Non-Newtonian fluid

In physical chemistry and fluid mechanics, a non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity; that is, it has variable viscosity dependent on stress. 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. Many salt solutions and molten polymers are , as are many commonly found substances such as custard, toothpaste, starch suspensions, paint, blood, melted butter and shampoo.

Most commonly, the viscosity (the gradual deformation by shear or tensile stresses) of non-Newtonian fluids is dependent on shear 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 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. The fluid can even exhibit time-dependent viscosity. Therefore, a constant coefficient of viscosity cannot be defined.

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 that 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.

For non-Newtonian fluid's viscosity, there are pseudoplastic, plastic, and dilatant flows that are time-independent, and there are thixotropic and rheopectic 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, Walters’ Liquid B and Williamson fluids.

Time-dependent self-similar analysis of the Ladyzenskaya-type model with a non-linear velocity dependent stress tensor was performed. No analytical solutions could be derived, but a rigorous mathematical existence theorem was given for the solution.

For time-independent non-Newtonian fluids the known analytic solutions are much broader.

Types of non-Newtonian behavior

Summary

thumb|right|alt=Graph of shear stress (vertical axis) against shear rate (horizontal axis). Three lines extend straight up and to the right from the origin: Newtonian (straight), pseudoplastic (bending down) and dilatant (bending up). Two others extend from a point on the vertical axis above the origin: Bingham plastic (straight) and Bingham pseudoplastic (bending down). |Classification of fluids with shear stress as a function of shear rate. The gradient of each line represents the material's viscosity at the given shear rate.

{| class="wikitable"

|+Comparison of non-Newtonian, Newtonian, and viscoelastic properties

! Behaviour

! Models

! Properties

! Examples

|rowspan=1|Viscoelastic

|Kelvin material, Maxwell material

|"Parallel" linear combination of elastic and viscous effects

|Some lubricants, whipped cream, Silly Putty

|rowspan=2|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

|Nail polish, whipped cream, ketchup, molasses, syrups, paper pulp in water, latex paint, ice, blood, some silicone oils, some silicone coatings, sand in water

|colspan=1|Generalized Newtonian fluids

|Viscosity is function of the shear strain rate.<br />Stress depends on normal and shear strain rates and also the pressure applied on it

|Blood plasma, custard, water

Shear thickening fluid

The viscosity of a shear thickeningi.e. dilatant fluid appears to increase when the shear rate increases. Corn starch suspended in water ("oobleck", see below) is a common example: when stirred slowly it looks milky, when stirred vigorously it feels like a very viscous liquid.

Shear thinning fluid

left|thumb|Paint is a non-Newtonian fluid. A flat surface covered with white paint is oriented vertically (before taking the picture the flat surface was horizontal, placed on a table). The fluid starts dripping down the surface but, because of its non-Newtonian nature, it is subjected to stress due to the [[gravitational acceleration. Therefore, instead of slipping along the surface, it forms very large and very dense droplets with limited dripping.]]

A familiar example of the opposite, a shear thinning fluid, or pseudoplastic fluid, is wall paint: The paint should flow readily off the brush when it is being applied to a surface but not drip excessively. Note that all thixotropic 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.

Bingham plastic

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 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 or anti-thixotropic

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

Many common substances exhibit non-Newtonian flows. These include:

Soap solutions, cosmetics, and toothpaste
Food such as butter, cheese, jam, mayonnaise, soup, and yogurt ]]

An inexpensive, non-toxic example of a non-Newtonian fluid is a suspension of starch (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). The name "oobleck" is derived from the Dr. Seuss book Bartholomew and the Oobleck.

Chilled caramel topping

Another example of non-Newtonian fluid flow is chilled caramel ice cream topping (so long as it incorporates hydrocolloids such as carrageenan and gellan gum). The sudden application of force—by stabbing the surface with a finger, for example, or rapidly inverting the container holding it—causes the fluid to behave 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.

Silly Putty

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

Plant resin

Plant resin is a viscoelastic solid polymer. 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

Quicksand is a shear thinning non-Newtonian colloid 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 its gel and sol phase and seemingly liquefying, causing objects on the surface of the quicksand to sink.

Ketchup

Ketchup is a shear thinning fluid. 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. 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.

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Ketchup behaves like a solid until even a slight force is applied to it. Once a force is applied, it acts like a liquid rather than a solid. If you have ever wondered why hitting the glass Heinz ketchup bottle on the bottom does not work, but a slight tap to the 57 imprint on the neck does, it is because hitting the bottle on the bottom only causes the ketchup at the very bottom to act like a liquid. The ketchup closer to the neck still acts like a solid blocking the ketchup from flowing out of the bottle. Hitting the bottle on the neck causes the ketchup at the neck of the bottle to act like a liquid and, thus, flow out of the bottle.

Pancakes

You can make tasty pancakes, using potato starch, sugar and eatable liquid, like milk or water, eggs optionally. Any starch solution shows properties of non-Newtonian liquid.

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Dry granular flows

Under certain circumstances, flows of granular materials can be modelled as a continuum, for example using the μ(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.