrate common non-Newtonian fluid behavior, including viscosity (which is the main descriptor). Here's one.

Non-Newtonian viscosity formula is

Viscosity=u(d∆/dt)^n where n is not equal to 1.

u= Newtonian constant

d∆/dt= rate of deformation

For non-newtonian fluids you can use a variety of equations like: a) Power Law model; b) Bingham Plastics; c) Herschel-Buckley; d)Roberston-Stiff among others

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A Newtonian fluid is one in which the shear stress is proportional to the velocity of deformation, according to the equation:

σ xy = µ ∂v = µ y

∂x

Non-Newtonian fluids have variable viscosity that changes with stress, causing them to become more liquid or more solid under force. The viscosity of these fluids varies based on the shear rate.

For most non-Newtonian fluids, the relationship between the stress tensor T and the applied strain rates E can be described by a time-independent scalar function μ=μ(˙γ), such that T=2μ(˙γ)E.

The viscosity of a non-Newtonian fluid is not described by a single, simple formula as in the case of Newtonian fluids. Non-Newtonian fluids exhibit a variable viscosity depending on the applied stress or strain rate. There are different models and equations used to describe the viscosity of non-Newtonian fluids, and the choice depends on the specific behavior of the fluid. Here are a few common models:

1. Power-law Model (Ostwald-de Waele Model):

τ=K(du/dy)n-1

where:

τ is the shear stress,

du/dy is the shear rate,

K is the consistency index, and

n is the flow behavior index.

2. Bingham Plastic Model:

τ=τ0+μB

where:

τ is the shear stress,

τ0​ is the yield stress,

μ is the plastic viscosity, and

B is the Bingham plasticity.

3. Casson Model:

√τ =√(τ0)+√μ (√(dy/du)​​

where:

τ is the shear stress,

τ0​ is the yield stress,

μ is the Casson viscosity, and

du/dy is the shear rate

4. Herschel-Bulkley Model:

τ=τ0 +K(du/dy)n

where:

τ is the shear stress, τ0​ is the yield stress, K is the consistency index, and n is the flow behavior index.

These models provide a way to correlate shear stress with shear rate for different types of non-Newtonian fluids. The appropriate model depends on the rheological behavior observed in experimental data for a specific fluid. It's important to note that these models are empirical and may not capture all nuances of non-Newtonian behavior in all situations. Complex fluids may require more sophisticated models or a combination of multiple models to accurately describe their viscosity.

Non-Newtonian is the rheological characteristic of a suspension that has a value between the non-linear shear rate and the shear stress value