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 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
Shear thickening fluid
The viscosity of a shear thickening – i.e. dilatant – fluid appears to increase when the shear rate increases. Corn starch suspended in water is a common example: when stirred slowly it looks milky, when stirred vigorously it feels like a very viscous liquid.Shear thinning fluid
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 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.Examples
Many common substances exhibit non-Newtonian flows. These include:- Soap solutions, cosmetics, and toothpaste
- Food such as butter, cheese, jam, mayonnaise, soup, taffy, and yogurt
- Natural substances such as magma, lava, gums, honey, and extracts such as vanilla extract
- Biological fluids such as blood, saliva, semen, mucus, and synovial fluid
- Slurries such as cement slurry and paper pulp, emulsions such as mayonnaise, and some kinds of dispersions
Oobleck
An inexpensive, non-toxic example of a non-Newtonian fluid is a suspension of starch in water, sometimes called "oobleck", "ooze", or "magic mud". The name "oobleck" is derived from the Dr. Seuss book Bartholomew and the Oobleck.Because of its dilatant 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 its shear 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 form standing 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.