Rheology

Rheology (play /riːˈɒlədʒi/) is the abstraction of the breeze of matter, primarily in the aqueous state, but aswell as 'soft solids' or debris beneath altitude in which they acknowledge with artificial breeze rather than deforming elastically in acknowledgment to an activated force.1 It applies to substances which accept a circuitous atomic structure, such as muds, sludges, suspensions, polymers and added bottle formers (e.g. silicates), as able-bodied as abounding foods and additives, actual fluids (e.g. blood) and added biological materials.

Newtonian fluids can be characterized by a individual accessory of bendability for a specific temperature. Although this bendability will change with temperature, it does not change with the breeze amount or ache rate. Only a baby accumulation of fluids display such connected viscosity, and they are accepted as Newtonian fluids. But for a ample chic of fluids, the bendability change with the ache amount (or about acceleration of flow) and are alleged non-Newtonian fluids. Rheology about accounts for the behavior of non-Newtonian fluids, by anecdotic the minimum amount of functions that are bare to chronicle stresses with amount of change of strains or ache rates. For example, ketchup can accept its bendability bargain by afraid (or added forms of automated agitation, area the about movement of altered layers in the actual in fact causes the abridgement in viscosity) but baptize cannot. Ketchup is a microburst abrasion material, as an access in about acceleration acquired a abridgement in viscosity, while some added non-Newtonian abstracts appearance the adverse behavior: bendability traveling up with about deformation, which are alleged microburst agglomeration or all-embracing materials. Since Sir Isaac Newton originated the abstraction of viscosity, the abstraction of liquids with ache amount abased bendability is aswell generally alleged Non-Newtonian aqueous mechanics.1

The appellation rheology was coined by Eugene C. Bingham, a assistant at Lafayette College, in 1920, from a advancement by a colleague, Markus Reiner.23 The appellation was aggressive by the adage of Simplicius (often misattributed to Heraclitus), panta rei, "everything flows"4 Plato in his chat Cratylus recounts on Heraclitus' adage that "all things move and annihilation charcoal still";5 he aswell compares the ancestry of the name of the Greek goddess Rhea (Ρέα) to the Greek name for breeze (ῥοή). He addendum the etymological accord of the names of "streams"6 accustomed to Cronus (Chronos - time) and Rhea (ῥοή – breeze or space) and he argues that this accord is not accidental.7

The beginning assuming of a material's rheological behavior is accepted as rheometry, although the appellation rheology is frequently acclimated synonymously with rheometry, decidedly by experimentalists. Theoretical aspects of rheology are the affiliation of the flow/deformation behavior of actual and its centralized anatomy (e.g., the acclimatization and addendum of polymer molecules), and the flow/deformation behavior of abstracts that cannot be declared by classical aqueous mechanics or elasticity.

Scope

In practice, rheology is principally anxious with extending continuum mechanics to characterize breeze of materials, that exhibits a aggregate of elastic, adhesive and artificial behavior by appropriately accumulation animation and (Newtonian) aqueous mechanics. It is aswell anxious with establishing predictions for automated behavior (on the continuum automated scale) based on the micro- or nanostructure of the material, e.g. the atomic admeasurement and architectonics of polymers in band-aid or the atom admeasurement administration in a solid suspension. Abstracts with the characteristics of a aqueous will breeze if subjected to a accent which is authentic as the force per area. There are altered sorts of accent (e.g. shear, torsional, etc.) and abstracts can acknowledge abnormally for altered stresses. Abundant of abstract rheology is anxious with advertence alien armament and torques with centralized stresses and centralized ache gradients and velocities.18910

Continuum mechanics

The abstraction of the physics of connected abstracts Solid mechanics

The abstraction of the physics of connected abstracts with a authentic blow shape. Elasticity

Describes abstracts that acknowledgment to their blow appearance afterwards an activated stress.

Plasticity

Describes abstracts that assuredly batter afterwards a acceptable activated stress. Rheology

The abstraction of abstracts with both solid and aqueous characteristics.

Fluid mechanics

The abstraction of the physics of connected abstracts which yield the appearance of their container. Non-Newtonian fluids

Newtonian fluids

Rheology unites the acutely different fields of bendability and non-Newtonian aqueous dynamics by acquainted that abstracts ability these types of anamorphosis are clumsy to abutment a accent (particularly a microburst stress, back it is easier to assay microburst deformation) in changeless equilibrium. In this sense, debris ability artificial anamorphosis is a fluid, although no bendability accessory is associated with this flow. Diminutive rheology refers to the continuum automated description of diminutive materials.

One of the above tasks of rheology is to empirically authorize the relationships amid deformations and stresses, appropriately their derivatives by able measurements, although a amount of abstract developments (such as acceptable anatomy invariants)are aswell appropriate afore application the empiric data. These beginning techniques are accepted as rheometry and are anxious with the assurance with categorical rheological actual functions. Such relationships are again acquiescent to algebraic analysis by the accustomed methods of continuum mechanics.

The assuming of breeze or anamorphosis basic from a simple microburst accent acreage is alleged microburst rheometry (or microburst rheology). The abstraction of analytic flows is alleged analytic rheology. Microburst flows are abundant easier to abstraction and appropriately abundant added beginning abstracts are accessible for microburst flows than for analytic flows.

Rheologist

A rheologist is an interdisciplinary scientist/engineer who studies the breeze of circuitous liquids or the anamorphosis of bendable solids. It is not taken as a primary bulk subject, and there is no accepted qualification. He or she will usually accept a primary accomplishment in one of several fields: mathematics, the concrete sciences (e.g. chemistry, physics, biology), engineering (e.g. mechanical, chemical, Abstracts Science & Engineering or civilian engineering), medicine, or assertive technologies, conspicuously abstracts or food. Typically, a baby bulk of rheology may be advised if accepting a degree, but the able will extend this ability during postgraduate analysis or by accessory abbreviate courses and by abutting one of the able associations (see below).

Viscoelasticity

The classical approach of animation deals with the behavior of adaptable debris beneath baby deformations, for which,(1) according to Hooke's Law, accent is anon proportional to the ache — but absolute of the amount of strain, or how fast the anamorphosis was applied, and (2) the strains are absolutely recoverable already the accent is removed. Abstracts that can be characterized by classical approach of animation is accepted as beeline adaptable materials, even for such abstracts the beeline accord amid accent and ache may be accurate alone for a assertive ambit of strains. A ample amount of debris appearance non-linear accord amid accent and ache even for baby stresses (such as rubber), but if the strains are still recoverable they are accepted as non-linear adaptable materials. The classical approach of aqueous mechanics, absolute by the Navier-Stokes equation, deals with the behavior of adhesive fluids, for which, according to Newton's Law, the accent is anon proportional to the amount of strain, but absolute of the ache itself. These behavior are, of course, about empiric for ideal abstracts beneath ideal conditions, although the behavior of abounding debris approaches Hooke's law for atomic strains, and that of abounding fluids approaches Newton's law for atomic ante of strain. Two types of deviations from breadth may be advised here.

If bound strains (larger strains, as against to atomic strains) are activated to solid bodies, the stress-strain relationships are about abundant added complicated (i.e. Non-Hookean). Similarly, in abiding breeze with bound ache rates, abounding fluids display apparent deviations in stress-strain amount arrangement from Newtons law.

Even if both ache and amount of ache are infinitesimal, a arrangement may display both liquid-like and solid-like characteristics. A acceptable archetype of this is if a physique which is not absolutely an adaptable solid (i.e. an breakable solid) does not advance a connected anamorphosis beneath connected stress, but rather continues to batter with time – or "creeps" beneath the aforementioned accent at connected temperature. If such a physique is accountable at connected deformation, the accent appropriate to authority it at that amplitude akin gradually diminishes—or "relaxes" with time.

Similarly, a aqueous while abounding beneath connected accent may appearance some adaptable backdrop as well, such as autumn some of the activity ascribe instead of administration it all as calefaction and accidental thermal motion of its atomic capacity or accepting some accretion of strains afterwards stresses are removed, although it may never balance all of its anamorphosis aloft abatement of the antecedent activated stress. If such bodies are subjected to a sinusoidally aquiver stress, the ache is neither absolutely in appearance with the accent (as it would be for a altogether adaptable solid) nor 90 degrees out of appearance (as it would be for a altogether adhesive liquid) but rather exhibits a ache that lags the accent at a amount amid aught and 90 degrees: i.e, Some of the activity is stored and recovered in anniversary cycle, and some is blown as heat. These are viscoelastic materials.

Thus, fluids are about associated with adhesive behavior (a blubbery oil is a adhesive liquid) and debris with adaptable behavior (an adaptable cord is an adaptable solid). A added accepted point of appearance is to accede the actual behavior at abbreviate times (relative to the continuance of the experiment/application of interest) and at continued times.

Aqueous and solid appearance are accordant at continued times:

We accede the appliance of a connected accent (a alleged edge experiment):

if the material, afterwards some deformation, eventually resists added deformation, it is advised a solid

if, by contrast, the actual flows indefinitely, it is advised a fluid

By contrast, adaptable and adhesive (or intermediate, viscoelastic) behavior is accordant at abbreviate times (transient behavior):

We afresh accede the appliance of a connected stress11:

if the actual anamorphosis ache increases linearly with accretion activated stress, again the actual is beeline adaptable aural the ambit it shows recoverable strains. Animation is about a time absolute processes, as the stains arise the moment the accent is appliled, afterwards any time delay.

if the actual anamorphosis amount increases linearly with accretion activated stress, again the actual is adhesive in the Newtonian sense. These abstracts are characterized due to the time adjournment amid the activated connected accent and the best strain.

if the abstracts behaves as a aggregate of adhesive and adaptable components, again the actual is viscoelastic. Theoretically such abstracts can appearance both direct anamorphosis as adaptable actual and a delayed time abased anamorphosis as in fluids.

Bendability is the behavior empiric afterwards the actual is subjected to a crop stress:

A actual that behaves as a solid beneath low activated stresses may alpha to breeze aloft a assertive akin of stress, alleged the crop accent of the material. The appellation artificial solid is about acclimated if this bendability beginning is rather high, while crop accent aqueous is acclimated if the beginning accent is rather low. However, there is no axiological aberration amid the two concepts.

Applications

Rheology has applications in abstracts science engineering, geophysics, physiology, animal analysis and pharmaceutics. Abstracts science is activated in the assembly of abounding industrially important substances, such as concrete, paint, and chocolate, which accept circuitous breeze characteristics. In addition, bendability approach has been analogously important for the architecture of metal basal processes. The science of rheology and the assuming of viscoelastic backdrop in the assembly and use of polymeric abstracts has been analytical for the assembly of abounding articles for use in both the automated and aggressive sectors. Abstraction of breeze backdrop of liquids is important for pharmacists alive in the accomplish of several dosage forms, such as simple liquids, ointments, creams, pastes etc. The breeze behavior of liquids below activated accent is of abundant appliance in the acreage of pharmacy. Breeze backdrop are acclimated as important superior ascendancy accoutrement to advance the ahead of the artefact and abate accumulation to accumulation variations.

edit Abstracts science

edit Polymers

The viscoelastic backdrop of polymers are bent by the furnishings of the abounding variables, including temperature, pressure, and time. Added important variables cover actinic composition, atomic weight and weight distribution, bulk of aberration and crystallinity, types of functionality, basal concentration, concoction with solvents or plasticizers, and admixture with added abstracts to anatomy blended systems. With advice by atomic theory, the assurance of viscoelastic backdrop on these variables can be simplified by introducing added concepts such as the chargeless volume, the monomeric abrasion coefficient, and the agreement amid affair loci, to accommodate a qualitative compassionate and in abounding cases a quantitative anticipation of how to accomplish adapted accurate and actinic backdrop and ultimate microstructure.

Viscoelastic behavior reflects the accumulated adhesive and adaptable responses, below automated stress, of abstracts which are average amid liquids and bits in character. Fundamentally, the viscoelasticity can be accompanying to the motions of adjustable polymer molecules and their entanglements and arrangement junctions—the atomic base of viscoelasticity. Thus, rearrangements on a bounded calibration (kinks) are almost rapid, while on a all-embracing calibration (convolutions) actual slow. In addition, a new array of configurations is acquired below stress. The acknowledgment to the bounded aspects of the new administration is rapid, while the acknowledgment to the all-embracing aspects is slow. Appropriately there is actual advanced and connected ambit of timescales accoutrement the acknowledgment of such a arrangement to evidently activated stress. From abstracts of the viscoelastic backdrop of polymers, advice can be acquired about the attributes and the ante of change of the configurational rearrangements, and the attributes of the (macro)molecular interactions over a ambit of time scales.

Examples may be accustomed to allegorize the abeyant applications of these attempt to activated problems in the processing and use of rubbers, plastics, and fibers. Polymers aggregate the basal abstracts of the adaptable and artificial industries and are of basic accent to the textile, petroleum, automobile, paper, and biologic industries. Their viscoelastic backdrop actuate the automated achievement of the final articles of these industries, and aswell the success of processing methods at average stages of production.

In viscoelastic materials, such as a lot of polymers and plastics, the attendance of liquid-like behavior depends on the backdrop of and so varies with bulk of activated load, i.e., how bound a force is applied. The silicone toy 'Silly Putty' behaves absolutely abnormally depending on the time bulk of applying a force. Pull on it boring and it exhibits connected flow, agnate to that credible in a awful adhesive liquid. Alternatively, if hit harder and directly, it shatters like a silicate glass.

In addition, accepted adaptable undergoes a bottle transition, (often alleged a rubber-glass transition). E.G. The Space Shuttle Challenger adversity was acquired by adaptable O-rings that were getting acclimated able-bodied below their bottle about-face temperature on an almighty algid Florida morning, and appropriately could not angle abundantly to anatomy able seals amid sections of the two solid-fuel rocket boosters.

edit Biopolymers

Linear anatomy of artificial -- the a lot of accepted basal of all amoebic bulb activity on Earth. * Note the affirmation of hydrogen bonding which increases the bendability at any temperature and pressure. This is an aftereffect agnate to that of polymer crosslinking, but below pronounced.

A above but defining aberration amid polymers and biopolymers can be begin in their structures. Polymers, including biopolymers, are fabricated of repetitive units alleged monomers. While polymers are generally about complete with massive entanglement, biopolymers generally accept a able-bodied authentic structure. In the case of proteins, the exact actinic agreement and the arrangement in which these units are abiding is alleged the primary structure.

Many proteins spontaneously bend into appropriate bunched shapes—which actuate their biological functions and depend in a complicated way on their primary structures. Structural analysis is the abstraction of the structural backdrop of the biopolymers, abundant of which can be bent by their viscoelastic acknowledgment to a advanced ambit of loading conditions.

edit Sol-gel

Main article: sol-gel

Polymerization action of tetraethylorthosilicate (TEOS) and baptize to anatomy baggy hydrated silica particles (Si-OH) can be monitored rheologically by a bulk of altered methods.

Sol-gel science (aka actinic band-aid deposition) is a wet-chemical address broadly acclimated in the fields of abstracts science, bottle assembly and bowl engineering. Such methods are acclimated primarily for the artifact of abstracts (typically a metal oxide) starting from a actinic band-aid which acts as the forerunner for an chip arrangement (or gel) of either detached nanoparticles or arrangement polymers. Typical precursors are metal alkoxides and metal chlorides, which abide assorted forms of hydrolysis and polycondensation reactions in adjustment to anatomy a viscoelastic arrangement (or solid).

One of the bigger appliance areas is attenuate films and coatings, which can be produced on a section of substrate by circuit blanket or dip coating. Added methods cover spraying, electrophoresis, inkjet press or cycle coating. Optical coatings, careful and adorning coatings, and electro-optic apparatus can be activated to glass, metal and added types of substrates with these methods. With the bendability of a sol adapted into a able range, both optical superior bottle cilia and adverse bowl cilia can be fatigued which are acclimated for cilia optic sensors and thermal insulation, respectively. The mechanisms of hydrolysis and condensation, and the rheological factors that bent the anatomy against beeline or angled structures are the a lot of analytical issues of sol-gel science and technology.

edit Geophysics

Geophysics includes the breeze of aqueous bedrock and bits flows (fluid mudslides). Aswell included in this antidotal annex are solid Earth abstracts which alone affectation breeze over continued time scales. Those that affectation adhesive behavior are accepted as rheids. E.G. granite can breeze plastically with a vanishingly baby crop accent at allowance temperatures, (i.e. a adhesive flow). Continued appellation edge abstracts (~ 10 years) announce that the bendability of granite below ambient altitude is on the adjustment of 1020 poises.12

Piledriving for a arch in Napa, California.

Deep foundations are acclimated for structures or abundant endless if bank foundations cannot accommodate acceptable able capacity. They may aswell be acclimated to about-face architecture endless accomplished anemic or compressible adobe layers. While bank foundations await alone on the address accommodation of the adobe below them, abysmal foundations can await on end address resistance, frictional attrition forth their length, or both in developing the appropriate capacity. Geotechnical engineers use specialized tools, such as the cone assimilation test, to appraisal the bulk of derma and end address attrition accessible in the subsurface.

In addition, accumulation active is generally acclimated to analysis for adherence in capricious adobe types such as clay, sand, gravels, burst shale, etc. Geotechnical engineering (or 'soil engineering') generally utilizes adobe logs or bore logs to appearance what may be credible while active bags through accustomed amount and adobe lenses. Wave equations accept to generally be active if appliance vibratory or automated appulse hammers. The accord set up by vibratory or appulse hammers acutely change the adeptness of accustomed soils to actualize bank abrasion on a accustomed accumulation type, as able-bodied as the adaptable about-face or attrition to assimilation in a accustomed state.

Dynamic testing of soils may absorb the adapter of transducers to pilings while they are getting driven. In addition, abstract address calculations appliance a nuclear densometer may be agitated out in the field. In the end, a adequately simple beeline blueprint may answer to accord a acceptable approximation of the address accommodation of the soil.

edit Physiology

Heme b

Physiology includes the abstraction of abounding actual fluids that accept circuitous anatomy and composition, and appropriately affectation a advanced ambit of viscoelastic breeze characteristics. In accurate there is a specialist abstraction of claret breeze alleged hemorheology. This is the abstraction of breeze backdrop of claret and its elements (plasma and formed elements, including red claret cells, white claret beef and platelets). Claret bendability is bent by claret viscosity, hematocrit (volume atom of red claret cell, which aggregate 99.9% of the cellular elements) and automated behavior of red claret cells. Therefore, red claret corpuscle mechanics is the above account of breeze backdrop of blood.13

edit Aliment rheology

Food rheology is important in the accomplish and processing of aliment products, eg cheese14. Aliment rheology is the abstraction of the rheological backdrop of food, that is, the bendability and breeze of aliment below deeply defined conditions. The consistency, bulk of fluidity, and added automated backdrop are important in compassionate how continued aliment can be stored, how abiding it will remain, and in free aliment texture. The acceptability of aliment articles to the customer is generally bent by aliment texture, such as how spreadable and buttery a aliment artefact is. Aliment rheology is important in superior ascendancy during aliment accomplish and processing.

Thickening agents, or thickeners, are substances which, if added to an aqueous mixture, access its bendability after essentially modifying its added properties, such as taste. They accommodate body, access stability, and advance abeyance of added ingredients. Agglomeration agents are generally acclimated as aliment additives and in cosmetics and claimed hygiene products. Some agglomeration agents are gelling agents, basal a gel. The agents are abstracts acclimated to thicken and balance aqueous solutions, emulsions, and suspensions. They deliquesce in the aqueous appearance as a colloid admixture that forms a abominably adamant centralized structure. Aliment thickeners frequently are based on either polysaccharides (starches, vegetable gums, and pectin), or proteins.15

edit Accurate rheology

Concrete's and mortar's workability is accompanying to the rheological backdrop of the beginning adhesive paste. The automated backdrop of accustomed accurate are bigger if below baptize is acclimated in the alertness of accurate paste, about abbreviation the water-to-cement arrangement may abatement the affluence of bond and application. To abstain these causeless effects, superplasticizers are about added to abatement the credible crop accent and the bendability of the beginning paste. Their accession awful improves accurate and adhesive properties16.

Measurement

Rheometers are instruments acclimated to characterize the rheological backdrop of materials, about fluids that are melts or solution. These instruments appoint a specific accent acreage or anamorphosis to the fluid, and adviser the resultant anamorphosis or stress. Instruments can be run in abiding breeze or oscillatory flow, in both microburst and extension.

Dimensionless numbers

Deborah number

Main article: Deborah number

On one end of the spectrum we accept an inviscid or a simple Newtonian aqueous and on the added end, a adamant solid; appropriately the behavior of all abstracts abatement about in amid these two ends. The aberration in actual behavior is characterized by the akin and attributes of animation present in the actual if it deforms, which takes the actual behavior to the non-Newtonian regime. The non-dimensional Deborah amount is advised to annual for the amount of non-Newtonain behavior in a flow. The Deborah amount is authentic as the arrangement of the appropriate time of alleviation (which absolutely depends on the actual and added altitude like the temperature) to the appropriate time of agreement or observation.1718 Baby Deborah numbers represent Newtonian flow, while non-Newtonian (with both adhesive and adaptable furnishings present) behavior occurs for average ambit Deborah numbers, and top Deborah numbers announce an elastic/rigid solid. Back Deborah amount is a about quantity, the numerator or the denominator can adapt the number. A actual baby Deborah amount can be acquired for a aqueous with acutely baby alleviation time or a actual ample beginning time, for example.

edit Reynolds number

Main article: Reynolds number

In aqueous mechanics, the Reynolds amount is a admeasurement of the arrangement of inertial armament (vsρ) to adhesive armament (μ/L) and appropriately it quantifies the about accent of these two types of aftereffect for accustomed breeze conditions. Under low Reynolds numbers adhesive furnishings boss and the breeze is laminar, admitting at top Reynolds numbers apathy predominates and the breeze may be turbulent. However, back rheology is anxious with fluids which do not accept a anchored viscosity, but one which can alter with breeze and time, adding of the Reynolds amount can be complicated.

It is one of the a lot of important dimensionless numbers in aqueous dynamics and is used, usually forth with added dimensionless numbers, to accommodate a archetype for free activating similitude. If two geometrically agnate breeze patterns, in conceivably altered fluids with possibly altered breeze rates, accept the aforementioned ethics for the accordant dimensionless numbers, they are said to be dynamically similar.

Typically it is accustomed as follows:

\mathit{Re} = {\rho v_{s}^2/L \over \mu v_{s}/L^2} = {\rho v_{s} L\over \mu} = {v_{s} L\over \nu}

where:

vs - beggarly aqueous velocity, m s−1

L - appropriate length, m

μ - (absolute) activating aqueous viscosity, N s m−2 or Pa s

ν - kinematic aqueous viscosity: ν = μ / ρ, m² s−1

ρ - aqueous density, kg m−3.