Rheology (; ) is the study of the flow of

matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...

, primarily in 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 ...

(

liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, a ...

gas Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...

) state, but also as "soft

solid Solid is one of the State of matter#Four fundamental states, four fundamental states of matter (the others being liquid, gas, and Plasma (physics), plasma). The molecules in a solid are closely packed together and contain the least amount o ...

s" or solids under conditions in which they respond with

plastic Plastics are a wide range of synthetic or semi-synthetic materials that use polymers as a main ingredient. Their plasticity makes it possible for plastics to be moulded, extruded or pressed into solid objects of various shapes. This adaptab ...

flow rather than deforming elastically in response to an applied force. Rheology is a branch of

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

, and it is the science that deals with the

deformation Deformation can refer to: * Deformation (engineering), changes in an object's shape or form due to the application of a force or forces. ** Deformation (physics), such changes considered and analyzed as displacements of continuum bodies. * Defor ...

and flow of materials, both solids and liquids.W. R. Schowalter (1978) Mechanics of Non-Newtonian Fluids Pergamon The term ''

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 appl ...

'' was coined by Eugene C. Bingham, a professor at

Lafayette College Lafayette College is a private liberal arts college in Easton, Pennsylvania. Founded in 1826 by James Madison Porter and other citizens in Easton, the college first held classes in 1832. The founders voted to name the college after General Laf ...

, in 1920, from a suggestion by a colleague,

Markus Reiner Markus Reiner ( he, מרכוס ריינר, born 5 January 1886, died 25 April 1976) was an Israeli scientist and a major figure in rheology. Biography Reiner was born in 1886 in Czernowitz, Bukovina, then part of Austria-Hungary, and obtained ...

.The Deborah Number
The term was inspired by the

aphorism An aphorism (from Greek ἀφορισμός: ''aphorismos'', denoting 'delimitation', 'distinction', and 'definition') is a concise, terse, laconic, or memorable expression of a general truth or principle. Aphorisms are often handed down by tra ...

Heraclitus Heraclitus of Ephesus (; grc-gre, Ἡράκλειτος , "Glory of Hera"; ) was an ancient Greek pre-Socratic philosopher from the city of Ephesus, which was then part of the Persian Empire. Little is known of Heraclitus's life. He wrote ...

(often mistakenly attributed to Simplicius), (, 'everything flows') 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 A MUD (; originally multi-user dungeon, with later variants multi-user dimension and multi-user domain) is a Multiplayer video game, multiplayer Time-keeping systems in games#Real-time, real-time virtual world, usually Text-based game, text-bas ...

sludge Sludge is a semi-solid slurry that can be produced from a range of industrial processes, from water treatment, wastewater treatment or on-site sanitation systems. For example, it can be produced as a settled suspension obtained from conventiona ...

suspensions In chemistry, a suspension is a heterogeneous mixture of a fluid that contains solid particles sufficiently large for sedimentation. The particles may be visible to the naked eye, usually must be larger than one micrometer, and will eventually ...

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 ...

s and other glass formers (e.g., silicates), as well as many foods and additives,

bodily fluid Body fluids, bodily fluids, or biofluids, sometimes body liquids, are liquids within the human body. In lean healthy adult men, the total body water is about 60% (60–67%) of the total body weight; it is usually slightly lower in women (52-55%). ...

s (e.g., blood) and other biological materials, and to other materials that belong to the class of soft matter such as food.

Newtonian fluids A Newtonian fluid is a fluid in which the viscous stresses arising from its flow are at every point linearly correlated to the local strain rate — the rate of change of its deformation over time. Stresses are proportional to the rate of chang ...

can be characterized by a single 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 inte ...

for a specific temperature. Although this

will change with temperature, it does not change with the

strain rate In materials science, strain rate is the change in strain (deformation) of a material with respect to time. The strain rate at some point within the material measures the rate at which the distances of adjacent parcels of the material change wi ...

. 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 In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the f ...

) are called

non-Newtonian fluids A non-Newtonian fluid is a fluid 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 ex ...

. 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 Ketchup or catsup is a table condiment with a sweet and tangy flavor. The unmodified term ("ketchup") now typically refers to tomato ketchup, although early recipes used egg whites, mushrooms, oysters, grapes, mussels, or walnuts, among other ...

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 Yogurt (; , from tr, yoğurt, also spelled yoghurt, yogourt or yoghourt) is a food produced by bacterial Fermentation (food), fermentation of milk. The bacteria used to make yogurt are known as ''yogurt cultures''. Fermentation of sugars in t ...

and

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. Althoug ...

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 ...

(US terminology

latex paint Acrylic paint is a fast-drying paint made of pigment suspended in acrylic polymer emulsion and plasticizers, silicone oils, defoamers, stabilizers, or metal soaps. Most acrylic paints are water-based, but become water-resistant when dry. Dep ...

acrylic paint Acrylic paint is a fast-drying paint made of pigment suspended in acrylic polymer emulsion and plasticizers, silicone oils, defoamers, stabilizers, or metal soaps. Most acrylic paints are water-based, but become water-resistant when dry. Depe ...

), exhibiting

thixotropy Thixotropy is a time-dependent shear thinning property. Certain gels or fluids that are thick or viscous under static conditions will flow (become thinner, less viscous) over time when shaken, agitated, shear-stressed, or otherwise stressed ( ...

, 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 In continuum mechanics, rheopecty or rheopexy is the rare property of some non-Newtonian fluids to show a time-dependent increase in viscosity (time-dependent viscosity); the longer the fluid undergoes shearing force, the higher its viscosity. R ...

: viscosity increasing with relative deformation, and are called shear-thickening 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 beha ...

materials. Since Sir

Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...

originated the concept of viscosity, the study of liquids with strain-rate-dependent viscosity is also often called '' Non-Newtonian fluid mechanics''. The experimental characterisation of a material's rheological behaviour is known as ''

rheometry Rheometry () generically refers to the experimental techniques used to determine the rheological properties of materials, that is the qualitative and quantitative relationships between stresses and strains and their derivatives. The techniques ...

'', 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 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 m ...

to characterize the flow of materials that exhibit a combination of

elastic Elastic is a word often used to describe or identify certain types of elastomer, elastic used in garments or stretchable fabrics. Elastic may also refer to: Alternative name * Rubber band, ring-shaped band of rubber used to hold objects togeth ...

viscous 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 inter ...

and

behavior by properly combining

elasticity Elasticity often refers to: *Elasticity (physics), continuum mechanics of bodies that deform reversibly under stress Elasticity may also refer to: Information technology * Elasticity (data store), the flexibility of the data model and the cl ...

and ( Newtonian)

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 bio ...

. 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

molecular A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...

size and architecture of

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 Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...

, 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.R. B. Bird, W. E. Stewart, E. N. Lightfoot (1960), Transport Phenomena, John Wiley & Sons, R. Byrin Bird, Charles F. Curtiss, Robert C. Armstrong (1989), Dynamics of Polymeric Liquids, Vol 1 & 2, Wiley Interscience, and 978-0471518440Faith A. Morrison (2001), Understanding Rheology, Oxford University Press, and 978-0195141665 Rheology unites the seemingly unrelated fields of

plasticity Plasticity may refer to: Science * Plasticity (physics), in engineering and physics, the propensity of a solid material to undergo permanent deformation under load * Neuroplasticity, in neuroscience, how entire brain structures, and the brain it ...

and

non-Newtonian fluid A non-Newtonian fluid is a fluid 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 exa ...

dynamics by recognizing that materials undergoing these types of deformation are unable to support a stress (particularly a

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 the ot ...

, since it is easier to analyze shear deformation) in static equilibrium. In this sense, a solid undergoing plastic

is a

, although no viscosity coefficient is associated with this flow. Granular rheology refers to the continuum mechanical description 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 gra ...

s. One of the major tasks of rheology is to establish by measurement the relationships between 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

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

. 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

* Fluid and solid character are relevant at long times:
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 In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly wi ...

) behaviour is relevant at short times (''transient behaviour''):
We again consider the application of a constant stress:William N. Findley, James S. Lai, Kasif Onaran (1989), Creep and Relaxation of Nonlinear Viscoelastic Materials, Dover Publications ** 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 Plasticity may refer to: Science * Plasticity (physics), in engineering and physics, the propensity of a solid material to undergo permanent deformation under load * Neuroplasticity, in neuroscience, how entire brain structures, and the brain it ...

is the behavior observed after the material is subjected to a ''yield stress'':
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 In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and wi ...

'' 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

On one end of the spectrum we have an

inviscid 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 inte ...

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. 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.

Reynolds number

, the

Reynolds number In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be domi ...

is a measure of the

ratio In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...

inertia Inertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his first law ...

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 p ...

s (

v_s\rho

) to

forces (

\frac

) 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 Laminar means "flat". Laminar may refer to: Terms in science and engineering: * Laminar electronics or organic electronics, a branch of material sciences dealing with electrically conductive polymers and small molecules * Laminar armour or "band ...

, whereas at high Reynolds numbers inertia predominates and the flow may be

turbulent In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between t ...

. 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 A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...

s in

fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...

and is used, usually along with other dimensionless numbers, to provide a criterion for determining

dynamic similitude Similitude is a concept applicable to the testing of engineering models. A model is said to have similitude with the real application if the two share geometric similarity, kinematic similarity and dynamic similarity. ''Similarity'' and ''simili ...

. 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: :

\mathrm = \frac = \frac = \frac

where: * ''u''_s – mean

, s⁻¹* ''L'' – characteristic length, * ''μ'' – (absolute) dynamic

, s m⁻²or

a s A, or a, is the first Letter (alphabet), letter and the first vowel of the Latin alphabet, Latin alphabet, used in the English alphabet, modern English alphabet, the alphabets of other western European languages and others worldwide. Its name ...

* ''ν'' – kinematic fluid viscosity:

v = \frac

, ² s⁻¹* ''ρ'' – fluid

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

, g m⁻³

Measurement

Rheometer A rheometer is a laboratory device used to measure the way in which a dense fluid (a liquid, suspension or slurry) flows in response to applied forces. It is used for those fluids which cannot be defined by a single value of viscosity and t ...

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 Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...

geophysics Geophysics () is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. The term ''geophysics'' som ...

physiology Physiology (; ) is the scientific study of functions and mechanisms in a living system. As a sub-discipline of biology, physiology focuses on how organisms, organ systems, individual organs, cells, and biomolecules carry out the chemical ...

, human

biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...

and

pharmaceutics Pharmaceutics is the discipline of pharmacy that deals with the process of turning a new chemical entity (NCE) or old drugs into a medication to be used safely and effectively by patients. It is also called the science of dosage form design. The ...

. Materials science is utilized in the production of many industrially important substances, such as

cement A cement is a binder, a chemical substance used for construction that sets, hardens, and adheres to other materials to bind them together. Cement is seldom used on its own, but rather to bind sand and gravel ( aggregate) together. Cement mix ...

, and

chocolate Chocolate is a food made from roasted and ground cacao seed kernels that is available as a liquid, solid, or paste, either on its own or as a flavoring agent in other foods. Cacao has been consumed in some form since at least the Olmec civ ...

, which have complex flow characteristics. In addition,

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

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 and use of

rubber Rubber, also called India rubber, latex, Amazonian rubber, ''caucho'', or ''caoutchouc'', as initially produced, consists of polymers of the organic compound isoprene, with minor impurities of other organic compounds. Thailand, Malaysia, and ...

plastics Plastics are a wide range of synthetic polymers, synthetic or semi-synthetic materials that use polymers as a main ingredient. Their Plasticity (physics), plasticity makes it possible for plastics to be Injection moulding, moulded, Extrusion, e ...

, and

fiber Fiber or fibre (from la, fibra, links=no) is a natural or artificial substance that is significantly longer than it is wide. Fibers are often used in the manufacture of other materials. The strongest engineering materials often incorporate ...

Polymers 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 an ...

constitute the basic materials of the rubber and plastic industries and are of vital importance to the textile,

petroleum Petroleum, also known as crude oil, or simply oil, is a naturally occurring yellowish-black liquid mixture of mainly hydrocarbons, and is found in geological formations. The name ''petroleum'' covers both naturally occurring unprocessed crud ...

automobile A car or automobile is a motor vehicle with Wheel, wheels. Most definitions of ''cars'' say that they run primarily on roads, Car seat, seat one to eight people, have four wheels, and mainly transport private transport#Personal transport, pe ...

paper Paper is a thin sheet material produced by mechanically or chemically processing cellulose fibres derived from wood, rags, grasses or other vegetable sources in water, draining the water through fine mesh leaving the fibre evenly distributed ...

, and

pharmaceutical industries The pharmaceutical industry discovers, develops, produces, and markets drugs or pharmaceutical drugs for use as medications to be administered to patients (or self-administered), with the aim to cure them, vaccinate them, or alleviate symptoms. ...

. 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

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 A silicone or polysiloxane is a polymer made up of siloxane (−R2Si−O−SiR2−, where R = organic group). They are typically colorless oils or rubber-like substances. Silicones are used in sealants, adhesives, lubricants, medicine, cooking ...

toy '

Silly Putty Silly Putty is a toy based on silicone polymers that have unusual physical properties. It bounces, but it breaks when given a sharp blow, and it can also flow like a liquid. It contains a viscoelastic liquid silicone, a type of non-Newtonian fl ...

' 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 Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of ...

. In addition, conventional rubber undergoes a

glass transition The glass–liquid transition, or glass transition, is the gradual and reversible transition in amorphous materials (or in amorphous regions within semicrystalline materials) from a hard and relatively brittle "glassy" state into a viscous or rubb ...

(often called a ''rubber-glass transition''). E.g. The 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 solid-fuel rocket boosters.

Biopolymers

Sol-gel

With the

of a sol adjusted into a proper range, both

optical Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...

quality glass fiber and

refractory In materials science, a refractory material or refractory is a material that is resistant to decomposition by heat, pressure, or chemical attack, and retains strength and form at high temperatures. Refractories are polycrystalline, polyphase, ...

ceramic fiber can be drawn which are used for

fiber-optic sensor A fiber-optic sensor is a sensor that uses optical fiber either as the sensing element ("intrinsic sensors"), or as a means of relaying signals from a remote sensor to the electronics that process the signals ("extrinsic sensors"). Fibers have m ...

s and

thermal insulation Thermal insulation is the reduction of heat transfer (i.e., the transfer of thermal energy between objects of differing temperature) between objects in thermal contact or in range of radiative influence. Thermal insulation can be achieved with s ...

, respectively. The mechanisms of

hydrolysis Hydrolysis (; ) is any chemical reaction in which a molecule of water breaks one or more chemical bonds. The term is used broadly for substitution reaction, substitution, elimination reaction, elimination, and solvation reactions in which water ...

and

condensation Condensation is the change of the state of matter from the gas phase into the liquid phase, and is the reverse of vaporization. The word most often refers to the water cycle. It can also be defined as the change in the state of water vapor to ...

, 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

includes study of the flow of molten

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 un ...

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 In geology, a rheid is a substance whose temperature is below its melting point and whose deformation by viscous flow during the time of observation is at least three orders of magnitude (1,000×) greater than the elastic deformation under the ...

s. For example,

granite Granite () is a coarse-grained (phaneritic) intrusive igneous rock composed mostly of quartz, alkali feldspar, and plagioclase. It forms from magma with a high content of silica and alkali metal oxides that slowly cools and solidifies undergro ...

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 10²⁰ poises.

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 Hemorheology, also spelled haemorheology (from Greek ‘αἷμα, ''haima'' 'blood' and rheology, from Greek ῥέω ''rhéō'', ' flow' and -λoγία, ''-logia'' 'study of'), or blood rheology, is the study of flow properties of blood and its ...

. This is the study of flow properties of blood and its elements (

plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral), a green translucent silica mineral * Quark–gluon plasma, a state of matter in quantum chromodynamics Biology * Blood pla ...

and formed elements, including

red blood cell Red blood cells (RBCs), also referred to as red cells, red blood corpuscles (in humans or other animals not having nucleus in red blood cells), haematids, erythroid cells or erythrocytes (from Greek ''erythros'' for "red" and ''kytos'' for "holl ...

white blood cell White blood cells, also called leukocytes or leucocytes, are the cell (biology), cells of the immune system that are involved in protecting the body against both infectious disease and foreign invaders. All white blood cells are produced and de ...

s and

platelet Platelets, also called thrombocytes (from Greek θρόμβος, "clot" and κύτος, "cell"), are a component of blood whose function (along with the coagulation factors) is to react to bleeding from blood vessel injury by clumping, thereby ini ...

s).

Blood viscosity Hemorheology, also spelled haemorheology (from Greek ‘αἷμα, ''haima'' 'blood' and rheology, from Greek ῥέω ''rhéō'', ' flow' and -λoγία, ''-logia'' 'study of'), or blood rheology, is the study of flow properties of blood and its ...

is determined by plasma viscosity,

hematocrit The hematocrit () (Ht or HCT), also known by several other names, is the volume percentage (vol%) of red blood cells (RBCs) in blood, measured as part of a blood test. The measurement depends on the number and size of red blood cells. It is norm ...

(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 leading characteristic for hemorheology has been

shear thinning In rheology, shear thinning is the non-Newtonian behavior of fluids whose viscosity decreases under shear strain. It is sometimes considered synonymous for pseudo-plastic behaviour, and is usually defined as excluding time-dependent effects, suc ...

in steady shear flow. Other non-Newtonian rheological characteristics that blood can demonstrate includes pseudoplasticity,

viscoelasticity In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly wi ...

, and

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. The foundation of hemorheology can also provide information for modeling of other biofluids. 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. 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. The effect of rouleaux aggregation tendency can be explained by hematocrit and fibrinogen concentration in whole blood rheology. Some techniques researchers use are optical trapping and microfluidics to measure cell interaction in vitro.

Disease and Diagnostics

Changes to viscosity has been shown to be linked with diseases like hyperviscosity, hypertension, sickle cell anemia, and diabetes. Hemorheological measurements and genomic testing technologies that act as preventative measures and diagnostic tools. 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.

Zoology

Many animals make use of rheological phenomena, for example sandfish that exploit the granular rheology of dry sand to "swim" in it or land gastropods that use

snail slime Snail slime (''mucopolysaccharide'') is a kind of mucus (an external bodily secretion) produced by snails, which are gastropod mollusks. Land snails and slugs both produce mucus, as does every other kind of gastropod, from marine, freshwater, ...

for adhesive

locomotion Locomotion means the act or ability of something to transport or move itself from place to place. Locomotion may refer to: Motion * Motion (physics) * Robot locomotion, of man-made devices By environment * Aquatic locomotion * Flight * Locomo ...

. Certain animals produce specialized

endogenous Endogenous substances and processes are those that originate from within a living system such as an organism, tissue, or cell. In contrast, exogenous substances and processes are those that originate from outside of an organism. For example, es ...

complex fluid Complex fluids are mixtures that have a coexistence between two phases: solid–liquid (suspensions or solutions of macromolecules such as polymers), solid–gas (granular), liquid–gas (foams) or liquid–liquid (emulsions). They exhibit unusua ...

s, such as the sticky slime produced by

velvet worm Onychophora (from grc, ονυχής, , "claws"; and , , "to carry"), commonly known as velvet worms (due to their velvety texture and somewhat wormlike appearance) or more ambiguously as peripatus (after the first described genus, '' Peripatus ...

s to immobilize prey or the fast-gelling underwater slime secreted by

hagfish Hagfish, of the class Myxini (also known as Hyperotreti) and order Myxiniformes , are eel-shaped, slime-producing marine fish (occasionally called slime eels). They are the only known living animals that have a skull but no vertebral column, a ...

to deter predators.

Food rheology

Food rheology Food rheology is the study of the rheological properties of food, that is, the consistency and flow of food under tightly specified conditions. The consistency, degree of fluidity, and other mechanical properties are important in understandin ...

is important in the manufacture and processing of food products, such as cheese and

gelato Gelato (; ) is the common word in Italian for all kinds of ice cream. In English, it specifically refers to a frozen dessert of Italian origin. Artisanal gelato in Italy generally contains 6%–9% butterfat, which is lower than other styles o ...

. An adequate rheology is important for the indulgence of many common foods, particularly in the case of sauces, dressings,

, or

fondue Fondue (, , ) is a Swiss melted cheese dish served in a communal pot ( ''caquelon'' or fondue pot) over a portable stove () heated with a candle or spirit lamp, and eaten by dipping bread into the cheese using long-stemmed forks. It was promote ...

Thickening agents A thickening agent or thickener is a substance which can increase the viscosity of a liquid without substantially changing its other properties. Edible thickeners are commonly used to thicken sauces, soups, and puddings without altering thei ...

, or

thickeners A thickening agent or thickener is a substance which can increase the viscosity of a liquid without substantially changing its other properties. Edible thickeners are commonly used to thicken sauces, soups, and puddings without altering their t ...

, are substances which, when added to an aqueous mixture, increase its

without substantially modifying its other properties, such as taste. They provide body, increase

stability Stability may refer to: Mathematics *Stability theory, the study of the stability of solutions to differential equations and dynamical systems **Asymptotic stability **Linear stability **Lyapunov stability **Orbital stability **Structural stabilit ...

, and improve

suspension Suspension or suspended may refer to: Science and engineering * Suspension (topology), in mathematics * Suspension (dynamical systems), in mathematics * Suspension of a ring, in mathematics * Suspension (chemistry), small solid particles suspend ...

of added ingredients. Thickening agents are often used as

food additive Food additives are substances added to food to preserve flavor or enhance taste, appearance, or other sensory qualities. Some additives have been used for centuries as part of an effort to preserve food, for example vinegar (pickling), salt (salt ...

s and in

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 protect ...

and

personal hygiene product Personal care or toiletries are consumer products used in personal hygiene, personal grooming or for beautification. Products Personal care includes products as diverse as cleansing pads, colognes, cotton swabs, cotton pads, deodorant, eye line ...

s. Some thickening agents are gelling agents, forming a

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 dif ...

. The agents are materials used to thicken and stabilize liquid solutions,

s, and

. They dissolve in the liquid phase as a

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 ...

mixture that forms a weakly cohesive internal structure. Food thickeners frequently are based on either

polysaccharide Polysaccharides (), or polycarbohydrates, are the most abundant carbohydrates found in food. They are long chain polymeric carbohydrates composed of monosaccharide units bound together by glycosidic linkages. This carbohydrate can react with wa ...

s (

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 diets ...

es,

vegetable gum Natural gums are polysaccharides of natural origin, capable of causing a large increase in a solution's viscosity, even at small concentrations. They are mostly botanical gums, found in the woody elements of plants or in seed coatings. Human u ...

s, and

pectin Pectin ( grc, πηκτικός ': "congealed" and "curdled") is a heteropolysaccharide, a structural acid contained in the primary lamella, in the middle lamella, and in the cell walls of terrestrial plants. The principal, chemical component of ...

), or

protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respo ...

Concrete rheology

Concrete Concrete is a composite material composed of fine and coarse aggregate bonded together with a fluid cement (cement paste) that hardens (cures) over time. Concrete is the second-most-used substance in the world after water, and is the most wi ...

's and mortar's workability is related to the rheological properties of the fresh

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 Superplasticizers (SPs), also known as high range water reducers, are additives used in making high strength concrete. Plasticizers are chemical compounds that enable the production of concrete with approximately 15% less water content. Superplast ...

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.

Filled polymer rheology

The incorporation of various types of

fillers In processed animal foods, a filler is an ingredient added to provide dietary fiber, bulk or some other non-nutritive purpose. Products like corncobs, feathers, soy, cottonseed hulls, peanut hulls, citrus pulp, screening, weeds, straw, and cere ...

into

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. 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 Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...

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. An additional factor is the

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 Surface finishing is a broad range of industrial processes that alter the surface of a manufactured item to achieve a certain property. Finishing processes may be employed to: improve appearance, adhesion or wettability, solderability, corrosion re ...

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.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

Rheologist

A rheologist is an

interdisciplinary Interdisciplinarity or interdisciplinary studies involves the combination of multiple academic disciplines into one activity (e.g., a research project). It draws knowledge from several other fields like sociology, anthropology, psychology, ec ...

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 Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...

geology Geology () is a branch of natural science concerned with Earth and other astronomical objects, the features or rocks of which it is composed, and the processes by which they change over time. Modern geology significantly overlaps all other Ear ...

), engineering (e.g.

mechanical Mechanical may refer to: Machine * Machine (mechanical), a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement * Mechanical calculator, a device used to perform the basic operations of ...

chemical A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., wi ...

, materials science, plastics engineering and engineering or

civil engineering Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewage ...

medicine Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care pract ...

, or certain technologies, notably

materials Material is a substance or mixture of substances that constitutes an object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical and chemical properties, or on their geologic ...

food Food is any substance consumed by an organism for nutritional support. Food is usually of plant, animal, or fungal origin, and contains essential nutrients, such as carbohydrates, fats, proteins, vitamins, or minerals. The substance is inge ...

. 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.

Scope

Viscoelasticity

Dimensionless numbers

Deborah number

Reynolds number

Measurement

Applications

Materials science

Polymers

Biopolymers

Sol-gel

Geophysics

Physiology

Red Blood Cell Aggregation

Disease and Diagnostics

Zoology

Food rheology

Concrete rheology

Filled polymer rheology

Rheologist

See also

References

External links