Rheology 25453 220845353 2008-06-21T22:02:21Z Chemical Engineer 2015158 link {{Continuum mechanics}} '''Rheology''' is the study of the deformation and flow of [[matter]] under the influence of an applied [[Stress (physics)|stress]], which might be, for example, a [[shear stress]] or [[extensional stress]]. The experimental characterisation of a material's rheological behaviour 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 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. This is also often called ''[[Non-Newtonian fluid|Non-Newtonian fluid mechanics]]'' in the case of fluids. The term ''rheology'' was coined by [[Eugene C. Bingham]], a professor at [[Lafayette College]], in [[1920]], from a suggestion by a colleague, [[Markus Reiner]]. The term was inspired by the quotation mistakenly attributed to [[Heraclitus]], (actually coming from the writings of [[Simplicius]]) ''[[panta rei]]'', "everything flows". == Scope == In practice, rheology is principally concerned with extending the "classical" disciplines of [[theory of elasticity|elasticity]] and ([[Newtonian fluid|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 [[Molecule|molecular]] size and architecture of [[polymer]]s in solution or the particle size distribution in a solid suspension. {|class="wikitable" width=400 |rowspan=4|[[Continuum mechanics]] |rowspan=2 width=200|[[Solid mechanics]] or [[strength of materials]] |colspan=2|[[elastic (solid mechanics)|Elasticity]] |- |bgcolor=lightgrey|[[plasticity (physics)|Plasticity]] |rowspan=2 bgcolor=lightgrey|'''Rheology''' |- |rowspan=2|[[Fluid mechanics]] |bgcolor=lightgrey width=150|[[Non-Newtonian fluid]]s |- |colspan=2|[[Newtonian fluid]]s |} Rheology unites the seemingly unrelated fields of [[plasticity (physics)|plasticity]] and [[non-Newtonian fluid]]s by recognizing that both these types of materials are unable to support a [[shear stress]] in static [[Mechanical equilibrium|equilibrium]]. In this sense, a plastic solid is a [[fluid]]. Granular rheology refers to the continuum mechanical description of [[granular material]]s. One of the tasks of rheology is to empirically establish the relationships between [[Strain (materials science)|deformations]] and stresses, respectively their [[derivative]]s 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. == Applications == Rheology has important applications in [[engineering]], [[geophysics]] 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 [[rheid]]s. In engineering, rheology has had its predominant application in the development and use of [[polymer]]ic materials ([[Plasticity (physics)|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 [[paint]]s in achieving paints that will level but not sag on vertical surfaces. == Elasticity, viscosity, solid- and liquid-like behavior, plasticity == One generally associates liquids with viscous behaviour (a ''thick'' oil is a viscous liquid) and solids with elastic behaviour (an elastic string is an elastic solid). A more general point of view is to consider the material behaviour 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]]) behaviour is relevant at short times (''transient behaviour''): We again consider the application of a constant stress: * if the material deformation follows the applied stress, then the material is purely elastic * if the deformation increases linearly at constant stress, then the material is viscous * if neither the deformation with time, nor its derivative (''deformation rate'') follows the stress, the material is viscoelastic ;[[Plasticity (physics)|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 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. Note that the Deborah number is relevant for materials that flow on long time scales (like a [[Maxwell material|Maxwell fluid]]) but ''not'' for the reverse kind of materials (like the Voigt or [[Kelvin material|Kelvin model]]) that are viscous on short time scales but solid on the long term. ;Reynolds number In [[fluid mechanics]], the [[Reynolds number]] is a measure of the [[ratio]] of [[inertia]]l [[force]]s (''v<sub>s</sub>ρ'') to [[viscosity|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 number]]s 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: :<math> \mathit{Re} = {\rho v_{s}^2/L \over \mu v_{s}/L^2} = {\rho v_{s} L\over \mu} = {v_{s} L\over \nu} </math> where: * ''v''<sub>s</sub> - mean fluid [[velocity]], [m s<sup>-1</sup>] * ''L'' - characteristic [[length]], [m] * μ - (absolute) dynamic [[fluid]] [[viscosity]], [N s m<sup>-2</sup>] or [Pa s] * ν - kinematic fluid viscosity: ν = μ / ρ, [m² s<sup>-1</sup>] * ρ - fluid [[density]], [kg m<sup>-3</sup>]. == External links == ;Journals covering rheology * [http://www.appliedrheology.org/ ''Applied Rheology''] * [http://www.rheology.org/sor/publications/j_rheology/default.htm ''Journal of Rheology''] * [http://www.jstage.jst.go.jp/browse/rheology ''Journal of the Society of Rheology, JAPAN''] * [http://www.sciencedirect.com/science/journal/03770257 ''Journal of Non-Newtonian Fluid Mechanics''] * [http://www.rheology.or.kr/karj/ ''Korea-Australia Rheology Journal''] * [http://link.springer.de/link/service/journals/00397/ ''Rheologica Acta''] ;Organizations concerned with the study of rheology * [http://www.rheology.org ''The Society of Rheology''] * [http://wwwsoc.nii.ac.jp/srj/ ''The Society of Rheology, JAPAN''] * [http://www.rheology-esr.org ''The European Society of Rheology''] * [http://www.bsr.org.uk ''The British Society of Rheology''] * [http://www.drg.bam.de ''Deutsche Rheologische Gesellschaft''] * [http://www.univ-lemans.fr/sciences/wgfr/ ''Groupe Français de Rhéologie''] * [http://cit.kuleuven.be/ltrk/bgr/bgr.html ''Belgian Group of Rheology''] * [http://www.ar.ethz.ch/FR/ ''Swiss Group of Rheology''] * [http://www.mate.tue.nl/nrv/index.html ''Nederlandse Reologische Vereniging''] * [http://www.sir-reologia.com ''Società Italiana di Reologia''] * [http://www.sik.se/nrs/ ''Nordic Rheology Society''] * [http://www.rheology.org.au ''Australian Society of Rheology''] ;Rheology Conferences, Seminars, and Workshops * [http://www.ar.ethz.ch/conf.html ''Conferences on Rheology & Soft Matter Materials''] ;Other Resources * [http://www.brookfieldengineering.com/products/rheometers/laboratory.asp Brookfield Rheometers] * [http://www.brookfieldengineering.com/services/educational-programs/index.asp Brookfield Courses on Rheology/Viscosity] * [http://www.campoly.com/application_notes.html Application notes on the rheological characterization of polymers] {{Physics-footer}} [[Category:Continuum mechanics]] [[Category:Fluid mechanics]] [[Category:Fluid dynamics]] [[cs:Reologie]] [[de:Rheologie]] [[es:Reología]] [[fr:Rhéologie]] [[hr:Reologija]] [[it:Reologia]] [[nl:Rheologie]] [[ja:レオロジー]] [[pl:Reologia]] [[pt:Reologia]] [[ru:Реология]] [[fi:Reologia]] [[sv:Reologi]] [[uk:Реологія]] [[zh:流变学]]