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Continuum mechanics

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 (and if one were to plot this relationship, it would pass 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 strain rate is nonlinear, and can even be time-dependent. Therefore a constant coefficient of viscosity cannot be defined.

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

Cornstarch and water mix on a subwoofer

An inexpensive, non-toxic example of a non-Newtonian fluid is a suspension of starch (e.g. cornflour) in water, sometimes called oobleck[1] (uncooked imitation custard, being a suspension of primarily cornflour, has the same properties). 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.[2]

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, 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.

There are fluids which have a linear shear stress/shear strain relationship which require a finite yield stress before they begin to flow. That is the shear stress, shear strain curve doesn't pass through the origin. These fluids are called Bingham plastics. Several examples are clay suspensions, drilling mud, toothpaste, mayonnaise, chocolate, and mustard. The classic case is ketchup which will not come out of the bottle until you stress it by shaking.

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).

Classification types

Classification of fluids based on the stress vs. rate of strain relationship.
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, whipped cream
Thixotropic Apparent viscosity decreases with duration of stress Some Clays, Some Drilling Mud, many paints, synovial fluid, Honey under certain conditions
Shear-stress-dependent viscosity Dilatant Apparent viscosity increases with increased stress Suspensions of corn starch or sand in water
Shear thinning Apparent viscosity decreases with increased stress Paper pulp in water, latex paint, ice, blood plasma, syrup, molasses
Generalized Newtonian fluids Stress depends on normal and shear strain rates and also the pressure applied on it Blood, Custard

See also

External Links


  1. ^ Oobleck: The Dr. Seuss Science Experiment
  2. ^ YouTube Video of Mythbusters- Walking on "Water"


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