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Continuum mechanics

General

Classical mechanics Stress / Strain Tensor Conservation of mass Conservation of momentum

Solid mechanics

Solids Elasticity Plasticity Hooke's law Poisson's ratio Rheology Viscoelasticity

Fluid mechanics

Fluids Fluid statics Fluid dynamics Navier-Stokes equations Viscosity Newtonian fluids Non-Newtonian fluids

A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. As a result, non-Newtonian fluids may not have a well-defined viscosity.

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 tensors under many different flow conditions, such as oscillatory shear, or extensional flow which are measured using different devices or rheometers. The rheological properties are better studied using tensor-valued constitutive equations, which are common in the field of continuum mechanics.

Contents 1 Common examples 2 Classification types 3 See also 4 External links

An inexpensive, non-toxic sample of a non-Newtonian fluid sometimes known as oobleck can be made very easily by adding corn starch (cornflour) to a cup of water. Add the starch in small portions and stir it in slowly. When the suspension nears the critical concentration - becoming like single cream (light cream) in consistency - the so called "shear thickening" property of this non-Newtonian fluid becomes apparent. 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. 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/or 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.

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.

Principal types of non-Newtonian fluid include:

Type of fluid	Behaviour	Characteristics	Examples
Plastic solids	Perfectly plastic	Strain does not result in opposing stress	Ductile metals past the yield point
	Bingham plastic	Linear relationship between shear stress and rate of strain once threshold shear stress exceeded	Mud, some colloids
	Yield pseudo-plastic	Pseudo-plastic above some threshold shear stress
	Yield dilatant	Dilatant above some threshold shear stress
Power-law fluids	Pseudoplastic or "shear thinning"	Apparent viscosity reducing with rate of shear	Some colloids, clay, milk, gelatin, blood and liquid cement
	Dilatant or "shear thickening"	Apparent viscosity increasing with rate of shear	Concentrated solution of sugar in water, suspensions of rice starch or corn starch
Viscoelastic - having both viscous and elastic properties	Maxwell material	"Series" linear combination of elastic and viscous effects	metals, composite materials
	Oldroyd-B fluid	Linear combination of Maxwell and Newtonian behaviour	Bitumen, dough, nylon, and Silly Putty
	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

• Newtonian fluid
• Rheology
• Viscosity
• Superfluids
• Navier-Stokes equations
• Finite deformation tensors
• Oobleck

• Viscosity Chart
• A pool filled with non-newtonian fluid (youtube video)
• Narrated scientific experiments on the effects of vibrations on a non-newtonian fluid (youtube video)
• Amateur experiments on the effects of vibrations on a non-newtonian fluid (google video)
• Cornstarch Lifeforms (youtube video)