Rheology is the study of the deformation and flow of matter under the influence of an applied stress. The term was coined by Eugene Bingham, a professor at Lehigh University, in 1920, from a suggestion by a colleague, Markus Reiner. The term was inspired by Heraclitus's famous expression panta rei, "everything flows". Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ... Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ... Classical mechanics is a branch of physics which studies the deterministic motion of objects. ... Stress is the internal distribution of force per unit area that balances and reacts to external loads applied to a body. ... This article is about the deformation of materials. ... In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ... The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov-Lavoisier law), states that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. ... In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... Solid mechanics is the branch of physics and mathematics that concern the behavior of solid matter under external actions (e. ... For other uses, see Solid (disambiguation). ... Elasticity is a branch of physics which studies the properties of elastic materials. ... For other uses, see Plasticity. ... Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ... Figure 1: Rectangular specimen subject to compression, with Poissons ratio circa 0. ... A viscoelastic material is one in which: hysteresis is seen in the stress-strain curve. ... Fluid mechanics is the subdiscipline of continuum mechanics that studies fluids, that is, liquids and gases. ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ... Fluid statics (also called hydrostatics) is the science of fluids at rest, and is a sub-field within fluid mechanics. ... Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluids (liquids and gases) in motion. ... The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations which describe the motion of fluid substances such as liquids and gases. ... The related Category:Units of viscosity has been nominated for deletion, merging, or renaming. ... A Newtonian fluid (named for Isaac Newton) is a fluid that flows like water—its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ... A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ... This article or section does not adequately cite its references or sources. ... Stress is the internal distribution of force per unit area that balances and reacts to external loads applied to a body. ... Lehigh University is a highly selective private, co-educational university located in Bethlehem, Pennsylvania, in the Lehigh Valley region of the United States. ... Year 1920 (MCMXX) was a leap year starting on Thursday. ... Heraclitus of Ephesus (Ancient Greek - Herákleitos ho Ephésios (Herakleitos the Ephesian)) (about 535 - 475 BC), known as The Obscure (Ancient Greek - ho Skoteinós), was a pre-Socratic Greek philosopher, a native of Ephesus on the coast of Asia Minor. ... Heraclitus of Ephesus (ca. ...

Scope

In practice, rheology is principally concerned with extending the "classical" disciplines of elasticity and (Newtonian) fluid mechanics to materials whose mechanical behaviour cannot be described with the classical theories. 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 molecular size and architecture of polymers in solution or the particle size distribution in a solid suspension. Solid mechanics (also known as the theory of elasticity) is a branch of physics, which governs the response of solid material to applied stress (e. ... A Newtonian fluid (named for Isaac Newton) is a fluid that flows like water—its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ... Fluid mechanics is the subdiscipline of continuum mechanics that studies fluids, that is, liquids and gases. ...

Rheology unites the seemingly unrelated fields of plasticity and non-Newtonian fluids by recognising 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. Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ... Solid mechanics is the branch of physics and mathematics that concern the behavior of solid matter under external actions (e. ... Strength of materials is materials science applied to the study of engineering materials and their mechanical behavior in general (such as stress, deformation, strain and stress-strain relations). ... Elasticity is a branch of physics which studies the properties of elastic materials. ... For other uses, see Plasticity. ... Fluid mechanics is the subdiscipline of continuum mechanics that studies fluids, that is, liquids and gases. ... A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ... A Newtonian fluid (named for Isaac Newton) is a fluid that flows like water—its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ... For other uses, see Plasticity. ... A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ... Shear stress is a stress state where the stress is parallel to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. ... A standard definition of mechanical equilibrium is: A system is in mechanical equilibrium when the sum of the forces, and torques, on each particle of the system is zero. ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ... A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when grains collide). ...

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. Such relationships are then amenable to mathematical treatment by the established methods of continuum mechanics. Look up strain in Wiktionary, the free dictionary. ... In some places this article assumes an acquaintance with algebra, analytic geometry, or the limit. ... Rheometry generically refers to the experimental techniques used to determine the rheological properties of materials, that is the quantitative and qualitative relationships between deformations and stresses, respectively their derivatives. ... Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ...

Applications

Rheology has important applications in engineering, geophysics, pharmaceutics and physiology. In particular, hemorheology, the study of blood flow, has an enormous medical significance. In geology, solid Earth materials that exhibit viscous flow over long time scales are known as rheids. In engineering, rheology has had its predominant application in the development and use of polymeric materials (plasticity theory has been similarly important for the design of metal forming processes, but in the engineering community is often not considered a part of rheology). Rheology Modifiers are also a key element in the development of paints in achieving paints that will level but not sag on vertical surfaces. Engineering is the design, analysis, and/or construction of works for practical purposes. ... ‹ The template below has been proposed for deletion. ... Pharmaceutics is the discipline of pharmacy which deals with all facets of the process of turning a new chemical entity (NCE) into a medication able to be safely and effectively used by patients in the community. ... Leonardo da Vincis Vitruvian Man, an important early achievement in the study of physiology. ... Categories: Pages needing attention | Stub ... Human blood smear: a - erythrocytes; b - neutrophil; c - eosinophil; d - lymphocyte. ... This article includes a list of works cited but its sources remain unclear because it lacks in-text citations. ... Adjectives: Terrestrial, Terran, Telluric, Tellurian, Earthly Atmosphere Surface pressure: 101. ... In geology, a rheid is a solid material that deforms by viscous flow. ... A polymer is a substance composed of molecules with large molecular mass consisting of repeating structural units, or monomers, connected by covalent chemical bonds. ... For other uses, see Plasticity. ...

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

One is used to associate liquid with viscous (a thick oil is a viscous liquid) as well as solid with elastic (an elastic string is an elastic solid). In fact, when one tries to deform a piece of material, some of the above properties appear at short times (relative to the duration of the experiment), others at long times.

Liquid and solid characters are long-time properties

Let us attempt to deform the material by applying a continuous, weak, constant stress:

• if the material, after some deformation , eventually resists further deformation, it is a solid ;
• if, by contrast, the material eventually flows, it is a liquid.

By contrast, elastic and viscous characters (or intermediate, viscoelastic behaviours) appear at short times

Again, let us attempt to deform the material by applying a weak stress varying in time:

• if the material deformation follows the applied force or stress, then the material is elastic;
• if the time-derivative of the deformation (deformation rate) follows the force or stress, then the material is viscous.

Plasticity appears at high stresses

Liquid, solid, viscous and elastic characters can be detected under weak applied stresses. If a high stress is applied, a material that behaves as a solid under low applied stresses may start to flow. It then reveals a plastic character: it is a plastic solid. Plasticity is thus characterised by a threshold stress (called plasticity threshold or yield stress) beyond which the material flows. For other uses, see Plasticity. ...

The term plastic solid is used when the 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

When the rheological behaviour 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 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. The Deborah number is a dimensionless number, used in rheology to characterize how fluid a material is. ...

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. A Maxwell material is a viscoelastic material having the properties both of elasticity and viscosity. ... A Kelvin material is a viscoelastic material having the properties both of elasticity and viscosity. ...

External links

Journals covering rheology

• Journal of Rheology
• Journal of the Society of Rheology, JAPAN
• Journal of Non-Newtonian Fluid Mechanics
• Rheologica Acta
• Applied Rheology
• Korea-Australia Rheology Journal

Organizations concerned with the study of rheology

• The Society of Rheology
• The Society of Rheology, JAPAN
• The European Society of Rheology
• The British Society of Rheology
• Deutsche Rheologische Gesellschaft
• Groupe Français de Rhéologie
• Belgian Group of Rheology
• Swiss Group of Rheology
• Nederlandse Reologische Vereniging
• Società Italiana di Reologia
• Nordic Rheology Society
• Australian Society of Rheology