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'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".

Contents

Scope

Applications

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

Dimensionless numbers in rheology

External links

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.

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. Such relationships are then amenable to mathematical treatment by the established methods of continuum mechanics.

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.

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.
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.
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
In fluid mechanics, the Reynolds number is the ratio of inertial forces (''v_sρ'') to viscous forces (''μ/L'') and consequently it quantifies the relative importance of these two types of forces for given flow conditions. Thus, it is used to identify different flow regimes, such as laminar or turbulent flow.
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 flowrates, have the same values for the relevant dimensionless numbers, they are said to be dynamically similar.
Typically it is given as follows:
:$mathit\{Re\}\; =\; \{$
ho v_{s}^2/L over mu v_{s}/L^2} = {
ho v_{s} Lover mu} = {v_{s} Lover
u} = rac{mbox{Inertial forces}}{mbox{Viscous forces}}
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].

External links

;Journals covering rheology

★ ''Applied Rheology''

★ ''Journal of Rheology''

★ ''Journal of the Society of Rheology, JAPAN''

★ ''Journal of Non-Newtonian Fluid Mechanics''

★ ''Korea-Australia Rheology Journal''

★ ''Rheologica Acta''
;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''
;Rheology Conferences, Seminars, and Workshops

★ ''Conferences on Rheology & Soft Matter Materials''