rheology

Dictionary: rhe·ol·o·gy (rē-ŏl'ə-jē) pronunciation

n.
The study of the deformation and flow of matter.

rheological rhe'o·log'i·cal (rē'ə-lŏj'ĭ-kəl) adj.
rheologically rhe'o·log'i·cal·ly adv.
rheologist rhe·ol'o·gist n.

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In the broadest sense of the term, that part of mechanics which deals with the relation between force and deformation in material bodies. The nature of this relation depends on the material of which the body is constituted. It is customary to represent the deformation behavior of metals and other solids by a model called the linear or hookean elastic solid (displaying the property known as elasticity) and that of fluids by the model of the linear viscous or newtonian fluid (displaying the property known as viscosity). These classical models are, however, inadequate to depict certain nonlinear and time-dependent deformation behavior that is sometimes observed. It is these nonclassical behaviors which are the chief interest of rheologists and hence referred to as rheological behavior. See also Elasticity; Stress and strain; Viscosity.

Rheological behavior is particularly readily observed in materials containing polymer molecules which typically contain thousands of atoms per molecule, although such properties are also exhibited in some experiments on metals, glasses, and gases. Thus rheology is of interest not only to mathematicians and physicists, who consider it to be a part of continuum mechanics, but also to chemists and engineers who have to deal with these materials. It is of special importance in the plastics, rubber, film, and coatings industries. See also Fluid mechanics; Paint; Plastics processing; Polymer; Rubber; Surface coating.

Models and properties

Consider a block of material of height h deformed in the manner indicated in Fig. 1; the bottom surface is fixed and the top moves a distance w parallel to itself. A measure of the deformation is the shear strain γ given by Eq. (1).
1. $\gamma = {w\over h}$

Simple shear. (a) Undeformed block of height h. (b) Deformed block after top has moved a distance w parallel to itself. The arrows indicate the net forces acting on the top and bottom faces. The forces which must be applied to left and right faces to maintain a steady state are not indicated.
Simple shear. (a) Undeformed block of height h. (b) Deformed block after top has moved a distance w parallel to itself. The arrows indicate the net forces acting on the top and bottom faces. The forces which must be applied to left and right faces to maintain a steady state are not indicated.

To achieve such a deformation if the block is a linear elastic material, it is necessary to apply uniformly distributed tangential forces on the top and bottom of the block as shown in Fig. 1b. The intensity of these forces, that is, the magnitude of the net force per unit area, is called the shear stress S. For a linear elastic material, γ is much less than unity and is related to S by Eq. (2),
2. $S = G\gamma$
where the proportionality constant G is a property of the material known as the shear modulus.

If the material in the block is a newtonian fluid and a similar set of forces is imposed, the result is a simple shearing flow, a deformation as pictured in Fig. 1b with the top surface moving with a velocity dw/dt. This type of motion is characterized by a rate of shear $\dot{\gamma}$ = (dw/dt)/h, which is proportional to the shear stress S as given by Eq. (3), where η is a property of the material called the viscosity.
3. $S = \eta \dot\gamma$

Linear viscoelasticity

If the imposed forces are small enough, time-dependent deformation behavior can often be described by the model of linear viscoelasticity. The material properties in this model are most easily specified in terms of simple experiments.

In a creep experiment a stress is suddenly applied and then held constant; the deformation is then followed as a function of time. This stress history is indicated in the solid line of Fig. 2a for the case of an applied constant shear stress S₀. If such an experiment is performed on a linear elastic solid, the resultant deformation is indicated by the full line in Fig. 2b and for the linear viscous fluid in Fig. 2c. In the case of elasticity, the result is an instantly achieved constant strain; in the case of the fluid, an instantly achieved constant rate of strain. In the case of viscoelastic materials, there are some which eventually attain a constant equilibrium strain (Fig. 2d) and hence are called viscoelastic solids. Others eventually achieve constant rate of strain (Fig. 2e) and are called viscoelastic fluids. If the material is linear viscoelastic, the deformation γ(S₀, t) is a function of the time t since the stress was applied and also a linear function of S₀; that is, Eq. (4)
4. $\gamma (S\,_0,t) = S\,_0J(t)$
is satisfied, where J(t) is independent of S₀. The function J(t) is a property of the material known as the shear creep compliance. See also Creep (materials).

viscoelastic fluid.">
Creep and recovery; solid lines indicate creep; broken lines indicate recovery. (a) Applied stress history. (b) Corresponding strain history for linear elastic solid, (c) linear viscous fluid, (d) viscoelastic solid, and (e) viscoelastic fluid.

Nonlinear viscoelasticity

If stresses become too high, linear viscoelasticity is no longer an adequate model for materials which exhibit time-dependent behavior. In a creep experiment, for example, the ratio of the strain to stress, γ(t, S₀)/S₀, is no longer independent of S₀; this ratio generally decreases with increasing S₀. Two examples of nonlinear viscoelasticity are shear thinning and thixotropy.

For polymer melts, solutions, and suspensions, generally speaking, the viscosity decreases as the shear rate increases. This type of behavior, called shear thinning, is of considerable industrial significance. For example, paints are formulated to be shear-thinning. A high viscosity at low flow rates keeps the paint from dripping from the brush or roller and prevents sagging of the paint film newly applied to a vertical wall. The lower viscosity at the high deformation rates while brushing or rolling means that less energy is required, and hence the painter's arm does not become overly tired.

Thixotropy is a property of suspensions (for example, bentonite clay in water) which, after remaining at rest for a long time, act as solids; for example, they cannot be poured. However, if it is stirred, such a suspension can be poured quite freely. If the suspension is then allowed to rest, the viscosity increases with time and finally sets again. This whole process is reversible; it can be repeated again and again. See also Gel; Non-newtonian fluid.

Food and Nutrition: rheology

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Study of deformation and flow of materials; in food technology it involves plasticity of fats, doughs, milk curd, etc. It provides a scientific basis for subjective measurements such as mouth feel, spreadability, pourability.

Dental Dictionary: rheology

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(rē-ol′ə-jē)
n

The study of blood flow, pressure, and velocity through the vascular system.

Architecture: rheology

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The science dealing with flow of materials, including studies of deformation of hardened concrete, the handling and placing of freshly mixed concrete, and the behavior of slurries, pastes, and the like.

Columbia Encyclopedia: rheology

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rheology (rēŏl'əjē), branch of physics dealing with the deformation and flow of matter. It is particularly concerned with the properties of matter that determine its behavior when a mechanical force is exerted on it. Rheology is distinguished from fluid dynamics (see fluid mechanics) in that it is concerned with all three of the traditional states of matter rather than only with liquids and gases. Unlike polymer physics it is concerned with macroscopic properties and behavior and not with molecular structure. The results of rheology provide a mathematical description of the viscoelastic behavior of matter (see elasticity; viscosity). Applications of rheology are important in many areas of industry, involving metals, plastics, and many other materials.

Veterinary Dictionary: rheology

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The science of the deformation and flow of matter, such as the flow of blood through the heart and blood vessels.

Wikipedia: Rheology

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Continuum mechanics

Laws
Conservation of mass Conservation of momentum Conservation of energy Entropy inequality

Solid mechanics
Solids · Stress · Deformation · Finite strain theory · Infinitesimal strain theory · Elasticity · Linear elasticity · Plasticity · Viscoelasticity · Hooke's law · Rheology

Fluid mechanics
Fluids · Fluid statics Fluid dynamics · Viscosity · Newtonian fluids Non-Newtonian fluids Surface tension

Scientists
Newton · Stokes · Navier · Cauchy· Hooke · Bernoulli

Rheology (pronounced /riˈɒlədʒi/) is the study of the flow of matter: mainly liquids but also soft solids or solids under conditions in which they flow rather than deform elastically^[1]. It applies to substances which have a complex structure, including muds, sludges, suspensions, polymers, many foods, bodily fluids, and other biological materials. The flow of these substances cannot be characterized by a single value of viscosity (at a fixed temperature)^[2] - instead the viscosity changes due to other factors. For example ketchup can have its viscosity reduced by shaking, but water cannot. Since Isaac Newton originated the concept of viscosity, the study of variable viscosity liquids is also often called Non-Newtonian fluid mechanics.^[1] The term rheology was coined by Eugene C. Bingham, a professor at Lafayette College, in 1920, from a suggestion by a colleague, Markus Reiner.^[3] The term was inspired by the quotation mistakenly attributed to Heraclitus, (actually coming from the writings of Simplicius) panta rei, "everything flows". The experimental characterisation of a material's rheological behavior 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 behavior of material and its internal structure (e.g., the orientation and elongation of polymer molecules), and the flow/deformation behavior of materials that cannot be described by classical fluid mechanics or elasticity.

1 Scope
2 Rheologist
3 Applications
4 Elasticity, viscosity, solid- and liquid-like behavior, plasticity
5 Dimensionless numbers in rheology
6 Rheometers
7 Notes and references
8 See also
9 Further reading
10 External links

Scope

In practice, rheology is principally concerned with extending the "classical" disciplines of elasticity and (Newtonian) fluid mechanics to materials whose mechanical behavior cannot be described with the classical theories. It is also concerned with establishing predictions for mechanical behavior (on the continuum mechanical scale) based on the micro- or nanostructure of the material, e.g. the molecular size and architecture of polymers in solution or the particle size distribution in a solid suspension. Materials flow when subjected to a stress, that is a force per area. There are different sorts of stress^[4] and materials can respond in various ways, so much of theoretical rheology is concerned with forces and stresses.^[1]

Continuum mechanics	Solid mechanics or strength of materials	Elasticity
		Plasticity	Rheology
	Fluid mechanics	Non-Newtonian fluids
		Newtonian fluids

Rheology unites the seemingly unrelated fields of plasticity and non-Newtonian fluids by recognizing that both these types of materials are unable to support a shear stress in static equilibrium. In this sense, a plastic solid is a fluid. Granular rheology refers to the continuum mechanical description of granular materials.

One of the tasks of rheology is to empirically establish the relationships between deformations and stresses, respectively their derivatives by adequate measurements. 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.

The characterisation 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.

Rheologist

A rheologist is an interdisciplinary scientist who studies the flow of complex liquids or the deformation of soft solids. It is not taken as a primary degree subject, and there is no general qualification. He or she will usually have a primary qualification in one of several fields: mathematics, the physical sciences^[5], engineering^[6], medicine, or certain technologies, notably materials or food. A small amount of rheology may be given during the first degree, but the professional will extend this knowledge during postgraduate research or by attending short courses and by joining one of the professional associations (see below).

Applications

Rheology has applications in engineering, geophysics, physiology and pharmaceutics. In engineering, it affects the production and use of polymeric materials, but plasticity theory has been similarly important for the design of metal forming processes. Many industrially important substances such as concrete, paint and chocolate have complex flow characteristics. Geophysics includes the flow of lava, but in addition measures the flow of solid Earth materials over long time scales: those that display viscous behavior, e.g. granite ^[7], are known as rheids. In physiology, many bodily fluids are have complex compositions and thus flow characteristics. In particular there is a specialist study of blood flow called hemorheology. The term biorheology is used for the wider field of study of the flow properties of biological fluids. Food rheology is important in the manufacture and processing of food products.^[8]

Elasticity, viscosity, solid- and liquid-like behavior, plasticity

One generally associates liquids with viscous behavior (a thick oil is a viscous liquid) and solids with elastic behavior (an elastic string is an elastic solid). A more general point of view is to consider the material behavior at short times (relative to the duration of the experiment/application of interest) and at long times.

Liquid 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 liquid

By contrast, elastic and viscous (or intermediate, viscoelastic) behavior is relevant at short times (transient behavior)

We again consider the application of a constant stress:

if the material deformation strain increases linearly with increasing applied stress , then the material is purely elastic
if the material deformation rate increases linearly with increasing applied stress, then the material is purely viscous
if neither the deformation strain, nor its derivative with time (rate) follows the applied stress, then the material is viscoelastic

Plasticity is equivalent to the existence of 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 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. There is no fundamental difference, however, between both concepts.

Dimensionless numbers in rheology

Deborah number

Main article: Deborah number

When the rheological behavior of a material includes a transition from elastic to viscous as the time scale increase (or, more generally, a transition from a more resistant to a less resistant behavior), one may define the relevant time scale as a relaxation time of the material. Correspondingly, the ratio of the relaxation time of a material to the timescale of a deformation is called Deborah number. Small Deborah numbers correspond to situations where the material has time to relax (and behaves in a viscous manner), while high Deborah numbers correspond to situations where the material behaves rather elastically.^[9]

Note that the Deborah number is relevant for materials that flow on long time scales (like a Maxwell fluid) but not for the reverse kind of materials (like the Voigt or Kelvin model) that are viscous on short time scales but solid on the long term.

Reynolds number

Main article: Reynolds number

In fluid mechanics, the Reynolds number is a measure of the ratio of inertial forces (v_sρ) to 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, whereas at high Reynolds numbers inertia predominates and the flow may be turbulent. However, since rheology is concerned with fluids which do not have a fixed viscosity, but one which can vary with flow and time, calculation of the Reynolds number can be complicated.

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

Typically it is given as follows:

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

where:

v_s - mean fluid velocity, [m s^-1]
L - characteristic length, [m]
μ - (absolute) dynamic fluid viscosity, [N s m^-2] or [Pa s]
ν - kinematic fluid viscosity: ν = μ / ρ, [m² s^-1]
ρ - fluid density, [kg m^-3].

Rheometers

Rheometers are instruments used to characterize the rheological properties of materials, typically fluids and melts. 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.

Notes and references

^ ^a ^b ^c W. R. Schowalter (1978) Mechanics of Non-Newtonian Fluids Pergamon ISBN 0-08021778-8
^ While the viscosity of liquids normally varies with temperature, it is variations with other factors which are studied in rheology
^ J. F. Steffe (1996) Rheological Methods in Food Process Engineering 2nd ed ISBN 0-9632036-1-4 page 1
^ for example, a shear stress or extensional stress
^ mainly chemistry, physics, biology
^ mainly mechanical, chemical or civil engineering
^ Kumagai, Naoichi; Sadao Sasajima, Hidebumi Ito (15 February 1978). "Long-term Creep of Rocks: Results with Large Specimens Obtained in about 20 Years and Those with Small Specimens in about 3 Years". Journal of the Society of Materials Science (Japan) (Japan Energy Society) 27 (293): 157–161. 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. Retrieved 2008-06-16.
^ B.M. McKenna, and J.G. Lyng. "Texture in food > Introduction to food rheology and its measurement". books.google.com. http://books.google.com/books?id=wM1asp1LL8EC&pg=PA130&dq=Food+Rheology&ei=6fqzSu-WJJHyMrSv_bcP#v=onepage&q=Food%20Rheology&f=false. Retrieved 2009-09-18.
^ M. Reiner (1964) Physics Today volume 17 no 1 page 62 The Deborah Number

External links

Journals covering rheology

Organizations concerned with the study of rheology

Rheology Conferences

General subfields within physics

Acoustics · Agrophysics (Soil physics) · Astrophysics · Atmospheric physics · Atomic, molecular, and optical physics · Biophysics (Medical physics · Neurophysics) · Chemical physics · Condensed matter physics · Econophysics · Electromagnetism · Mechanics (Classical mechanics · Quantum mechanics · Fluid mechanics · Optomechanics · Thermodynamics) · Nuclear physics · Optics · Particle physics · Quantum field theory · Relativity (Special relativity · General relativity)

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