A Newtonian fluid has shear stress proportional to shear rate with a constant viscosity. Many real fluids do not follow that simple relation.

A non-Newtonian fluid has an apparent viscosity that changes with shear rate, time under shear or loading history.

Shear thinning

In a shear-thinning fluid, apparent viscosity decreases as shear rate increases. Paints, polymer solutions and many biological fluids show this behaviour over some range.

Shear thickening

In a shear-thickening fluid, apparent viscosity increases with shear rate. Concentrated suspensions can exhibit this behaviour.

Yield-stress fluids

Some materials behave approximately like solids until a threshold shear stress is exceeded, after which they flow. Idealized Bingham-plastic models capture this type of response.

A constitutive relation

The distinction is not about whether the flow is laminar or turbulent. It concerns the local constitutive relationship between stress and deformation rate.

Non-Newtonian models are needed whenever a single constant $\mu$ in Newton's law of viscosity cannot describe the fluid over the conditions of interest.