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| {{Continuum mechanics|cTopic=Rheology}}
| | Greetings. Allow me begin by telling you the author's title - Phebe. California is our beginning place. To collect coins is 1 of the things I love most. I am a meter reader but I strategy on altering it.<br><br>Here is my weblog [http://www.teenvalley.net/blog/17832 www.teenvalley.net] |
| '''Rheology''' {{IPAc-en|r|iː|ˈ|ɒ|l|ə|dʒ|i}} is the study of the flow of matter, primarily in the liquid 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 applied force.<ref name=Schowalter>W. R. Schowalter (1978) Mechanics of Non-Newtonian Fluids Pergamon ISBN 0-08-021778-8</ref>
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| It applies to substances which have a complex microstructure, such as [[mud]]s, [[sludge]]s, [[Suspension (chemistry)|suspensions]], [[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 biological materials or other materials which belong to the class of [[soft matter]].
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| [[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, and they are known as Newtonian fluids. But for a large class of fluids, the viscosity changes with the strain rate (or relative velocity of flow) are called non-Newtonian fluids.
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| Rheology generally accounts for the behaviour of non-Newtonian fluids, by characterizing the minimum number of functions that are needed to relate stresses with rate of change of strains 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, as an increase in relative velocity caused a reduction in viscosity, while some other non-Newtonian materials show the opposite behaviour: viscosity going up with relative deformation, which 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/>
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| 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>J. F. Steffe (1996) ''Rheological Methods in Food Process Engineering'' 2nd ed ISBN 0-9632036-1-4 page 1</ref><ref = "deb1">[http://www.chbmeng.ohio-state.edu/classes/775/rsb/deborah.pdf The Deborah Number]</ref> The term was inspired by the [[aphorism]] of [[Simplicius of Cilicia|Simplicius]] (often misattributed to [[Heraclitus]]), ''[[Heraclitus#Panta rhei, "everything flows"|panta rhei]],'' "everything flows"<ref name=Barnes1982>{{cite book
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| | title = The presocratic philosophers
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| | year = 1982
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| | author = Barnes, Jonathan
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| | isbn = 978-0-415-05079-1
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| }}</ref>
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| The experimental characterization 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.
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| == Scope ==
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| In practice, rheology is principally concerned with extending [[continuum mechanics]] to characterize flow of materials, that exhibits a combination of elastic, viscous and plastic behaviour by properly combining [[theory of elasticity|elasticity]] and ([[Newtonian fluid|Newtonian]]) [[fluid mechanics]]. It is also concerned with establishing predictions for mechanical behaviour (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.
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| 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 for different stresses. Much of theoretical rheology is concerned with associating external forces and torques with internal stresses and internal strain gradients and 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</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</ref><ref name = "morris1">Faith A. Morrison (2001), Understanding Rheology, Oxford University Press, ISBN 0-19-514166-0 and 978-0195141665</ref>
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| {{Continuum mechanics context}}
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| 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, solids undergoing plastic 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.
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| One of the major tasks of rheology is to empirically establish the relationships between [[Strain (materials science)|deformations]] and stresses, respectively their [[derivative]]s by adequate measurements, 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 with well-defined ''rheological material functions''. Such relationships are then amenable to mathematical treatment by the established methods of [[continuum mechanics]].
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| 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.
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| == Rheologist ==
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| 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]], [[biology]]), engineering (e.g. [[Mechanical engineering|mechanical]], [[Chemical engineering|chemical]], [[Materials science|materials science 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 below).
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| == Viscoelasticity ==
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| {{main|Viscoelasticity}}
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| The classical theory of elasticity deals with the behaviour of elastic solids under small deformations, for which,(1) according to Hooke's Law, stress is directly proportional to the strain — but independent of the rate of strain, or how fast the deformation was applied, and (2) the strains are completely recoverable once the stress is removed. Materials that can be characterized by classical theory of elasticity are known as linear elastic materials, even for such materials the linear relationship between stress and strain may be valid only for a certain range of strains. A large number of solids show non-linear relationship between stress and strain even for small stresses (such as rubber), but if the strains are still recoverable they are known as non-linear elastic materials. The classical theory of fluid mechanics, governed by the Navier-Stokes equation, deals with the behaviour of viscous fluids, for which, according to Newton's Law, the stress is directly proportional to the rate of strain, but independent of the strain itself. These behaviour are, of course, generally observed for ideal materials under ideal conditions, although the behaviour of many solids approaches Hooke's law for infinitesimal strains, and that of many fluids approaches Newton's law for infinitesimal rates of strain. Two types of deviations from linearity may be considered here.
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| # When finite strains (larger strains, as opposed to infinitesimal strains) are applied to solid bodies, the stress-strain relationships are often much more complicated (i.e. Non-Hookean). Similarly, in steady flow with finite strain rates, many fluids exhibit marked deviations in stress-strain rate proportionality from Newtons law.
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| # Even if both strain and rate of strain are infinitesimal, a system may exhibit both liquid-like and solid-like characteristics. A good example of this is when a body which is not quite an elastic solid (i.e. an inelastic solid) does not maintain a constant deformation under constant stress, but rather continues to deform with time – or "creeps" under the same stress at constant temperature. When such a body is constrained at constant deformation, the stress required to hold it at that stretch level gradually diminishes—or "relaxes" with time.
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| Similarly, a fluid while flowing under constant stress may show some elastic properties as well, such as storing some of the energy input instead of dissipating it all as heat and random thermal motion of its molecular constituents or having some recovery of strains after stresses are removed, although it may never recover all of its deformation upon removal of the initial applied stress. When such bodies are subjected to a sinusoidally oscillating stress, the strain is neither exactly in phase with the stress (as it would be for a perfectly elastic solid) nor 90 degrees out of phase (as it would be for a perfectly viscous liquid) but rather exhibits a strain that lags the stress at a value between zero and 90 degrees: i.e., Some of the energy is stored and recovered in each cycle, and some is dissipated as heat. These are viscoelastic materials.
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| Thus, fluids are generally associated with viscous behaviour (a ''thick'' oil is a viscous liquid) and solids with elastic behaviour (an elastic string is an elastic solid). A more general point of view is to consider the material behaviour at short times (relative to the duration of the experiment/application of interest) and at long times.
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| * Fluid and solid character are relevant at long times:<br>We consider the application of a constant stress (a so-called ''creep experiment''):
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| ** if the material, after some deformation, eventually resists further deformation, it is considered a solid
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| ** if, by contrast, the material flows indefinitely, it is considered a fluid
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| * 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>
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| ** 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.
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| ** if the material deformation 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.
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| ** 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.
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| * [[Plasticity (physics)|Plasticity]] is the behaviour 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.
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| == Applications ==
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| 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.
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| 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 behaviour 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.
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| === Materials science ===
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| ==== Polymers ====
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| The viscoelastic properties of polymers are determined by the effects of the many variables, including temperature, pressure, and time. Other important variables include chemical composition, molecular weight and weight distribution, degree of branching and crystallinity, types of functionality, component concentration, dilution with solvents or plasticizers, and mixture with other materials to form composite systems. With guidance by molecular theory, the dependence of viscoelastic properties on these variables can be simplified by introducing additional concepts such as the free volume, the monomeric friction coefficient, and the spacing between entanglement loci, to provide a qualitative understanding and in many cases a quantitative prediction of how to achieve desired physical and chemical properties and ultimate microstructure.
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| Viscoelastic behaviour reflects the combined viscous and elastic responses, under mechanical stress, of materials which are intermediate between liquids and solids in character. Fundamentally, the viscoelasticity can be related to the motions of flexible polymer molecules and their entanglements and network junctions—the molecular basis of viscoelasticity. Thus, rearrangements on a local scale (kinks) are relatively rapid, while on a long-range scale (convolutions) very slow. In addition, a new assortment of configurations is obtained under stress. The response to the local aspects of the new distribution is rapid, while the response to the long-range aspects is slow. Thus there is very wide and continuous range of timescales covering the response of such a system to externally applied stress. From measurements of the viscoelastic properties of polymers, information can be obtained about the nature and the rates of change of the configurational rearrangements, and the nature of the (macro)molecular interactions over a range of time scales.
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| Examples may be given to illustrate the potential applications of these principles to practical problems in the processing and use of rubbers, plastics, and fibers. Polymers constitute the basic materials of the rubber and plastic industries and are of vital importance to the textile, petroleum, automobile, 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.
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| In [[Viscoelasticity|viscoelastic]] materials, such as most [[polymer]]s 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.
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| In addition, conventional [[rubber]] undergoes a [[glass transition]], (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 [[Space Shuttle Solid Rocket Booster|solid-fuel rocket boosters]].
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| ==== Biopolymers ====
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| [[Image: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]] [[crosslinking]], but less pronounced.]]
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| A major but defining difference between polymers and biopolymers can be found in their structures. Polymers, including biopolymers, are made of repetitive units called monomers. While polymers are often randomly constructed with massive entanglement, biopolymers often have a well defined structure. In the case of proteins, the exact chemical composition and the sequence in which these units are arranged is called the primary structure.
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| Many proteins spontaneously fold into characteristic compact shapes—which determine their biological functions and depend in a complicated way on their primary structures. Structural biology is the study of the structural properties of the biopolymers, much of which can be determined by their viscoelastic response to a wide range of loading conditions.
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| ==== Sol-gel ====
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| {{main|sol-gel}}
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| [[Image: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.]]
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| [[Sol-gel]] science (aka chemical solution deposition) is a wet-chemical technique widely used in the fields of [[materials science]], [[glass]] production and [[ceramic engineering]]. Such methods are used primarily for the fabrication of materials (typically a metal oxide) starting from a chemical solution which acts as the precursor for an integrated network (or gel) of either discrete [[nanoparticle]]s or network [[polymer]]s. Typical precursors are metal [[alkoxide]]s and metal [[chloride]]s, which undergo various forms of [[hydrolysis]] and [[polycondensation]] reactions in order to form a [[viscoelastic]] network (or [[solid]]).
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| One of the largest application areas is thin films and coatings, which can be produced on a piece of substrate by spin coating or dip coating. Other methods include spraying, electrophoresis, inkjet printing or roll coating. Optical coatings, protective and decorative coatings, and electro-optic components can be applied to glass, metal and other types of substrates with these 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 [[sensors]] 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.
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| === Geophysics ===
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| [[Geophysics]] includes the flow of molten [[lava]] and debris flows (fluid mudslides). Also included in this disciplinary branch are solid Earth materials which only exhibit flow over extended time scales. Those that display viscous behaviour are known as [[rheid]]s. E.G. [[granite]] can flow plastically with a vanishingly small 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>
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| Kumagai, N., Sasajima, S., Ito, H., ''Long-term Creep of Rocks'', J. Soc. Mat. Sci. (Japan), Vol. 27, p. 157 (1978) [http://translate.google.com/translate?hl=en&sl=ja&u=http://ci.nii.ac.jp/naid/110002299397/&sa=X&oi=translate&resnum=4&ct=result&prev=/search%3Fq%3DIto%2BHidebumi%26hl%3Den Online]
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| </ref><ref>
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| {{cite journal
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| | last1 =Vannoni
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| | first1 =M.
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| | last2 =Sordoni
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| | first2 =A.
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| | last3 =Molesini
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| | first3 =G.
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| | year = 2011
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| | title =Relaxation time and viscosity of fused silica glass at room temperature
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| | journal =Eur. Phys. J. E
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| | volume = 34
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| | pages = 9–14
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| | doi = 10.1140/epje/i2011-11092-9
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| }}</ref>
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| === Physiology ===
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| 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.<ref>The ocular [[Vitreous humor]] is subject to rheologic observations, particularly during studies of age-related vitreous liquefaction, or [[synaeresis]].
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| {{cite journal |doi= 10.1055/s-2003-44551 |author= Baskurt OK, Meiselman HJ |title= Blood rheology and hemodynamics |journal= Seminars in Thrombosis and Haemostasis |volume=29 |issue= 5 |pages=435–450 |year=2003 |pmid= 14631543 }}
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| </ref>
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| === Food rheology ===
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| [[Food rheology]] is important in the manufacture and processing of food products, e.g. cheese.<ref>
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| S. Gunasekaran, M. Mehmet (2003), Cheese rheology and texture, CRC Press, ISBN 1-58716-021-8
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| </ref> 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 understanding how long food can be stored, how stable it will remain, and in determining food texture. The acceptability of food products to the consumer is often determined by food texture, such as how spreadable and creamy a food product is. Food rheology is important in quality control during food manufacture and processing.
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| [[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)|suspension]]s. 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>
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| {{cite book
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| |url=http://books.google.com/?id=wM1asp1LL8EC&pg=PA130&dq=Food+Rheology&q=Food%20Rheology
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| |title=Texture in food > Introduction to food rheology and its measurement
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| |publisher=|accessdate=2009-09-18
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| |last=B.M. McKenna
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| |first=and J.G. Lyng
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| |isbn=978-1-85573-673-3
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| |year=2003
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| }}
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| </ref>
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| === Concrete rheology ===
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| [[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|pages=1058|year=2011|doi=10.1016/j.cemconres.2011.06.010|issue=10}}</ref>
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| == Measurement ==
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| [[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.
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| == Dimensionless numbers ==
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| === Deborah number ===
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| {{main|Deborah number}}
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| 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 behaviour of all materials fall somewhere in between these two ends. The difference in material behaviour is characterized by the level and nature of elasticity present in the material when it deforms, which takes the material behaviour to the non-Newtonian regime. The non-dimensional Deborah number is designed to account for the degree of non-Newtonian behaviour 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>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> Small Deborah numbers represent Newtonian flow, while non-Newtonian (with both viscous and elastic effects present) behaviour 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.
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| <!-- When the rheological behaviour 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 behaviour), 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>
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| 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.-->
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| === Reynolds number ===
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| {{main|Reynolds number}}
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| In [[fluid mechanics]], the [[Reynolds number]] is a measure of the [[ratio]] of [[inertia]]l [[force]]s (''v<sub>s</sub>ρ'') to [[viscosity|viscous]] forces (''μ/L'') 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.
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| 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.
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| Typically it is given as follows:
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| :<math> \mathit{Re} = {\rho v_{s}^2/L \over \mu v_{s}/L^2} = {\rho v_{s} L\over \mu} = {v_{s} L\over \nu} </math>
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| where:
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| * ''v''<sub>s</sub> - mean fluid [[velocity]], [m s<sup>−1</sup>]
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| * ''L'' - characteristic length, [m]
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| * μ - (absolute) dynamic [[fluid]] [[viscosity]], [N s m<sup>−2</sup>] or [Pa s]
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| * ν - kinematic fluid viscosity: ν = μ / ρ, [m² s<sup>−1</sup>]
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| * ρ - fluid [[density]], [kg m<sup>−3</sup>].
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| ==See also==
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| * [[Bingham plastic]]
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| * [[Die swell]]
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| * [[Glass transition]]
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| * [[Liquid]]
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| * [[List of rheologists]]
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| * [[Microrheology]]
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| * [[Rheological weldability]] for thermoplastics
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| * [[Solid]]
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| * [[Transport phenomena]]
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| == References ==
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| {{reflist|30em}}
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| ==External links==
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| * [http://www.ae.su.oz.au/rheology/Origin_of_Rheology.pdf The Origins of Rheology: A short historical excursion] by Deepak Doraiswamy, University of Sydney
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| * [http://www.legfr.fr/ French Society of Rheology]
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| * [http://reologie.ro/ Romanian Society of Rheology]
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| * [http://www.rheology-esr.net/ European Society of Rheology]
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| * [http://www.bsr.org.uk/ British Society of Rheology]
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| * [http://www.rheology.org.au Australian Society of Rheology]
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| * [http://www.rheology.org/sor/ American Society of Rheology]
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| * [http://link.springer.com/journal/397 Rheologica Acta]
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| * [http://www.journalofrheology.org/ Journal of Rheology]
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| * [http://www.journals.elsevier.com/journal-of-non-newtonian-fluid-mechanics/ Journal of Non-Newtonian Fluid Mechanics]
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| * [http://www.ar.ethz.ch/ Applied Rheology]
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| [[Category:Rheology| ]]
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