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Rheology (/riːˈɒlədʒi/; from Greek ῥέω (rhéō) 'flow' and -λoγία (-logia) 'study of') is the study of the flow ofmatter, primarily in afluid (liquid orgas) state but also as "softsolids" or solids under conditions in which they respond withplastic flow rather than deformingelastically in response to an applied force.[1] Rheology is the branch ofphysics that deals with thedeformation and flow of materials, both solids and liquids.[1]
The termrheology was coined byEugene C. Bingham, a professor atLafayette College, in 1920 from a suggestion by a colleague,Markus Reiner.[2][3] The term was inspired by theaphorism ofHeraclitus (often mistakenly attributed toSimplicius),panta rhei (πάντα ῥεῖ, 'everything flows'[4][5]) 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 asmuds,sludges,suspensions, andpolymers and otherglass formers (e.g., silicates), as well as many foods and additives,bodily fluids (e.g., blood) and otherbiological materials, and other materials that belong to the class ofsoft matter such as food.
Newtonian fluids can be characterized by a single coefficient ofviscosity for a specific temperature. Although this viscosity will change with temperature, it does not change with thestrain rate. Only a small group of fluids exhibit such constant viscosity. The large class of fluids whose viscosity changes with the strain rate (the relativeflow velocity) are callednon-Newtonian fluids.
Rheology generally accounts for the behavior of non-Newtonian fluids by characterizing the minimum number of functions that are needed to relate stresses with rate of change of strain or strain rates. For example,ketchup can have itsviscosity 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, likeyogurt andemulsionpaint (US terminologylatex paint oracrylic paint), exhibitingthixotropy, where an increase in relative flow velocity will cause a reduction in viscosity, for example, by stirring. Some other non-Newtonian materials show the opposite behavior,rheopecty (viscosity increasing with relative deformation), and are called shear-thickening ordilatant materials. Since SirIsaac Newton originated the concept of viscosity, the study of liquids with strain-rate-dependent viscosity is also often calledNon-Newtonian fluid mechanics.[1]
The experimental characterisation of a material's rheological behaviour is known asrheometry, although the termrheology 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.
In practice, rheology is principally concerned with extendingcontinuum mechanics to characterize the flow of materials that exhibit a combination ofelastic,viscous andplastic behavior by properly combiningelasticity and (Newtonian)fluid mechanics. It is also concerned with predicting mechanical behavior (on the continuum mechanical scale) based on the micro- or nanostructure of the material, e.g. themolecular size and architecture ofpolymers in solution or the particle size distribution in a solid suspension.Materials with the characteristics of a fluid will flow when subjected to astress, 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.[1][6][7][8]
| Continuum mechanics The study of the physics of continuous materials | Solid mechanics The study of the physics of continuous materials with a defined rest shape. | Elasticity Describes materials that return to their rest shape after appliedstresses are removed. | |
| Plasticity Describes materials that permanently deform after a sufficient applied stress. | Rheology The study of materials with both solid and fluid characteristics. | ||
| Fluid mechanics The study of the physics of continuous materials which deform when subjected to a force. | Non-Newtonian fluid Do not undergo strain rates proportional to the applied shear stress. | ||
| Newtonian fluids undergo strain rates proportional to the applied shear stress. | |||
Rheology unites the seemingly unrelated fields ofplasticity andnon-Newtonian fluid dynamics by recognizing that materials undergoing these types of deformation are unable to support a stress (particularly ashear stress, since it is easier to analyze shear deformation) in staticequilibrium. In this sense, a solid undergoing plasticdeformation is afluid, although no viscosity coefficient is associated with this flow. Granular rheology refers to the continuum mechanical description ofgranular materials.
One of the major tasks of rheology is to establish by measurement the relationships betweenstrains (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 asrheometry and are concerned with the determination of well-definedrheological material functions. Such relationships are then amenable to mathematical treatment by the established methods ofcontinuum mechanics.
The characterization of flow or deformation originating from a simple shear stress field is calledshear rheometry (or shear rheology). The study of extensional flows is calledextensional rheology. Shear flows are much easier to study and thus much more experimental data are available for shear flows than for extensional flows.
On one end of the spectrum we have aninviscid 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.[3][10] 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.
Influid mechanics, theReynolds number is a measure of theratio ofinertialforces () toviscous forces () 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 islaminar, whereas at high Reynolds numbers inertia predominates and the flow may beturbulent. However, since rheology is concerned with fluids which do not have a fixedviscosity, but one which can vary with flow and time, calculation of the Reynolds number can be complicated.
It is one of the most importantdimensionless numbers influid dynamics and is used, usually along with other dimensionless numbers, to provide a criterion for determiningdynamic similitude. When two geometrically similar flow patterns, in perhaps different fluids with possibly different flow rates, have the same values for the relevant dimensionless numbers, they are said to be dynamically similar.
Typically it is given as follows:
where:
Rheometers 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.
Rheology has applications inmaterials science,engineering,geophysics,physiology, humanbiology andpharmaceutics. Materials science is utilized in the production of many industrially important substances, such ascement,paint, andchocolate, which have complex flow characteristics. In addition,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 ofpolymeric 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.
Examples may be given to illustrate the potential applications of these principles to practical problems in the processing[11] and use ofrubbers,plastics, andfibers.Polymers constitute the basic materials of the rubber and plastic industries and are of vital importance to the textile,petroleum,automobile,paper, andpharmaceutical 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.
Inviscoelastic 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. Thesilicone 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 asilicate glass.
In addition, conventional rubber undergoes aglass transition (often called arubber-glass transition). E.g. TheSpace ShuttleChallenger 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 twosolid-fuel rocket boosters.
With theviscosity of asol adjusted into a proper range, bothoptical quality glass fiber andrefractory ceramic fiber can be drawn which are used forfiber-optic sensors andthermal insulation, respectively. The mechanisms ofhydrolysis andcondensation, and the rheological factors that bias the structure toward linear or branched structures are the most critical issues ofsol-gel science and technology.
The scientific discipline ofgeophysics includes study of the flow of moltenlava 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 asrheids. For example,granite can flow plastically with a negligible yield stress at room temperatures (i.e. a viscous flow). Long-term creep experiments (~10 years) indicate that the viscosity of granite and glass under ambient conditions are on the order of 1020 poises.[12][13]
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 calledhemorheology. This is the study of flow properties of blood and its elements (plasma and formed elements, includingred blood cells,white blood cells andplatelets).Blood viscosity is determined by plasma viscosity,hematocrit (volume fraction of red blood cell, which constitute 99.9% of the cellular elements) and mechanical behaviour of red blood cells. Therefore, red blood cell mechanics is the major determinant of flow properties of blood.(The ocularVitreous humor is subject to rheologic observations, particularly during studies of age-related vitreous liquefaction, orsynaeresis.)[14]
The leading characteristic for hemorheology has beenshear thinning in steady shear flow. Other non-Newtonian rheological characteristics that blood can demonstrate includespseudoplasticity,viscoelasticity, andthixotropy.[15]
There are two current major hypotheses to explain blood flow predictions andshear 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.[16] The foundation ofhemorheology can also provide information for modeling of other biofluids.[15] 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.[15][16] 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.[15] The effect of rouleaux aggregation tendency can be explained byhematocrit and fibrinogen concentration in whole blood rheology.[15] Some techniques researchers use are optical trapping and microfluidics to measure cell interaction in vitro.[16]
Changes to viscosity has been shown to be linked with diseases like hyperviscosity, hypertension, sickle cell anemia, and diabetes.[15]Hemorheological measurements and genomic testing technologies act as preventative measures and diagnostic tools.[15][17]
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.[18]
Many animals make use of rheological phenomena, for examplesandfish that exploit the granular rheology of dry sand to "swim" in it orland gastropods that usesnail slime for adhesivelocomotion. Certain animals produce specializedendogenouscomplex fluids, such as the sticky slime produced byvelvet worms to immobilize prey or the fast-gelling underwater slime secreted byhagfish to deter predators.[19]
Food rheology is important in the manufacture and processing of food products, such as cheese[20] andgelato.[21] An adequate rheology is important for the indulgence of many common foods, particularly in the case of sauces,[22] dressings,[23]yogurt,[24] orfondue.[25]
Thickening agents, or thickeners, are substances which, when added to an aqueous mixture, increase itsviscosity without substantially modifying its other properties, such as taste. They provide body, increasestability, and improvesuspension of added ingredients. Thickening agents are often used asfood additives and incosmetics andpersonal hygiene products. Some thickening agents aregelling agents, forming agel. The agents are materials used to thicken and stabilize liquid solutions,emulsions, andsuspensions. They dissolve in the liquid phase as acolloid mixture that forms a weakly cohesive internal structure. Food thickeners frequently are based on eitherpolysaccharides (starches,vegetable gums, andpectin), orproteins.[26][27]
Concrete's andmortar's workability is related to the rheological properties of the freshcement 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,superplasticizers are typically added to decrease the apparent yield stress and the viscosity of the fresh paste. Their addition highly improves concrete and mortar properties.[28]
The incorporation of various types offillers intopolymers 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.[29]
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 uniformdispersion 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 theFarris effect. An additional factor is thestress 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 ofsurface treatment on the filler are thus additional parameters affecting the rheological and material properties of filled polymeric systems.
It is important to take into consideration wall slip when performing the rheological characterization of highly filled materials, as there can be a large difference between the actual strain and the measured strain.[30]
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A rheologist is aninterdisciplinary scientist or engineer who studies the flow of complex liquids or the deformation of soft solids. It is not a primary degree subject; there is no qualification of rheologist as such. Most rheologists have a qualification in mathematics, the physical sciences (e.g.chemistry,physics,geology,biology), engineering (e.g.mechanical,chemical,materials science, plastics engineering and engineering orcivil engineering),medicine, or certain technologies, notablymaterials orfood. 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.
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