Definitions

# Non-Newtonian fluid

A non-Newtonian fluid is a fluid whose flow properties are not described by a single constant value of viscosity. Many polymer solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as ketchup, starch suspensions, paint, blood and shampoo. In a Newtonian fluid, the relation between the shear stress and the strain rate is linear, the constant of proportionality being the coefficient of viscosity. In a non-Newtonian fluid, the relation between the shear stress and the strain rate is nonlinear, and can even be time-dependent. Therefore a constant coefficient of viscosity can not be defined. A ratio between shear stress and rate of strain (or shear-dependent viscosity) can be defined, this concept being more useful for fluids without time-dependent behavior.

Although the concept of viscosity is commonly used to characterize a material, it can be inadequate to describe the mechanical behavior of a substance, particularly non-Newtonian fluids. They are best studied through several other rheological properties which relate the relations between the stress and strain rate tensors under many different flow conditions, such as oscillatory shear, or extensional flow which are measured using different devices or rheometers. The properties are better studied using tensor-valued constitutive equations, which are common in the field of continuum mechanics.

## Common examples

An inexpensive, non-toxic example of a non-Newtonian fluid is a suspension of corn starch (corn flour) in water, sometimes called oobleck. The application of force - for example by stabbing the surface with a finger, or rapidly inverting the container holding it - leads to the fluid behaving like a solid rather than a liquid. This is the "shear thickening" property of this non-Newtonian fluid. More gentle treatment, such as slowly inserting a spoon, will leave it in its liquid state. Trying to jerk the spoon back out again, however, will trigger the return of the temporary solid state. A person moving quickly and applying sufficient force with his feet can literally walk across such a liquid.

Shear thickening fluids of this sort are being researched for bullet resistant body armor, useful for their ability to absorb the energy of a high velocity projectile impact but remain soft and flexible while worn. Some shear thickening fluids are also used in all wheel drive systems utilising a viscous coupling unit for power transmission.

A familiar example of the opposite, a shear thinning fluid, is paint: one wants the paint to flow readily off the brush when it is being applied to the surface being painted, but not to drip excessively.

## Classification types

Kelvin material "Parallel" linear combination of elastic and viscous effects
Anelastic Material returns to a well-defined "rest shape"
Time-dependent viscosity Rheopectic Apparent viscosity increases with duration of stress Some lubricants
Thixotropic Apparent viscosity decreases with duration of stress Non-drip paints and tomato ketchup and most honey varieties.
Generalized Newtonian fluids Stress depends on normal and shear strain rates and also the pressure applied on it Blood, Custard

## References

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