Editing Non-Newtonian fluid

{{short description|Fluid whose viscosity varies with the amount of force/stress applied to it}}
{{More references needed|date=March 2024}}
{{Continuum mechanics|cTopic=fluid}}
In [[physics]] and [[chemistry]], 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 (mechanics)|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 {{nobr|non-Newtonian fluids}}, as are many commonly found substances such as [[custard]],<ref name=ScientificAmerican>{{cite magazine| title=An-Ti-Ci-Pa-Tion: The Physics of Dripping Honey |first=Jennifer| last=Ouellette |magazine=Scientific American| year = 2013| url=https://blogs.scientificamerican.com/cocktail-party-physics/an-ti-ci-pa-tion-the-physics-of-dripping-honey/}}</ref> [[toothpaste]], [[starch]] suspensions, [[paint]], [[blood]], melted [[butter]] and [[shampoo]].

Most commonly, the [[viscosity]] (the gradual deformation by shear or [[tensile stress]]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]] and the shear rate is linear, passing through the [[Origin (mathematics)|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 [[rheology|rheological]] properties that relate [[Stress (physics)|stress]] and [[strain rate]] tensors under many different flow conditions—such as [[Oscillation|oscillatory]] shear or extensional flow—which are measured using different devices or [[rheometer]]s. 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 flow|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,<ref>{{Cite journal |last=Oldroyd |first=J. |date=1950 |title=On the Formulation of Rheological Equations of State |url=https://royalsocietypublishing.org/doi/10.1098/rspa.1950.0035 |journal= Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences|volume=200 |issue=1063 |pages=523–541 |doi=10.1098/rspa.1950.0035|bibcode=1950RSPSA.200..523O }}</ref> Walters’ Liquid B<ref>{{Cite journal |last=Walters |first=K. |date=1963 |title=Non -Newtonian effects in some elastic-viscous liquids whose behavior at small rates of shear is characterized by a general linear equations of state |journal=Quart. J. Mech. Appl. Math. |volume=6 |pages=63}}</ref> and Williamson<ref>{{Cite journal |last=Williamson |first=R.V |title=The flow of pseudoplastic materials |url=https://pubs.acs.org/doi/abs/10.1021/ie50239a035 |journal=Ind. Eng. Chem. |date=1929 |volume=21 |issue=11 |pages=1108–1111 |doi=10.1021/ie50239a035}}</ref> fluids.

Time-dependent [[Self-similar solution|self-similar]] analysis of the [[Olga Ladyzhenskaya|Ladyzenskaya]]-type model with a non-linear velocity dependent stress tensor was performed<ref>{{Cite journal |last1=I.F. |first1=Barna |last2=Bognár |first2=G. |last3=Hriczó |first3=K. |date=2016 |title=Self-Similar Analytic Solution of the Two-Dimensional Navier-Stokes Equation with a Non-Newtonian Type of Viscosity |url=https://journals.vilniustech.lt/index.php/MMA/article/view/797 |journal=Mathematical Modelling and Analysis |volume=21 |issue=1 |pages=83–94 |arxiv=1410.1303 |doi=10.3846/13926292.2016.1136901}}</ref> unfortunately no analytical solutions could be derived, however a rigorous mathematical existence theorem<ref>{{Cite journal |last1=Wei |first1=D. |last2=Al-Ashhab |first2=S. |date=2019 |title=Existence of self-similar solutions of the two-dimensional Navier–Stokes equation for non-Newtonian fluids |journal=Arab Journal of Mathematical Sciences |volume=26 |issue=(1/2) |pages=167 |doi=10.1016/j.ajmsc.2019.04.001|doi-access=free }}</ref> was given for the solution.

For time-independent non-Newtonian fluids the known analytic solutions are much broader.<ref>{{Cite journal |last1=Guedda |first1=M. |last2=Hammouch |first2=Z. |date=2008 |title=Similarity flow solutions of a non-Newtonian power-law fluid |url=https://hal.science/hal-00372650/ |journal=International Journal of Nonlinear Science |volume=6 |issue=3 |pages=255–264 |arxiv=0904.0315}}</ref><ref>{{Cite journal |last1=Guedda |first1=M. |last2=Kersner |first2=R. |date=2011 |title=Non-Newtonian pseudoplastic fluids: Analytical results and exact solutions |url=https://www.sciencedirect.com/science/article/abs/pii/S002074621100062X |journal=International Journal of Non-Linear Mechanics |volume=46 |issue=7 |pages=949–957 |doi=10.1016/j.ijnonlinmec.2011.04.009|bibcode=2011IJNLM..46..949G }}</ref><ref>{{Cite journal |last1=Wei |first1=D.H. |last2=Al-Ashhab |first2=S. |date=2014 |title=Similarity solutions for non-newtonian power-law fluid flow. |url=https://www.amm.shu.edu.cn/EN/10.1007/s10483-014-1854-6 |journal=Applied Mathematics and Mechanics |volume=35 |issue=9 |pages=1155–1166 |doi=10.1007/s10483-014-1854-6}}</ref><ref>{{Cite journal |last=Bognár |first=G. |date=2009 |title=Similarity solution of boundary layer flow for non-Newtonian fluids |url=https://www.sciencedirect.com/science/article/pii/S089812211000725X |journal=International Journal of Nonlinear Sciences and Numerical Simulation |volume=10 |pages=555–1566 |doi=10.1016/j.camwa.2010.09.039}}</ref>

==Types of non-Newtonian behavior==

===Summary===
[[File:Rheology of time independent fluids.svg|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<ref name=springer2>{{cite book| title=Springer handbook of experimental fluid mechanics |first1=Cameron |last1=Tropea |first2=Alexander L. |last2=Yarin |first3=John F. |last3=Foss |publisher=Springer |year=2007 |isbn=978-3-540-25141-5 |pages=661, 676 |url=https://books.google.com/books?id=y0xDUAdQAlkC&q=thixotropic&pg=PA667}}</ref>
|Some [[lubricant]]s, [[whipped cream]], [[Silly Putty]]
|-
|rowspan=2|[[Time-dependent viscosity]]
|[[Rheopecty|Rheopectic]]
|[[Apparent viscosity]] increases with duration of stress
|[[Synovial fluid]], [[printer ink]], [[gypsum]] paste
|-
|[[Thixotropy|Thixotropic]]
|Apparent viscosity decreases with duration of stress<ref name=springer2/>
|[[Yogurt]], [[peanut butter]], [[xanthan gum]] solutions, aqueous [[iron oxide]] gels, [[gelatin]] gels, [[pectin]] gels, [[castor wax|hydrogenated castor oil]], some [[clay]]s (including [[bentonite]], and [[montmorillonite]]), [[carbon black]] suspension in molten tire rubber, some [[drilling mud]]s, many [[paint]]s, many [[Flocculant|floc]] suspensions, many [[colloid]]al suspensions
|-
|rowspan=3|Non-Newtonian viscosity
|[[Shear thickening]] (dilatant)
|Apparent viscosity increases with increased stress<ref name=padb/>
|Suspensions of [[corn starch]] in water (oobleck)
|-
|[[Shear thinning]] (pseudoplastic)
|Apparent viscosity decreases with increased stress<ref>{{cite book|title=Rheology of Fluid and Semisolid Foods: Principles and Applications |first=M. A. |last=Rao |publisher=Springer |edition=2nd|year=2007 |isbn=978-0-387-70929-1 |page=8 |url=https://books.google.com/books?id=BLlmimePW18C&q=%22shear+thinning%22&pg=PA8}}</ref><ref>{{cite book| title=Emulsions, Foams, and Suspensions: Fundamentals and Applications |first=Laurier L. |last=Schramm |publisher=Wiley VCH |year=2005 |isbn=978-3-527-30743-2 |page=173 |url=https://books.google.com/books?id=qFi61f1NqNIC&q=pseudoplastic&pg=PA173}}</ref>
|[[Nail polish]], [[whipped cream]], [[ketchup]], [[molasses]], syrups, paper pulp in water, [[Acrylic paint|latex paint]], [[ice sheet dynamics|ice]], [[blood]], some [[silicone oil]]s, some [[silicone resin|silicone coatings]], [[quicksand|sand in water]]
|-
|-
|colspan=1|[[Generalized Newtonian fluid]]s
|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 thickening{{snd}}i.e. [[dilatant]]{{snd}} fluid appears to increase when the shear rate increases. [[Corn starch]] suspended in water ("oobleck", see [[#Oobleck|below]]) is a common example: when stirred slowly it looks milky, when stirred vigorously it feels like a very viscous liquid.

===Shear thinning fluid===
[[File:Painting with non-newtonian fluid.jpg|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|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 [[Thixotropy|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 plastic]]s. 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 fluid|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:<ref>{{cite book|last=Chhabra|first=R.P.|title=Bubbles, Drops, and Particles in Non-Newtonian Fluids.|year=2006|publisher=Taylor & Francis Ltd.|location=Hoboken|isbn=978-1-4200-1538-6|pages=9–10|edition=2nd}}</ref><ref>{{Cite book |last1=Astarita |first1=G. |title=Principles of Non-Newtonian Fluid Mechanics |last2=Marucci |first2=G. |publisher=McGraw-Hill |year=1972 |isbn=9780070840225}}</ref><ref>{{Cite book |last=Fridtjov |first=I. |title=Rheology and Non-Newtonian Fluids |date=2014 |publisher=Springer |isbn=9783319010526}}</ref><ref>{{Cite book |last1=Patel |first1=M. |title=Non-Newtonian Fluid Models and Boundary Layer Flow |last2=Timol |first2=M. |publisher=LAP Lambert Academic Publishing |year=2020 |isbn=9786203198614}}</ref><ref>{{Cite book |last=Hori |first=Y. |title=Hydrodynamic Lubrication |date=2006 |publisher=Springer |isbn=9784431278986}}</ref><ref>{{Cite book |last=Böhme |first=G. |title=Non-Newtonian Fluid Mechanics. |date=1987 |publisher=North-Holland |isbn=9780444567826}}</ref>

* Soap solutions, [[cosmetics]], and toothpaste
* Food such as [[butter]], [[cheese]], [[jam]], [[mayonnaise]], [[soup]], [[Taffy (candy)|taffy]], and [[yogurt]] 
* Natural substances such as [[magma]], [[lava]], [[Natural gum|gums]], [[honey]], and [[extract]]s such as [[vanilla extract]]
* Biological fluids such as [[blood]], [[saliva]], [[semen]], [[mucus]], and [[synovial fluid]]
* [[Slurry|Slurries]] such as cement slurry and paper pulp, [[emulsion]]s such as mayonnaise, and some kinds of [[Dispersion (chemistry)|dispersions]]

===Oobleck===
[[File:UniversumUNAM55 (cropped).JPG|thumb|Demonstration of a non-Newtonian fluid at [[Universum (UNAM)|Universum]] in Mexico City]]
[[File:Corn speaker.jpg|thumb|right|Oobleck on a subwoofer. Applying force to oobleck, by sound waves in this case, makes the non-Newtonian fluid thicken.<ref>This demonstration of oobleck is a popular subject for YouTube videos.{{which|date=March 2021}}</ref>]]
An inexpensive, [[Toxicity|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).<ref name="Oobleck: The Dr. Seuss Science Experiment">{{cite web|url=http://www.instructables.com/id/Oobleck/|title=Oobleck: The Dr. Seuss Science Experiment|website=instructables.com}}</ref><ref name="Outrageous Ooze">{{cite web|url=http://www.exploratorium.edu/science_explorer/ooze.html|title=Outrageous Ooze|website=Exploratorium|date=7 March 2023 }}</ref><ref name="Magic Mud and Other Great Experiments">{{cite book|chapter-url=https://books.google.com/books?id=v4qow8T1qsYC&pg=PA235|pages=235–236|title=The Complete Home Learning Source Book|last=Rupp|first=Rebecca|chapter=Magic Mud and Other Great Experiments|year=1998|publisher=Three Rivers Press |isbn=978-0-609-80109-3}}</ref> The name "oobleck" is derived from the [[Dr. Seuss]] book ''[[Bartholomew and the Oobleck]]''.<ref name="Oobleck: The Dr. Seuss Science Experiment"/>

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 wave]]s 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)===
{{main|Flubber (material)}}
[[File:Pouring Slime.JPG|thumb|Slime flows under low stresses but breaks under higher stresses]]
Flubber, also commonly known as slime, is a non-Newtonian fluid, easily made from [[polyvinyl alcohol]]–based [[glue]]s (such as white "school" glue) and [[borax]]. 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 material|Maxwell fluid]]. Its behaviour can also be described as being [[viscoplasticity|viscoplastic]] or [[gelatinous]].<ref>[http://www.extension.iastate.edu/e-set/science_is_here/glurch.html Glurch Meets Oobleck] {{webarchive|url=https://web.archive.org/web/20100706182730/http://www.extension.iastate.edu/e-set/science_is_here/glurch.html |date=6 July 2010 }}. [[Iowa State University]] Extension.</ref>

===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.<ref>{{cite thesis |title=The Rheology of Caramel |year=2004 |first=Giuseppina |last=Barra |type=PhD |publisher=University of Nottingham |url=http://eprints.nottingham.ac.uk/11837}}</ref>

===Silly Putty===
{{main|Silly Putty}}
Silly Putty is a silicone polymer based [[Suspension (chemistry)|suspension]] that will flow, bounce, or break, depending on strain rate.

===Plant resin===
{{main|Pitch (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===
{{Main|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 (colloid)|sol]] phase and seemingly liquefying, causing objects on the surface of the quicksand to sink.

===Ketchup===
[[Ketchup]] is a [[shear thinning]] fluid.<ref name=padb>{{cite book |title=Pump Application Desk Book |edition=3rd |first=Paul N. |last=Garay |publisher=Prentice Hall |year=1996 |isbn=978-0-88173-231-3 |page=358 |url=https://books.google.com/books?id=pww5cxwitHAC&q=thixotropic&pg=PA359}}</ref><ref>{{cite journal |title=Microscopy reveals why ketchup squirts |url=http://www.rsc.org/chemistryworld/News/2011/September/02091103.asp |journal=Chemistry World |last=Cartwright |first=Jon |date=2 September 2011 |publisher=Royal Society of Chemistry}}</ref> 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.
<!-- unreferenced, potential original research:
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{{citation needed|date=February 2012}}, using [[potato starch]], [[sugar]] and eatable liquid, like milk or water, eggs optionally. Any starch solution shows properties of non-Newtonian liquid.
--->

===Dry granular flows===
Under certain circumstances, flows of [[granular material]]s can be modelled as a continuum, for example using the [[Μ(I) rheology|''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.

=== Radioactive waste vitrification ===
Important issue for non-Newtonian fluids is glass behavior during [[High-level radioactive waste management|radioactive waste]] vitrification when special attention is given to [[Viscosity models for mixtures|viscosity]] of the molten multicomponent glass being described by Douglas-Doremus-[[Michael Ojovan|Ojovan]] (DDO) model of viscosity of glasses and melts <ref>{{Cite journal |last1=Yudintsev |first1=Sergey V. |last2=Ojovan |first2=Michael I. |last3=Malkovsky |first3=Victor I. |date=February 2024 |title=Thermal Effects and Glass Crystallization in Composite Matrices for Immobilization of the Rare-Earth Element–Minor Actinide Fraction of High-Level Radioactive Waste |journal=Journal of Composites Science |language=en |volume=8 |issue=2 |pages=70 |doi=10.3390/jcs8020070 |doi-access=free |issn=2504-477X}}</ref>

==See also==
{{div col|colwidth=20em}}
* [[Complex fluid]]
* [[Dilatant]]
* [[Dissipative particle dynamics]]
* [[Generalized Newtonian fluid]]
* [[Herschel–Bulkley fluid]]
* [[Liquefaction]] 
* [[Navier–Stokes equations]]
* [[Newtonian fluid]]
* [[Pseudoplastic]]
* [[Quicksand]]
* [[Quick clay]]
* [[Rheology]]
* [[Superfluids]]
* [[Thixotropy]]
* [[Weissenberg effect]]
{{div col end}}

==References==
{{Reflist|30em}}

==External links==
{{Commons category|Non-Newtonian fluids}}
* {{YouTube|id=Ol6bBB3zuGc|title=Classical experiments with Non-Newtonian fluids by the National Committee for Fluid Mechanics}}

{{Non-Newtonian fluids}}

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