Editing Rheology (section)

== Scope ==

In practice, rheology is principally concerned with extending [[continuum mechanics]] to characterize the flow of materials that exhibit a combination of [[elastic deformation|elastic]], [[Viscosity|viscous]] and [[plastic]] behavior by properly combining [[theory of elasticity|elasticity]] and ([[Newtonian fluid|Newtonian]]) [[fluid mechanics]]. It is also concerned with predicting 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.
Materials with the characteristics of a fluid will flow when subjected to a [[Stress (physics)|stress]], which is defined as the force per area. There are different sorts of stress (e.g. shear, torsional, etc.), and materials can respond differently under different stresses. Much of theoretical rheology is concerned with associating external forces and torques with internal stresses, internal strain gradients, and flow velocities.<ref name=Schowalter /><ref name="bird1">R. B. Bird, W. E. Stewart, E. N. Lightfoot (1960), Transport Phenomena, John Wiley & Sons, {{ISBN|0-471-07392-X}}.{{pn|date=June 2024}}</ref><ref name="bird2">R. Byrin Bird, Charles F. Curtiss, Robert C. Armstrong (1989), Dynamics of Polymeric Liquids, Vol 1 & 2, Wiley Interscience, {{ISBN|0-471-51844-1}} and 978-0471518440.{{pn|date=June 2024}}</ref><ref name="morris1">Faith A. Morrison (2001), Understanding Rheology, Oxford University Press, {{ISBN|0-19-514166-0}} and 978-0195141665.{{pn|date=June 2024}}</ref>

{{Continuum mechanics context}}

Rheology unites the seemingly unrelated fields of [[plasticity (physics)|plasticity]] and [[non-Newtonian fluid]] dynamics by recognizing that materials undergoing these types of deformation are unable to support a stress (particularly a [[shear stress]], since it is easier to analyze shear deformation) in static [[Mechanical equilibrium|equilibrium]]. In this sense, a solid undergoing plastic [[deformation (mechanics)|deformation]] is a [[fluid]], although no viscosity coefficient is associated with this flow. Granular rheology refers to the continuum mechanical description of [[granular material]]s.

One of the major tasks of rheology is to establish by measurement the relationships between [[Strain (materials science)|strains]] (or rates of strain) and stresses, although a number of theoretical developments (such as assuring frame invariants) are also required before using the empirical data. These experimental techniques are known as [[rheometry]] and are concerned with the determination of well-defined ''rheological material functions''. Such relationships are then amenable to mathematical treatment by the established methods of [[continuum mechanics]].

The characterization 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.