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A non-Newtonian fluid is a
fluid In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
that does not follow Newton's law of viscosity, i.e., constant viscosity independent of stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. Ketchup, for example, becomes runnier when shaken and is thus a non-Newtonian fluid. Many
salt Salt is a mineral composed primarily of sodium chloride (NaCl), a chemical compound belonging to the larger class of salts; salt in the form of a natural crystalline mineral is known as rock salt or halite. Salt is present in vast quant ...
solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as
custard Custard is a variety of culinary preparations based on sweetened milk, cheese, or cream cooked with egg or egg yolk to thicken it, and sometimes also flour, corn starch, or gelatin. Depending on the recipe, custard may vary in consistency fr ...
,
toothpaste Toothpaste is a paste or gel dentifrice used with a toothbrush to clean and maintain the aesthetics and health of teeth. Toothpaste is used to promote oral hygiene: it is an abrasive that aids in removing dental plaque and food from the teeth, ...
,
starch Starch or amylum is a polymeric carbohydrate consisting of numerous glucose units joined by glycosidic bonds. This polysaccharide is produced by most green plants for energy storage. Worldwide, it is the most common carbohydrate in human die ...
suspensions,
corn starch Corn starch, maize starch, or cornflour (British English) is the starch derived from corn (maize) grain. The starch is obtained from the endosperm of the kernel. Corn starch is a common food ingredient, often used to thicken sauces or sou ...
,
paint Paint is any pigmented liquid, liquefiable, or solid mastic composition that, after application to a substrate in a thin layer, converts to a solid film. It is most commonly used to protect, color, or provide texture. Paint can be made in many ...
,
blood Blood is a body fluid in the circulatory system of humans and other vertebrates that delivers necessary substances such as nutrients and oxygen to the cells, and transports metabolic waste products away from those same cells. Blood in the cir ...
, melted
butter Butter is a dairy product made from the fat and protein components of churned cream. It is a semi-solid emulsion at room temperature, consisting of approximately 80% butterfat. It is used at room temperature as a spread, melted as a condim ...
, and
shampoo Shampoo () is a hair care product, typically in the form of a viscous liquid, that is used for cleaning hair. Less commonly, shampoo is available in solid bar format. Shampoo is used by applying it to wet hair, massaging the product into the ...
. Most commonly, the
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the int ...
(the gradual deformation by shear or
tensile stress In continuum mechanics, stress is a physical quantity. It is a quantity that describes the magnitude of forces that cause deformation. Stress is defined as ''force per unit area''. When an object is pulled apart by a force it will cause elonga ...
es) 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 Shear stress, often denoted by ( Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. '' Normal stress'', on ...
and the shear rate is linear, passing through the
origin Origin(s) or The Origin may refer to: Arts, entertainment, and media Comics and manga * Origin (comics), ''Origin'' (comics), a Wolverine comic book mini-series published by Marvel Comics in 2002 * The Origin (Buffy comic), ''The Origin'' (Bu ...
, the constant of proportionality being the coefficient of
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the int ...
. 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 Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and ...
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 Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
shear or extensional flow—which are measured using different devices or rheometers. The properties are better studied using
tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensor ...
-valued
constitutive equations In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and approx ...
, which are common in the field of
continuum mechanics Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such mo ...
.


Types of non-Newtonian behavior


Summary


Shear thickening fluid

The viscosity of a shear thickening fluid, or
dilatant A dilatant (, ) (also termed shear thickening) material is one in which viscosity increases with the rate of shear strain. Such a ''shear thickening fluid'', also known by the initialism ''STF'', is an example of a non-Newtonian fluid. This be ...
fluid, appears to increase when the shear rate increases.
Corn starch Corn starch, maize starch, or cornflour (British English) is the starch derived from corn (maize) grain. The starch is obtained from the endosperm of the kernel. Corn starch is a common food ingredient, often used to thicken sauces or sou ...
suspended in water ("oobleck", see
below Below may refer to: *Earth * Ground (disambiguation) *Soil *Floor * Bottom (disambiguation) *Less than *Temperatures below freezing *Hell or underworld People with the surname *Ernst von Below (1863–1955), German World War I general *Fred Below ...
) 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 Paint is any pigmented liquid, liquefiable, or solid mastic composition that, after application to a substrate in a thin layer, converts to a solid film. It is most commonly used to protect, color, or provide texture. Paint can be made in many ...
: 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 Cosmetics are constituted mixtures of chemical compounds derived from either natural sources, or synthetically created ones. Cosmetics have various purposes. Those designed for personal care and skin care can be used to cleanse or protec ...
, and toothpaste * Food such as
butter Butter is a dairy product made from the fat and protein components of churned cream. It is a semi-solid emulsion at room temperature, consisting of approximately 80% butterfat. It is used at room temperature as a spread, melted as a condim ...
,
cheese Cheese is a dairy product produced in wide ranges of flavors, textures, and forms by coagulation of the milk protein casein. It comprises proteins and fat from milk, usually the milk of cows, buffalo, goats, or sheep. During productio ...
, jam,
mayonnaise Mayonnaise (; ), colloquially referred to as "mayo" , is a thick, cold, and creamy sauce or dressing commonly used on sandwiches, hamburgers, composed salads, and French fries. It also forms the base for various other sauces, such as tarta ...
,
soup Soup is a primarily liquid food, generally served warm or hot (but may be cool or cold), that is made by combining ingredients of meat or vegetables with stock, milk, or water. Hot soups are additionally characterized by boiling soli ...
, taffy, and
yogurt Yogurt (; , from tr, yoğurt, also spelled yoghurt, yogourt or yoghourt) is a food produced by bacterial fermentation of milk. The bacteria used to make yogurt are known as ''yogurt cultures''. Fermentation of sugars in the milk by these bac ...
* Natural substances such as
magma Magma () is the molten or semi-molten natural material from which all igneous rocks are formed. Magma is found beneath the surface of the Earth, and evidence of magmatism has also been discovered on other terrestrial planets and some natura ...
,
lava Lava is molten or partially molten rock (magma) that has been expelled from the interior of a terrestrial planet (such as Earth) or a moon onto its surface. Lava may be erupted at a volcano or through a fracture in the crust, on land or ...
,
gums The gums or gingiva (plural: ''gingivae'') consist of the mucosal tissue that lies over the mandible and maxilla inside the mouth. Gum health and disease can have an effect on general health. Structure The gums are part of the soft tissue li ...
,
honey Honey is a sweet and viscous substance made by several bees, the best-known of which are honey bees. Honey is made and stored to nourish bee colonies. Bees produce honey by gathering and then refining the sugary secretions of plants (primar ...
, and
extract An extract is a substance made by extracting a part of a raw material, often by using a solvent such as ethanol, oil or water. Extracts may be sold as tinctures, absolutes or in powder form. The aromatic principles of many spices, nuts ...
s such as vanilla extract * Biological fluids such as
blood Blood is a body fluid in the circulatory system of humans and other vertebrates that delivers necessary substances such as nutrients and oxygen to the cells, and transports metabolic waste products away from those same cells. Blood in the cir ...
,
saliva Saliva (commonly referred to as spit) is an extracellular fluid produced and secreted by salivary glands in the mouth. In humans, saliva is around 99% water, plus electrolytes, mucus, white blood cells, epithelial cells (from which DNA can ...
,
semen Semen, also known as seminal fluid, is an organic bodily fluid created to contain spermatozoa. It is secreted by the gonads (sexual glands) and other sexual organs of male or hermaphroditic animals and can fertilize the female ovum. Sem ...
,
mucus Mucus ( ) is a slippery aqueous secretion produced by, and covering, mucous membranes. It is typically produced from cells found in mucous glands, although it may also originate from mixed glands, which contain both serous and mucous cells. It ...
, and
synovial fluid Synovial fluid, also called synovia, elp 1/sup> is a viscous, non-Newtonian fluid found in the cavities of synovial joints. With its egg white–like consistency, the principal role of synovial fluid is to reduce friction between the articul ...
* Slurries such as cement slurry and paper pulp,
emulsion An emulsion is a mixture of two or more liquids that are normally immiscible (unmixable or unblendable) owing to liquid-liquid phase separation. Emulsions are part of a more general class of two-phase systems of matter called colloids. Alth ...
s such as mayonnaise, and some kinds of dispersions


Oobleck

An inexpensive,
non-toxic Toxicity is the degree to which a chemical substance or a particular mixture of substances can damage an organism. Toxicity can refer to the effect on a whole organism, such as an animal, bacterium, or plant, as well as the effect on a subst ...
example of a non-Newtonian fluid is a suspension of
starch Starch or amylum is a polymeric carbohydrate consisting of numerous glucose units joined by glycosidic bonds. This polysaccharide is produced by most green plants for energy storage. Worldwide, it is the most common carbohydrate in human die ...
(e.g., cornstarch) 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''. Because of its
dilatant A dilatant (, ) (also termed shear thickening) material is one in which viscosity increases with the rate of shear strain. Such a ''shear thickening fluid'', also known by the initialism ''STF'', is an example of a non-Newtonian fluid. This be ...
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.


Flubber (slime)

Flubber, also commonly known as slime, is a non-Newtonian fluid, easily made from
polyvinyl alcohol Poly(vinyl alcohol) (PVOH, PVA, or PVAl) is a water- soluble synthetic polymer. It has the idealized formula H2CH(OH)sub>''n''. It is used in papermaking, textile warp sizing, as a thickener and emulsion stabilizer in polyvinyl acetate (PVAc) ...
–based
glue Adhesive, also known as glue, cement, mucilage, or paste, is any non-metallic substance applied to one or both surfaces of two separate items that binds them together and resists their separation. The use of adhesives offers certain advant ...
s (such as white "school" glue) and
borax Borax is a salt (ionic compound), a hydrated borate of sodium, with chemical formula often written . It is a colorless crystalline solid, that dissolves in water to make a basic solution. It is commonly available in powder or granular form ...
. It flows under low stresses but breaks under higher stresses and pressures. This combination of fluid-like and solid-like properties makes it a Maxwell fluid. Its behaviour can also be described as being viscoplastic or gelatinous.


Chilled caramel topping

Another example of this is chilled caramel
ice cream Ice cream is a sweetened frozen food typically eaten as a snack or dessert. It may be made from milk or cream and is flavoured with a sweetener, either sugar or an alternative, and a spice, such as cocoa or vanilla, or with fruit such as ...
topping (so long as it incorporates hydrocolloids such as carrageenan and gellan gum). The sudden application of
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...
—by stabbing the surface with a finger, for example, or rapidly inverting the container holding it—causes the fluid to behave like a
solid Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structur ...
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 Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structur ...
polymer A polymer (; Greek '' poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
. 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 A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend ...
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 A gel is a semi-solid that can have properties ranging from soft and weak to hard and tough. Gels are defined as a substantially dilute cross-linked system, which exhibits no flow when in the steady-state, although the liquid phase may still di ...
and
Sol Sol or SOL may refer to: Astronomy * The Sun Currency * SOL Project, a currency project in France * French sol, or sou * Argentine sol * Bolivian sol, the currency of Bolivia from 1827 to 1864 * Peruvian sol, introduced in 1991 * Peruvian 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 Shear stress, often denoted by ( Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. '' Normal stress'', on ...
. 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, resulting in a sudden gush of the shear-thinned condiment.


Dry granular flows

Under certain circumstances, flows of
granular material A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when grains collide). The constituents that compose ...
s 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.


See also

* Complex fluid *
Dilatant A dilatant (, ) (also termed shear thickening) material is one in which viscosity increases with the rate of shear strain. Such a ''shear thickening fluid'', also known by the initialism ''STF'', is an example of a non-Newtonian fluid. This be ...
*
Dissipative particle dynamics Dissipative particle dynamics (DPD) is an off-lattice mesoscopic simulation technique which involves a set of particles moving in continuous space and discrete time. Particles represent whole molecules or fluid regions, rather than single atoms, and ...
* Generalized Newtonian fluid * Herschel–Bulkley fluid *
Liquefaction In materials science, liquefaction is a process that generates a liquid from a solid or a gas or that generates a non-liquid phase which behaves in accordance with fluid dynamics. It occurs both naturally and artificially. As an example of th ...
*
Navier–Stokes equations In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician Geo ...
* Newtonian fluid * Pseudoplastic * Quicksand * Quick clay *
Rheology Rheology (; ) is the study of the flow of matter, primarily in a fluid ( liquid or gas) state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an ap ...
* Superfluids * Thixotropy *
Weissenberg effect The Weissenberg effect is a phenomenon that occurs when a spinning rod is inserted into a solution of elastic liquid. Instead of being thrown outward, the solution is drawn towards the rod and rises up around it. This is a direct consequence of the ...


References


External links

* {{DEFAULTSORT:Non-Newtonian Fluid Continuum mechanics Fluid dynamics Viscosity Polymers Tribology