View source for Rheology

{{short description|Study of the flow of matter, primarily in a fluid state}}
{{morerefs|date=May 2023}}
{{Continuum mechanics|cTopic=rheology}}
'''Rheology''' ({{IPAc-en|r|iː|ˈ|ɒ|l|ə|dʒ|i}}; {{ety|el|''ῥέω'' (rhéō)|flow||''-λoγία'' (-logia)|study of}}) is the study of the flow of [[matter]], primarily in a [[fluid]] ([[liquid]] or [[gas]]) state but also as "soft [[solid]]s" or solids under conditions in which they respond with [[Plasticity (physics)|plastic]] flow rather than deforming [[Elasticity (physics)|elastically]] in response to an applied force.[https://books.google.com/books?id=B1e0uxFg4oYC&dq=rheology&pg=PA1] Rheology is the branch of [[physics]] that deals with the [[Deformation (physics)|deformation]] and flow of materials, both solids and liquids.<ref name=Schowalter>W. R. Schowalter (1978) Mechanics of Non-Newtonian Fluids Pergamon {{ISBN|0-08-021778-8}}</ref>

The term ''[[wikt:rheology|rheology]]'' was coined by [[Eugene C. Bingham]], a professor at [[Lafayette College]], in 1920 from a suggestion by a colleague, [[Markus Reiner]].<ref>{{cite book|author=James Freeman Steffe|title=Rheological Methods in Food Process Engineering|url=https://books.google.com/books?id=LrrdONuST9kC|date=1 January 1996|publisher=Freeman Press|isbn=978-0-9632036-1-8}}</ref><ref name="deb1">[http://rrc.engr.wisc.edu/deborah.html The Deborah Number] {{webarchive|url=https://web.archive.org/web/20110413144406/http://rrc.engr.wisc.edu/deborah.html |date=2011-04-13 }}</ref> The term was inspired by the [[aphorism]] of  [[Heraclitus]] (often mistakenly attributed to [[Simplicius of Cilicia|Simplicius]]), {{lang|grc-Latn|[[Heraclitus#Panta rhei, "everything flows"|panta rhei]]}} ({{lang|grc|πάντα ῥεῖ}}, 'everything flows'<ref name=Barnes1982>{{cite book |title=The presocratic philosophers |year=1982 |last=Barnes |first=Jonathan |publisher=Routledge |isbn=978-0-415-05079-1 }}</ref><ref>{{cite journal |last1=Beris |first1=A. N. |first2=A. J. |last2=Giacomin |title=πάντα ῥεῖ&nbsp;: Everything Flows |journal=Applied Rheology |volume=24 |page=52918 |year=2014 |doi=10.3933/ApplRheol-24-52918 |s2cid=195789095 }}</ref>) and was first used to describe the flow of liquids and the deformation of solids. It applies to substances that have a complex microstructure, such as [[mud]]s, [[sludge]]s, [[suspension (chemistry)|suspensions]], and [[polymer]]s and other [[glass transition|glass formers]] (e.g., silicates), as well as many foods and additives, [[bodily fluid]]s (e.g., blood) and other [[Body fluid|biological materials]], and other materials that belong to the class of [[soft matter]] such as food.

[[Newtonian fluids]] can be characterized by a single coefficient of [[viscosity]] for a specific temperature. Although this viscosity will change with temperature, it does not change with the [[strain rate]]. Only a small group of fluids exhibit such constant viscosity. The large class of fluids whose viscosity changes with the strain rate (the relative [[flow velocity]]) are called [[non-Newtonian fluids]].

Rheology generally accounts for the behavior of non-Newtonian fluids by characterizing the minimum number of functions that are needed to relate stresses with rate of change of strain or strain rates. For example, [[ketchup]] can have its [[viscosity]] reduced by shaking (or other forms of mechanical agitation, where the relative movement of different layers in the material actually causes the reduction in viscosity), but water cannot. Ketchup is a shear-thinning material, like [[yogurt]] and [[emulsion]] [[paint]] (US terminology [[latex paint]] or [[acrylic paint]]), exhibiting [[thixotropy]], where an increase in relative flow velocity will cause a reduction in viscosity, for example, by stirring. Some other non-Newtonian materials show the opposite behavior, [[rheopecty]] (viscosity increasing with relative deformation), and are called shear-thickening or [[dilatant]] materials. Since Sir [[Isaac Newton]] originated the concept of viscosity, the study of liquids with strain-rate-dependent viscosity is also often called ''[[non-Newtonian fluid|Non-Newtonian fluid mechanics]]''.<ref name=Schowalter />

The experimental characterisation of a material's rheological behaviour is known as ''[[rheometry]]'', although the term ''rheology'' is frequently used synonymously with rheometry, particularly by experimentalists. Theoretical aspects of rheology are the relation of the flow/deformation behaviour of material and its internal structure (e.g., the orientation and elongation of polymer molecules) and the flow/deformation behaviour of materials that cannot be described by classical fluid mechanics or elasticity.

== Scope ==

In practice, rheology is principally concerned with extending [[continuum mechanics]] to characterize the flow of materials that exhibit a combination of [[elastic deformation|elastic]], [[Viscosity|viscous]] and [[plastic]] behavior by properly combining [[theory of elasticity|elasticity]] and ([[Newtonian fluid|Newtonian]]) [[fluid mechanics]]. It is also concerned with predicting mechanical behavior (on the continuum mechanical scale) based on the micro- or nanostructure of the material, e.g. the [[Molecule|molecular]] size and architecture of [[polymer]]s in solution or the particle size distribution in a solid suspension.
Materials with the characteristics of a fluid will flow when subjected to a [[Stress (physics)|stress]], which is defined as the force per area. There are different sorts of stress (e.g. shear, torsional, etc.), and materials can respond differently under different stresses. Much of theoretical rheology is concerned with associating external forces and torques with internal stresses, internal strain gradients, and flow velocities.<ref name=Schowalter /><ref name="bird1">R. B. Bird, W. E. Stewart, E. N. Lightfoot (1960), Transport Phenomena, John Wiley & Sons, {{ISBN|0-471-07392-X}}.{{pn|date=June 2024}}</ref><ref name="bird2">R. Byrin Bird, Charles F. Curtiss, Robert C. Armstrong (1989), Dynamics of Polymeric Liquids, Vol 1 & 2, Wiley Interscience, {{ISBN|0-471-51844-1}} and 978-0471518440.{{pn|date=June 2024}}</ref><ref name="morris1">Faith A. Morrison (2001), Understanding Rheology, Oxford University Press, {{ISBN|0-19-514166-0}} and 978-0195141665.{{pn|date=June 2024}}</ref>

{{Continuum mechanics context}}

Rheology unites the seemingly unrelated fields of [[plasticity (physics)|plasticity]] and [[non-Newtonian fluid]] dynamics by recognizing that materials undergoing these types of deformation are unable to support a stress (particularly a [[shear stress]], since it is easier to analyze shear deformation) in static [[Mechanical equilibrium|equilibrium]]. In this sense, a solid undergoing plastic [[deformation (mechanics)|deformation]] is a [[fluid]], although no viscosity coefficient is associated with this flow. Granular rheology refers to the continuum mechanical description of [[granular material]]s.

One of the major tasks of rheology is to establish by measurement the relationships between [[Strain (materials science)|strains]] (or rates of strain) and stresses, although a number of theoretical developments (such as assuring frame invariants) are also required before using the empirical data. These experimental techniques are known as [[rheometry]] and are concerned with the determination of well-defined ''rheological material functions''. Such relationships are then amenable to mathematical treatment by the established methods of [[continuum mechanics]].

The characterization of flow or deformation originating from a simple shear stress field is called '''shear rheometry''' (or shear rheology). The study of extensional flows is called '''extensional rheology'''. Shear flows are much easier to study and thus much more experimental data are available for shear flows than for extensional flows.

== Viscoelasticity ==
{{Main|Viscoelasticity}}
* Fluid and solid character are relevant at long times:<br />We consider the application of a constant stress (a so-called ''creep experiment''):
** if the material, after some deformation, eventually resists further deformation, it is considered a solid
** if, by contrast, the material flows indefinitely, it is considered a fluid
* By contrast, ''elastic and viscous'' (or intermediate, [[viscoelastic]]) behaviour is relevant at short times (''transient behaviour''):<br />We again consider the application of a constant stress:<ref name="creep1">William N. Findley, James S. Lai, Kasif Onaran (1989), Creep and Relaxation of Nonlinear Viscoelastic Materials, Dover Publications</ref>
** if the material deformation strain increases linearly with increasing applied stress, then the material is linear elastic within the range it shows recoverable strains. Elasticity is essentially a time independent processes, as the strains appear the moment the stress is applied, without any time delay.
** if the material deformation strain rate increases linearly with increasing applied stress, then the material is viscous in the Newtonian sense. These materials are characterized due to the time delay between the applied constant stress and the maximum strain.
** if the materials behaves as a combination of viscous and elastic components, then the material is viscoelastic. Theoretically such materials can show both instantaneous deformation as elastic material and a delayed time dependent deformation as in fluids.
* [[Plasticity (physics)|Plasticity]] is the behavior observed after the material is subjected to a ''yield stress'':<br />A material that behaves as a solid under low applied stresses may start to flow above a certain level of stress, called the ''[[yield stress]]'' of the material. The term ''plastic solid'' is often used when this plasticity threshold is rather high, while ''yield stress fluid'' is used when the threshold stress is rather low. However, there is no fundamental difference between the two concepts.

== Dimensionless numbers ==

=== Deborah number ===

{{Main|Deborah number}}

On one end of the spectrum we have an [[inviscid flow|inviscid]] or a simple Newtonian fluid and on the other end, a rigid solid; thus the behavior of all materials fall somewhere in between these two ends. The difference in material behavior is characterized by the level and nature of elasticity present in the material when it deforms, which takes the material behavior to the non-Newtonian regime. The non-dimensional Deborah number is designed to account for the degree of non-Newtonian behavior in a flow.  The Deborah number is defined as the ratio of the characteristic time of relaxation (which purely depends on the material and other conditions like the temperature) to the characteristic time of experiment or observation.<ref name="deb1" /><ref>{{cite journal|last1=Reiner|first1=M.|title=The Deborah Number|journal=Physics Today|volume=17|issue=1|year=1964|pages=62 |doi=10.1063/1.3051374|bibcode = 1964PhT....17a..62R }}</ref> Small Deborah numbers represent Newtonian flow, while   non-Newtonian (with both viscous and elastic effects present) behavior occurs for intermediate range Deborah numbers, and high Deborah numbers indicate an elastic/rigid solid. Since Deborah number is a relative quantity, the numerator or the denominator can alter the number. A very small Deborah number can be obtained for a fluid with extremely small relaxation time or a very large experimental time, for example.
<!--
When the rheological behavior of a material includes a transition from elastic to viscous as the time scale increases (or, more generally, a transition from a more resistant to a less resistant behavior), one may define the relevant time scale as a relaxation time of the material. Correspondingly, the ratio of the relaxation time of a material to the timescale of a deformation is called [[Deborah number]]. Small Deborah numbers correspond to situations where the material has time to relax (and behaves in a viscous manner), while high Deborah numbers correspond to situations where the material behaves rather elastically.<ref>M. Reiner (1964) ''Physics Today'' volume 17 no 1 page 62 ''The Deborah Number''</ref><ref>[http://rrc.engr.wisc.edu/deborah.html The Deborah Number]</ref>
Note that the Deborah number is relevant for materials that flow on long time scales (like a [[Maxwell material|Maxwell fluid]]) but ''not'' for the reverse kind of materials ([[Kelvin–Voigt material]]s) that are viscous on short time scales but solid on the long term.-->

=== Reynolds number ===
{{Main|Reynolds number}}
In [[fluid mechanics]], the [[Reynolds number]] is a measure of the [[ratio]] of [[inertia]]l [[force]]s (<math>v_s\rho</math>) to [[viscosity|viscous]] forces (<math>\frac{\mu}{L}</math>) and consequently it quantifies the relative importance of these two types of effect for given flow conditions.  Under low Reynolds numbers viscous effects dominate and the flow is [[Laminar flow|laminar]], whereas at high Reynolds numbers inertia predominates and the flow may be [[turbulent]]. However, since rheology is concerned with fluids which do not have a fixed [[viscosity]], but one which can vary with flow and time, calculation of the Reynolds number can be complicated.

It is one of the most important [[dimensionless number]]s in [[fluid dynamics]] and is used, usually along with other dimensionless numbers, to provide a criterion for determining [[dynamic similitude]]. When two geometrically similar flow patterns, in perhaps different fluids with possibly different flow rates, have the same values for the relevant dimensionless numbers, they are said to be dynamically similar.

Typically it is given as follows:

:<math> \mathrm{Re} = \frac{\rho \frac{u_{s}^2}{L} }{ \mu \frac{u_{s}}{L^2}} = \frac{\rho u_{s} L}{ \mu} = \frac{u_{s} L}{ \nu} </math>

where:
* ''u''<sub>s</sub> – mean [[flow velocity]], [m s<sup>−1</sup>]
* ''L'' – characteristic length, [m]
* ''μ'' – (absolute) dynamic [[fluid]] viscosity, [N s m<sup>−2</sup>] or [Pa s]
* ''ν'' – kinematic fluid viscosity: <math>v = \frac{\mu}{\rho}</math>, [m<sup>2</sup> s<sup>−1</sup>]
* ''ρ'' – fluid [[density]], [kg m<sup>−3</sup>].

== Measurement ==
[[Rheometer]]s are instruments used to characterize the rheological properties of materials, typically fluids that are melts or solution. These instruments impose a specific stress field or deformation to the fluid, and monitor the resultant deformation or stress. Instruments can be run in steady flow or oscillatory flow, in both shear and extension.

== Applications ==

Rheology has applications in [[materials science]], [[engineering]], [[geophysics]], [[physiology]], human [[biology]] and [[pharmaceutics]]. Materials science is utilized in the production of many industrially important substances, such as [[cement]], [[paint]], and [[chocolate]], which have complex flow characteristics. In addition, [[Plasticity (physics)|plasticity]] theory has been similarly important for the design of metal forming processes. The science of rheology and the characterization of viscoelastic properties in the production and use of [[polymer]]ic materials has been critical for the production of many products for use in both the industrial and military sectors.
Study of flow properties of liquids is important for pharmacists working in the manufacture of several dosage forms, such as simple liquids, ointments, creams, pastes etc. The flow behavior of liquids under applied stress is of great relevance in the field of pharmacy. Flow properties are used as important quality control tools to maintain the superiority of the product and reduce batch to batch variations.

=== Materials science ===

==== Polymers ====

Examples may be given to illustrate the potential applications of these principles to practical problems in the processing<ref>{{cite book |last1=Shenoy |first1=Aroon V. |last2=Saini |first2=D. R. |title=Thermoplastic melt rheology and processing |date=1996 |publisher=Marcel Dekker Inc. |location=New York |isbn=9780824797232}}</ref> and use of [[rubber]]s, [[plastics]], and [[fiber]]s. [[Polymers]] constitute the basic materials of the rubber and plastic industries and are of vital importance to the textile, [[petroleum industry|petroleum]], [[automobile industry|automobile]], [[paper industry|paper]], and [[pharmaceutical industries]]. Their viscoelastic properties determine the mechanical performance of the final products of these industries, and also the success of processing methods at intermediate stages of production.

In [[Viscoelasticity|viscoelastic]] materials, such as most polymers and plastics, the presence of liquid-like behaviour depends on the properties of  and so varies with rate of applied load, i.e., how quickly a force is applied. The [[silicone]] toy '[[Silly Putty]]' behaves quite differently depending on the time rate of applying a force. Pull on it slowly and it exhibits continuous flow, similar to that evidenced in a highly viscous liquid. Alternatively, when hit hard and directly, it shatters like a [[silicate glass]].

In addition, conventional rubber undergoes a [[glass transition]] (often called a ''rubber-glass transition''). E.g. The [[Space Shuttle Challenger|Space Shuttle ''Challenger'']] disaster was caused by rubber O-rings that were being used well below their glass transition temperature on an unusually cold Florida morning, and thus could not flex adequately to form proper seals between sections of the two [[Space Shuttle Solid Rocket Booster|solid-fuel rocket boosters]].

==== Biopolymers ====
[[File:Cellulose strand.svg|thumb|right|300px|Linear structure of [[cellulose]] — the most common component of all [[organic matter|organic]] plant life on Earth. * Note the evidence of [[hydrogen bonding]] which increases the [[viscosity]] at any temperature and pressure. This is an effect similar to that of [[polymer]] [[Cross-link|crosslinking]], but less pronounced.]]

==== Sol-gel ====
{{Main|sol-gel}}
[[File:Sol-gel silicate bonds.svg|thumb|right|300px|[[Polymerization]] process of [[tetraethylorthosilicate]] (TEOS) and water to form [[amorphous]] [[hydrated]] [[silica]] particles (Si-OH) can  be monitored [[rheolog]]ically by a number of different methods.]]

With the [[viscosity]] of a [[sol (colloid)|sol]] adjusted into a proper range, both [[optical]] quality glass fiber and [[refractory]] ceramic fiber can be drawn which are used for [[fiber-optic sensor]]s and [[thermal insulation]], respectively. The mechanisms of [[hydrolysis]] and [[condensation]], and the rheological factors that bias the structure toward linear or branched structures are the most critical issues of [[sol-gel]] science and technology.

=== Geophysics ===
The scientific discipline of [[geophysics]] includes study of the flow of molten [[lava]] and study of debris flows (fluid mudslides). This disciplinary branch also deals with solid Earth materials which only exhibit flow over extended time-scales. Those that display viscous behaviour are known as [[rheid]]s. For example, [[granite]] can flow plastically with a negligible yield stress at room temperatures (i.e. a viscous flow). Long-term creep experiments (~10 years) indicate that the viscosity of granite and glass under ambient conditions are on the order of 10<sup>20</sup> poises.<ref>{{cite journal |last1=Kumagai |first1=Naoichi |last2=Sasajima |first2=Sadao |last3=Ito |first3=Hidebumi |title=岩石の長年クリープ実験--巨大試片約20年間・小試片約3年間の結果 (岩石力学<特集>) |trans-title=Long-term creep experiment on rocks: Results of 20 years on large specimens and 3 years on small specimens |language=ja |journal=Journal of the Society of Materials Science, Japan |date=1978 |volume=27 |issue=293 |pages=155–161 |doi=10.2472/jsms.27.155 }}</ref><ref>
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=== Physiology ===

Physiology includes the study of many bodily fluids that have complex structure and composition, and thus exhibit a wide range of viscoelastic flow characteristics.  In particular there is a specialist study of blood flow called [[hemorheology]]. This is the study of flow properties of blood and its elements ([[Blood plasma|plasma]] and formed elements, including [[red blood cell]]s, [[white blood cell]]s and [[platelet]]s). [[Blood viscosity]] is determined by plasma viscosity, [[hematocrit]] (volume fraction of red blood cell, which constitute 99.9% of the cellular elements) and mechanical behaviour of red blood cells. Therefore, red blood cell mechanics is the major determinant of flow properties of blood.(The ocular [[Vitreous humor]] is subject to rheologic observations, particularly during studies of age-related vitreous liquefaction, or [[synaeresis]].)<ref>{{cite journal |doi= 10.1055/s-2003-44551 |author= Baskurt OK, Meiselman HJ |title= Blood rheology and hemodynamics |journal= Seminars in Thrombosis and Hemostasis |volume=29 |issue= 5 |pages=435–450 |year=2003 |pmid= 14631543 |last2= Meiselman |s2cid= 17873138 }}</ref>

The leading characteristic for hemorheology has been [[shear thinning]] in steady shear flow. Other non-Newtonian rheological characteristics that blood can demonstrate includes [[pseudoplasticity]], [[viscoelasticity]], and [[thixotropy]].<ref name="Beris-2021">{{Cite journal |last1=Beris |first1=Antony N. |last2=Horner |first2=Jeffrey S. |last3=Jariwala |first3=Soham |last4=Armstrong |first4=Matthew J. |last5=Wagner |first5=Norman J. |date=2021 |title=Recent advances in blood rheology: a review |journal=Soft Matter |volume=17 |issue=47 |pages=10591–10613 |doi=10.1039/D1SM01212F |pmid=34787149 |arxiv=2109.05088 |bibcode=2021SMat...1710591B |s2cid=237492003 }}</ref>

==== Red blood cell aggregation ====
There are two current major hypotheses to explain blood flow predictions and [[shear thinning]] responses. The two models also attempt to demonstrate the drive for reversible red blood cell aggregation, although the mechanism is still being debated. There is a direct effect of red blood cell aggregation on blood viscosity and circulation.<ref name="Lee-2017">{{Cite journal |last1=Lee |first1=Kisung |last2=Wagner |first2=Christian |last3=Priezzhev |first3=Alexander V. |date=2017 |title=Assessment of the "cross-bridge"-induced interaction of red blood cells by optical trapping combined with microfluidics |journal=Journal of Biomedical Optics |volume=22 |issue=9 |pages=091516 |doi=10.1117/1.JBO.22.9.091516 |pmid=28636066 |bibcode=2017JBO....22i1516L |s2cid=27534435 |doi-access=free }}</ref> The foundation of [[hemorheology]] can also provide information for modeling of other biofluids.<ref name="Beris-2021" /> The bridging or "cross-bridging" hypothesis suggests that macromolecules physically crosslink adjacent red blood cells into rouleaux structures. This occurs through adsorption of macromolecules onto the red blood cell surfaces.<ref name="Beris-2021" /><ref name="Lee-2017" /> The depletion layer hypothesis suggests the opposite mechanism. The surfaces of the red blood cells are bound together by an osmotic pressure gradient that is created by depletion layers overlapping.<ref name="Beris-2021" /> The effect of rouleaux aggregation tendency can be explained by [[hematocrit]] and fibrinogen concentration in whole blood rheology.<ref name="Beris-2021" /> Some techniques researchers use are optical trapping and microfluidics to measure cell interaction in vitro.<ref name="Lee-2017" />

==== Disease and diagnostics ====
Changes to viscosity has been shown to be linked with diseases like hyperviscosity, hypertension, sickle cell anemia, and diabetes.<ref name="Beris-2021" /> [[Hemorheological]] measurements and genomic testing technologies act as preventative measures and diagnostic tools.<ref name="Beris-2021" /><ref>{{Cite journal |last1=Hurst |first1=Anna C. E. |last2=Robin |first2=Nathaniel H. |date=2020 |title=Dysmorphology in the Era of Genomic Diagnosis |journal=Journal of Personalized Medicine |volume=10 |issue=1 |pages=18 |doi=10.3390/jpm10010018 |pmc=7151624 |pmid=32192103 |doi-access=free }}</ref>

[[Hemorheology]] has also been correlated with aging effects, especially with impaired blood fluidity, and studies have shown that physical activity may improve the thickening of blood rheology.<ref>{{Cite journal |last1=Simmonds |first1=Michael J. |last2=Meiselman |first2=Herbert J. |last3=Baskurt |first3=Oguz K. |date=2013 |title=Blood rheology and aging |journal=Journal of Geriatric Cardiology |volume=10 |issue=3 |pages=291–301 |doi=10.3969/j.issn.1671-5411.2013.03.010 |doi-broken-date=1 November 2024 |pmid=24133519 |pmc=3796705 }}</ref>

=== Zoology ===

Many animals make use of rheological phenomena, for example [[Scincus scincus|sandfish]] that exploit the granular rheology of dry sand to "swim" in it or [[Gastropoda|land gastropods]] that use [[snail slime]] for adhesive [[animal locomotion|locomotion]]. Certain animals produce specialized [[Endogeny|endogenous]] [[complex fluid]]s, such as the sticky slime produced by [[velvet worm]]s to immobilize prey or the fast-gelling underwater slime secreted by [[hagfish]] to deter predators.<ref>{{cite journal |last1=Rühs |first1=Patrick A. |last2=Bergfreund |first2=Jotam |last3=Bertsch |first3=Pascal |last4=Gstöhl |first4=Stefan J. |last5=Fischer |first5=Peter |title=Complex fluids in animal survival strategies |journal=Soft Matter |date=2021 |volume=17 |issue=11 |pages=3022–3036 |doi=10.1039/D1SM00142F|pmid=33729256 | arxiv=2005.00773  |bibcode=2021SMat...17.3022R |s2cid=232260738 |url=https://pubs.rsc.org/en/content/articlelanding/2021/sm/d1sm00142f}}</ref>

=== Food rheology ===

[[Food rheology]] is important in the manufacture and processing of food products, such as cheese<ref>S. Gunasekaran, M. Mehmet (2003), ''Cheese rheology and texture'', CRC Press, {{ISBN|1-58716-021-8}}</ref> and [[gelato]].<ref>{{Cite journal|last=Silaghi|first=Florina |display-authors=etal |date=July 2010|title=Estimation of rheological properties of gelato by FT-NIR spectroscopy|journal=Food Research International|volume=43|issue=6|pages=1624–1628|doi=10.1016/j.foodres.2010.05.007}}</ref> An adequate rheology is important for the indulgence of many common foods, particularly in the case of sauces,<ref>{{cite journal |last1=Okonkwo |first1=Valentine C. |last2=Mba |first2=Ogan I. |last3=Kwofie |first3=Ebenezer M. |last4=Ngadi |first4=Michael O. |title=Rheological Properties of Meat Sauces as Influenced by Temperature |journal=Food and Bioprocess Technology |date=November 2021 |volume=14 |issue=11 |pages=2146–2160 |doi=10.1007/s11947-021-02709-9 |s2cid=238223322 |url=https://link.springer.com/article/10.1007/BF00712312}}</ref> dressings,<ref>{{cite journal |last1=Franco |first1=Jose Maria |last2=Guerrero |first2=Antonio |last3=Gallegos |first3=Crispulo |title=Rheology and processing of salad dressing emulsions |journal=Rheologica Acta |date=1995 |volume=34 |issue=6 |pages=513–524 |doi=10.1007/BF00712312 |s2cid=94776693 |url=https://link.springer.com/article/10.1007/BF00712312}}</ref> [[yogurt]],<ref>{{cite journal |last1=Benezech |first1=T. |last2=Maingonnat |first2=J.F. |title=Characterization of the rheological properties of yoghurt—A review |journal=Journal of Food Engineering |date=January 1994 |volume=21 |issue=4 |pages=447–472 |doi=10.1016/0260-8774(94)90066-3 |url=https://dx.doi.org/10.1016/0260-8774%2894%2990066-3}}</ref> or [[fondue]].<ref>{{cite journal |last1=Bertsch |first1=Pascal |last2=Savorani |first2=Laura |last3=Fischer |first3=Peter |title=Rheology of Swiss Cheese Fondue |journal=ACS Omega |date=31 January 2019 |volume=4 |issue=1 |pages=1103–1109 |doi=10.1021/acsomega.8b02424 |pmid=31459386 |pmc=6648832 }}</ref>

[[Thickening agents]], or thickeners, are substances which, when added to an aqueous mixture, increase its [[viscosity]] without substantially modifying its other properties, such as taste. They provide body, increase [[strength of materials|stability]], and improve [[suspension (chemistry)|suspension]] of added ingredients. Thickening agents are often used as [[food additive]]s and in [[cosmetics]] and [[personal hygiene product]]s. Some thickening agents are '''gelling agents''', forming a [[gel]]. The agents are materials used to thicken and stabilize liquid solutions, [[emulsion]]s, and [[suspension (chemistry)|suspensions]]. They dissolve in the liquid phase as a [[colloid]] mixture that forms a weakly cohesive internal structure. Food thickeners frequently are based on either [[polysaccharide]]s ([[starch]]es, [[vegetable gum]]s, and [[pectin]]), or [[protein]]s.<ref>{{cite book
|url=https://books.google.com/books?id=wM1asp1LL8EC&q=Food%20Rheology&pg=PA130
|title=Texture in food – Introduction to food rheology and its measurement
|access-date=2009-09-18
|last=B.M. McKenna
|first=and J.G. Lyng
|isbn=978-1-85573-673-3
|year=2003
|publisher=Elsevier Science
}}</ref><ref>Nikolaev L.K., Nikolaev B.L., [http://processes.ihbt.ifmo.ru/en/article/10760/Experimental_study_of_rheological_characteristics_of_melted_cheese_%C2%ABMilk%C2%BB.htm "EXPERIMENTAL STUDY OF RHEOLOGICAL CHARACTERISTICS OF MELTED CHEESE «MILK»"], Processes and equipment for food production, Number 4(18), 2013</ref>

=== Concrete rheology ===
[[Concrete]]'s and [[Mortar (masonry)|mortar]]'s workability is related to the rheological properties of the fresh [[cement]] paste. The mechanical properties of hardened concrete increase if less water is used in the concrete mix design, however reducing the water-to-cement ratio may decrease the ease of mixing and application. To avoid these undesired effects, [[superplasticizer]]s are typically added to decrease the apparent yield stress and the viscosity of the fresh paste. Their addition highly improves concrete and mortar properties.<ref>{{cite journal|last1=Ferrari|first1=L|last2=Kaufmann|first2=J|last3=Winnefeld|first3=F|last4=Plank|first4=J|title=Multi-method approach to study influence of superplasticizers on cement suspensions|journal=Cement and Concrete Research|volume=41|page=1058|year=2011|doi=10.1016/j.cemconres.2011.06.010|issue=10}}</ref>

=== Filled polymer rheology ===
The incorporation of various types of [[Filler (materials)|fillers]] into [[polymer]]s is a common means of reducing cost and to impart certain desirable mechanical, thermal, electrical and magnetic properties to the resulting material. The advantages that filled polymer systems have to offer come with an increased complexity in the rheological behavior.<ref>{{cite book|doi=10.1007/978-94-015-9213-0|title=Rheology of Filled Polymer Systems|year=1999|last1=Shenoy|first1=Aroon V.|isbn=978-90-481-4029-9}}</ref>

Usually when the use of fillers is considered, a compromise has to be made between the improved mechanical properties in the solid state on one side and the increased difficulty in melt processing, the problem of achieving uniform [[dispersion (chemistry)|dispersion]] of the filler in the polymer matrix and the economics of the process due to the added step of compounding on the other.  The rheological properties of filled polymers are determined not only by the type and amount of filler, but also by the shape, size and  size distribution of its particles. The viscosity of filled systems generally increases with increasing filler fraction. This can be partially ameliorated via broad particle size distributions via the [[Farris effect (rheology)|Farris effect]]. An additional factor is the [[stress (mechanics)|stress]] transfer at the filler-polymer interface.  The interfacial adhesion can be substantially enhanced via a coupling agent that adheres well to both the polymer and the filler particles.  The type and amount of [[surface treatment]] on the filler are thus additional parameters affecting the rheological and material properties of filled polymeric systems.

It is important to take into consideration wall slip when performing the rheological characterization of highly filled materials, as there can be a large difference between the actual strain and the measured strain.<ref>C. Feger, M. McGlashan-Powell, I. Nnebe, D.M. Kalyon, Rheology and Stability of Highly Filled Thermal Pastes, IBM Research Report, RC23869 (W0602-065) 2006. http://domino.research.ibm.com/library/cyberdig.nsf/papers/7AAC28E89CA36CC785257116005F824E/$File/rc23869.pdf</ref>

== Rheologist ==
{{norefs|section|date=May 2023}}
A rheologist is an [[interdisciplinary]] scientist or engineer who studies the flow of complex liquids or the deformation of soft solids. It is not a primary degree subject; there is no qualification of rheologist as such. Most rheologists have a qualification in mathematics, the physical sciences (e.g. [[chemistry]], [[physics]], [[geology]], [[biology]]), engineering (e.g. [[Mechanical engineering|mechanical]], [[Chemical engineering|chemical]], [[Materials science|materials science, plastics engineering and engineering]] or [[civil engineering]]), [[medicine]], or certain technologies, notably [[Materials science|materials]] or [[Food science|food]]. Typically, a small amount of rheology may be studied when obtaining a degree, but a person working in rheology will extend this knowledge during postgraduate research or by attending short courses and by joining a professional association.

== See also ==
* [[Bingham plastic]]
* [[Die swell]]
* [[Fluid dynamics]]
* [[Glass transition]]
* [[Interfacial rheology]]
* [[Liquid]]
* [[List of rheologists]]
* [[Microrheology]]
* [[Nordic Rheology Society]]<ref>{{Cite web|title=Nordic Rheology Society {{!}} UIA Yearbook Profile {{!}} Union of International Associations|url=https://uia.org/s/or/en/1100064780|access-date=2021-12-01|website=uia.org}}</ref>
* [[Rheological weldability]] for thermoplastics
* [[Rheopectic]]
* [[Solid]]
* [[Transport phenomena]]
* [[μ(I) rheology]]: one model of the rheology of a granular flow.

== References ==
{{reflist|30em}}

== External links ==
{{wiktionary}}
* [http://www.rheology.org/sor/publications/rheology_b/jan02/origin_of_rheology.pdf "The Origins of Rheology: A short historical excursion"] {{Webarchive|url=https://web.archive.org/web/20190819032440/http://www.rheology.org/sor/publications/rheology_b/jan02/origin_of_rheology.pdf |date=2019-08-19 }} by Deepak Doraiswamy, DuPont iTechnologies
* [https://web.archive.org/web/20160316132753/http://www.rheotest.de/english/company/history RHEOTEST Medingen GmbH] – Short history and collection of rheological instruments from the time of Fritz Höppler
* [http://www.rheology.org/sor/publications/rheology_b/RB2014Jul.pdf] {{Webarchive|url=https://web.archive.org/web/20181220171954/http://www.rheology.org/sor/publications/rheology_b/RB2014Jul.pdf |date=2018-12-20 }} - On the Rheology of Cats

; Societies
* [http://www.rheology.org/sor/ American Society of Rheology]
* [http://www.rheology.org.au/ Australian Society of Rheology]
* [http://www.bsr.org.uk/ British Society of Rheology]
* [http://www.rheology-esr.net/ European Society of Rheology]
* [http://www.legfr.fr/ French Society of Rheology]
* [https://nordicrheologysociety.org/ Nordic Rheology Society]
* [http://reologie.ro/ Romanian Society of Rheology]
* [https://www.rheology.or.kr/ Korean Society of Rheology]

; Journals
* ''[http://www.ar.ethz.ch/ Applied Rheology]''
* ''[http://www.journals.elsevier.com/journal-of-non-newtonian-fluid-mechanics/ Journal of Non-Newtonian Fluid Mechanics]''
* ''[http://www.journalofrheology.org/ Journal of Rheology]''
* ''[https://link.springer.com/journal/397 Rheologica Acta]''

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