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Inphysical chemistry andfluid mechanics, anon-Newtonian fluid is afluid that does not followNewton's law of viscosity, that is, it has variable viscosity dependent onstress. In particular, the viscosity of non-Newtonian fluids can change when subjected to force.Ketchup, for example, becomes runnier when shaken and is thus a non-Newtonian fluid. Manysalt solutions and molten polymers arenon-Newtonian fluids, as are many commonly found substances such ascustard,[1]toothpaste,starch suspensions,paint,blood, meltedbutter andshampoo.
Most commonly, theviscosity (the gradual deformation by shear or tensile stresses) of non-Newtonian fluids is dependent onshear rate or shear rate history. Some non-Newtonian fluids with shear-independent viscosity, however, still exhibit normal stress-differences or other non-Newtonian behavior. In a Newtonian fluid, the relation between theshear stress and the shear rate is linear, passing through theorigin, 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. The fluid can even exhibittime-dependent viscosity. Therefore, a constant coefficient of viscosity cannot be defined.
Although the concept of viscosity is commonly used influid mechanics to characterize the shear properties of a fluid, it can be inadequate to describe non-Newtonian fluids. They are best studied through several otherrheological properties that relatestress andstrain rate tensors under many different flow conditions—such asoscillatory shear or extensional flow—which are measured using different devices orrheometers. The properties are better studied usingtensor-valuedconstitutive equations, which are common in the field ofcontinuum mechanics.
For non-Newtonian fluid's viscosity, there arepseudoplastic,plastic, anddilatant flows that are time-independent, and there arethixotropic andrheopectic flows that are time-dependent. Three well-known time-dependent non-newtonian fluids which can be identified by the defining authors are the Oldroyd-B model,[2] Walters’ Liquid B[3] and Williamson[4] fluids.
Time-dependentself-similar analysis of theLadyzenskaya-type model with a non-linear velocity dependent stress tensor was performed.[5] No analytical solutions could be derived, but a rigorous mathematical existence theorem[6] was given for the solution.
For time-independent non-Newtonian fluids the known analytic solutions are much broader.[7][8][9][10]
| Behaviour | Models | Properties | Examples |
|---|---|---|---|
| Viscoelastic | Kelvin material,Maxwell material | "Parallel" linear combination of elastic and viscous effects[11] | Somelubricants,whipped cream,Silly Putty |
| Time-dependent viscosity | Rheopectic | Apparent viscosity increases with duration of stress | Synovial fluid,printer ink,gypsum paste |
| Thixotropic | Apparent viscosity decreases with duration of stress[11] | Yogurt,peanut butter,xanthan gum solutions, aqueousiron oxide gels,gelatin gels,pectin gels,hydrogenated castor oil, someclays (includingbentonite, andmontmorillonite),carbon black suspension in molten tire rubber, somedrilling fluids, manypaints, manyflocculant suspensions, manycolloidal suspensions | |
| Non-Newtonian viscosity | Shear thickening (dilatant) | Apparent viscosity increases with increased stress[12] | Suspensions ofcorn starch in water (oobleck) |
| Shear thinning (pseudoplastic) | Apparent viscosity decreases with increased stress[13][14] | Nail polish,whipped cream,ketchup,molasses, syrups, paper pulp in water,latex paint,ice,blood, somesilicone oils, somesilicone coatings,sand in water | |
| Generalized Newtonian fluids | Viscosity is function of the shear strain rate. Stress depends on normal and shear strain rates and also the pressure applied on it | Blood plasma,custard,water |
The viscosity of a shear thickening – i.e.dilatant – fluid appears to increase when the shear rate increases.Corn starch suspended in water ("oobleck", seebelow) is a common example: when stirred slowly it looks milky, when stirred vigorously it feels like a very viscous liquid.
A familiar example of the opposite, ashear thinning fluid, or pseudoplastic fluid, is wallpaint: The paint should flow readily off the brush when it is being applied to a surface but not drip excessively. Note that allthixotropic fluids are extremely shear thinning, but they are significantly time dependent, whereas the colloidal "shear thinning" fluids respond instantaneously to changes in shear rate. Thus, to avoid confusion, the latter classification is more clearly termed pseudoplastic.
Another example of a shear thinning fluid is blood. This application is highly favoured within the body, as it allows the viscosity of blood to decrease with increased shear strain rate.
Fluids that have a linear shear stress/shear strain relationship but require a finite yield stress before they begin to flow (the plot of shear stress against shear strain does not pass through the origin) are calledBingham 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 contrastNewtonian fluids have flat featureless surfaces when still.
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 asrheopectic. 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).
Many common substances exhibit non-Newtonian flows. These include:
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An inexpensive,non-toxic example of a non-Newtonian fluid is a suspension ofstarch (e.g., cornstarch/cornflour) in water, sometimes called "oobleck", "ooze", or "magic mud" (1 part of water to 1.5–2 parts of corn starch).[17][18][19] The name "oobleck" is derived from theDr. Seuss bookBartholomew and the Oobleck.[17]
Because of itsdilatant properties, oobleck is often used in demonstrations that exhibit its unusual behavior. A person may walk on a large tub of oobleck without sinking due to itsshear thickening properties, as long as the individual moves quickly enough to provide enough force with each step to cause the thickening. Also, if oobleck is placed on a large subwoofer driven at a sufficiently high volume, it will thicken and formstanding waves in response to low frequency sound waves from the speaker. If a person were to punch or hit oobleck, it would thicken and act like a solid. After the blow, the oobleck will go back to its thin liquid-like state.
Flubber, also commonly known as slime, is a non-Newtonian fluid, easily made frompolyvinyl acetate–basedglues (such as white "school" glue) andborax. It flows under low stresses but breaks under higher stresses and pressures. This combination of fluid-like and solid-like properties makes it aMaxwell fluid. Its behaviour can also be described as beingviscoplastic orgelatinous.[20]
Another example of non-Newtonian fluid flow is chilled caramelice cream topping (so long as it incorporates hydrocolloids such ascarrageenan andgellan gum). The sudden application offorce—by stabbing the surface with a finger, for example, or rapidly inverting the container holding it—causes the fluid to behave like asolid 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.[21]
Silly Putty is a silicone polymer basedsuspension that will flow, bounce, or break, depending on strain rate.
Plant resin is aviscoelasticsolidpolymer. When left in a container, it will flow slowly as a liquid to conform to the contours of its container. If struck with greater force, however, it will shatter as a solid.
Quicksand is ashear thinning non-Newtoniancolloid that gains viscosity at rest. Quicksand's non-Newtonian properties can be observed when it experiences a slight shock (for example, when someone walks on it or agitates it with a stick), shifting between itsgel andsol phase and seemingly liquefying, causing objects on the surface of the quicksand to sink.[citation needed]
Ketchup is ashear thinning fluid.[12][22] Shear thinning means that the fluid viscosity decreases with increasingshear stress. In other words, fluid motion is initially difficult at slow rates of deformation, but will flow more freely at high rates. Shaking an inverted bottle of ketchup can cause it to transition to a lower viscosity through shear thinning, making it easier to pour from the bottle.
Under certain circumstances, flows ofgranular materials can be modelled as a continuum, for example using theμ(I) rheology. Such continuum models tend to be non-Newtonian, since the apparent viscosity of granular flows increases with pressure and decreases with shear rate. The main difference is the shearing stress and rate of shear.
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