Non-Newtonian fluid

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A non-Newtonian fluid is a fluid whose flow properties differ in any way from those of Newtonian fluids. Most commonly the viscosity (resistance to deformation or other forces) of non-Newtonian fluids is not independent of shear rate or shear rate history. However, there are some non-Newtonian fluids with shear-independent viscosity, that nonetheless exhibit normal stress-differences or other non-Newtonian behaviour. Many salt solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as ketchup, custard, toothpaste, starch suspensions, paint, blood, and shampoo. In a Newtonian fluid, the relation between the shear stress and the shear rate is linear, passing through the origin, the constant of proportionality being the coefficient of viscosity. In a non-Newtonian fluid, the relation between the shear stress and the shear rate is different, and can even be time-dependent. Therefore a constant coefficient of viscosity cannot be defined.

Therefore, although the concept of viscosity is commonly used in fluid mechanics to characterize the shear properties of a fluid, it can be inadequate to describe non-Newtonian fluids. They are best studied through several other rheological properties which relate 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.

Types of non-Newtonian behaviour

Summary

Comparison of non-Newtonian, Newtonian, and viscoelastic properties

Viscoelastic	Kelvin material	"Parallel" linearstic 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[1]	Some lubricants, whipped cream
	Thixotropic	Apparent viscosity decreases with duration of stress[2]	Some clays, some drilling mud, many paints, synovial fluid
Time-independent viscosity	Shear thickening (dilatant)	Apparent viscosity increases with increased stress[3]	Suspensions of corn starch or sand in water
	Shear thinning (pseudoplastic)	Apparent viscosity decreases with increased stress[4][5]	Paper pulp in water, latex paint, ice, blood, syrup, molasses
	Generalized Newtonian fluids		Viscosity is constant Stress depends on normal and shear strain rates and also the pressure applied on it	Blood plasma, custard

Shear thickening fluids

Shear thickening fluids are also used in all wheel drive systems utilising a viscous coupling unit for power transmission.

Shear thinning fluid

A familiar example of the opposite, a shear thinning fluid, or pseudoplastic 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.

Bingham plastic

There are fluids which have a linear shear stress/shear strain relationship which require a finite yield stress before they begin to flow (the plot of shear stress against shear strain does not pass through the origin). These fluids are called Bingham plastics. Several examples are clay suspensions, drilling mud, toothpaste, mayonnaise, chocolate, and mustard. The surface of a Bingham plastic can hold peaks when it is still. By contrast Newtonian fluids have flat featureless surfaces when still.

Rheopectic

There are also fluids whose strain rate is a function of time. Fluids that require a gradually increasing shear stress to maintain a constant strain rate are referred to as rheopectic. An opposite case of this, is a fluid that thins out with time and requires a decreasing stress to maintain a constant strain rate (thixotropic).

Examples

Oobleck

Oobleck on a subwoofer. Applying force to oobleck, by sound waves in this case, makes the non-Newtonian fluid thicken.^[6]

An inexpensive, non-toxic example of a non-Newtonian fluid is a suspension of starch (e.g. cornstarch) in water, sometimes called "oobleck" or "ooze" (1 part of water to 1.5–2 parts of corn starch).^[7][8] Uncooked imitation custard, being a suspension of primarily cornflour, has the same properties. The name "oobleck" is derived from the children's book Bartholomew and the Oobleck.

Flubber

Main article: Flubber (material)

Flubber is a non-Newtonian fluid, easily made from polyvinyl alcohol based glues and borax, that flows under low stresses, but breaks under higher stresses and pressures. This combination of fluid-like and solid-like properties makes it a Maxwell solid. Its behaviour can also be described as being viscoplastic or gelatinous.^[9]

Chilled caramel topping

Another example of this is chilled caramel ice cream topping. The sudden 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 their feet can literally walk across such a liquid.

Silly Putty

Main article: Silly Putty

Silly Putty is a silicone polymer based suspension which will flow, bounce, or break depending on strain rate.

Ketchup

Ketchup is a shear thinning fluid.^[3] Shear thinning means that the fluid viscosity decreases with increasing shear stress. In other words, fluid motion is initially difficult at slow rates of deformation, but will flow more freely at high rates.

See also

• Bingham plastic
• Complex fluid
• Dissipative particle dynamics
• Newtonian fluid
• Herschel–Bulkley fluid
• Navier–Stokes equations
• Pseudoplastic
• Dilatant
• Quicksand
• Rheology
• Superfluids

References

1. ^ Springer handbook of experimental fluid mechanics, Cameron Tropea, Alexander L. Yarin, John F. Foss, Publisher: Springer, 9 October 2007, ISBN 3540251413, ISBN 978-3540251415, p.676, Google books
2. ^ Springer handbook of experimental fluid mechanics, Cameron Tropea, Alexander L. Yarin, John F. Foss, Publisher: Springer, 9 October 2007, ISBN 3540251413, ISBN 978-3540251415, p.661, Google books
3. ^ ^{a b} Pump Application Desk Book, 3rd edition, Paul N. Garay, Prentice Hall, August 1996, ISBN 0881732311, ISBN 978-0881732313, p.358, Google books
4. ^ Rheology of Fluid and Semisolid Foods: Principles and Applications, M. A. Rao, Publisher: Springer, 2nd edition, 28 August 2007, ISBN 0387709290, ISBN 978-0387709291, p.8, Google books
5. ^ Emulsions, Foams, and Suspensions: Fundamentals and Applications, Laurier L. Schramm, Publisher: Wiley VCH, 26 July 2005, ISBN 3527307435, ISBN 978-3527307432p.173, Google books
6. ^ This demonstration of oobleck is a popular subject for YouTube videos, such as this.
7. ^ Oobleck: The Dr. Seuss Science Experiment
8. ^ Outrageous Ooze
9. ^ Glurch Meets Oobleck. Iowa State University Extension.

External links

• Classical experiments with Non-Newtonian fluids by the National Committee for Fluid Mechanics on YouTube