Rheology is the study of the flow of matter, primarily in the liquid state, but also as 'soft solids' or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force.[1] It applies to substances which have a complex microstructure, such as muds, sludges, suspensions, polymers and other glass formers (e.g., silicates), as well as many foods and additives, bodily fluids (e.g., blood) and other biological materials or other materials which belong to the class of soft matter. Newtonian fluids can be characterized by a single coefficient of viscosity for a specific temperature. Although this viscosity will change with temperature, it does not change with the strain rate. Only a small group of fluids exhibit such constant viscosity, and they are known as Newtonian fluids. But for a large class of fluids, the viscosity changes with the strain rate (or relative velocity of flow) and are called non-Newtonian fluids. Rheology generally accounts for the behaviour of non-Newtonian fluids, by characterizing the minimum number of functions that are needed to relate stresses with rate of change of strains or strain rates. For example, ketchup can have its viscosity reduced by shaking (or other forms of mechanical agitation, where the relative movement of different layers in the material actually causes the reduction in viscosity) but water cannot. Ketchup is a shear thinning material, as an increase in relative velocity caused a reduction in viscosity, while some other non-Newtonian materials show the opposite behaviour: viscosity going up with relative deformation, which are called shear thickening or dilatant materials. Since Sir Isaac Newton originated the concept of viscosity, the study of liquids with strain rate dependent viscosity 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.[2][3] The term was inspired by the aphorism of Simplicius (often misattributed to Heraclitus), panta rhei, "everything flows"[4] The experimental characterization 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.

Scope

In practice, rheology is principally concerned with extending continuum mechanics to characterize flow of materials, that exhibits a combination of elastic, viscous and plastic behaviour by properly combining elasticity and (Newtonian) fluid mechanics. 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. Materials with the characteristics of a fluid will flow when subjected to a 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 for different stresses. Much of theoretical rheology is concerned with associating external forces and torques with internal stresses and internal strain gradients and velocities.[1][5][6][7]

Rheology unites the seemingly unrelated fields of 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 equilibrium. In this sense, solids undergoing plastic deformation is a fluid, although no viscosity coefficient is associated with this flow. Granular rheology refers to the continuum mechanical description of granular materials. One of the major tasks of rheology is to empirically establish the relationships between deformations and stresses, respectively their derivatives by adequate measurements, 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 with 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.

Rheologist

A rheologist is an interdisciplinary scientist/engineer 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 (e.g. chemistry, physics, biology), engineering (e.g. mechanical, chemical, Materials Science & Engineering or civil engineering), medicine, or certain technologies, notably materials or food. Typically, a small amount of rheology may be studied when obtaining a degree, but the professional will extend this knowledge during postgraduate research or by attending short courses and by joining one of the professional associations

Viscoelasticity

The classical theory of elasticity deals with the behaviour of elastic solids under small deformations, for which,(1) according to Hooke's Law, stress is directly proportional to the strain — but independent of the rate of strain, or how fast the deformation was applied, and (2) the strains are completely recoverable once the stress is removed. Materials that can be characterized by classical theory of elasticity are known as linear elastic materials, even for such materials the linear relationship between stress and strain may be valid only for a certain range of strains. A large number of solids show non-linear relationship between stress and strain even for small stresses (such as rubber), but if the strains are still recoverable they are known as non-linear elastic materials. The classical theory of fluid mechanics, governed by the Navier-Stokes equation, deals with the behaviour of viscous fluids, for which, according to Newton's Law, the stress is directly proportional to the rate of strain, but independent of the strain itself. These behaviour are, of course, generally observed for ideal materials under ideal conditions, although the behaviour of many solids approaches Hooke's law for infinitesimal strains, and that of many fluids approaches Newton's law for infinitesimal rates of strain. Two types of deviations from linearity may be considered here. When finite strains (larger strains, as opposed to infinitesimal strains) are applied to solid bodies, the stress-strain relationships are often much more complicated (i.e. Non-Hookean). Similarly, in steady flow with finite strain rates, many fluids exhibit marked deviations in stress-strain rate proportionality from Newtons law. Even if both strain and rate of strain are infinitesimal, a system may exhibit both liquid-like and solid-like characteristics. A good example of this is when a body which is not quite an elastic solid (i.e. an inelastic solid) does not maintain a constant deformation under constant stress, but rather continues to deform with time – or "creeps" under the same stress at constant temperature. When such a body is constrained at constant deformation, the stress required to hold it at that stretch level gradually diminishes—or "relaxes" with time. Similarly, a fluid while flowing under constant stress may show some elastic properties as well, such as storing some of the energy input instead of dissipating it all as heat and random thermal motion of its molecular constituents or having some recovery of strains after stresses are removed, although it may never recover all of its deformation upon removal of the initial applied stress. When such bodies are subjected to a sinusoidally oscillating stress, the strain is neither exactly in phase with the stress (as it would be for a perfectly elastic solid) nor 90 degrees out of phase (as it would be for a perfectly viscous liquid) but rather exhibits a strain that lags the stress at a value between zero and 90 degrees: i.e., Some of the energy is stored and recovered in each cycle, and some is dissipated as heat. These are viscoelastic materials. Thus, fluids are generally associated 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.

Fluid 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 fluid

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[8]:

if the material deformation strain increases linearly with increasing applied stress, then the material is linear elastic within the range it shows recoverable strains. Elasticity is essentially a time independent processes, as the strains appear the moment the stress is appliled, without any time delay.

if the material deformation rate increases linearly with increasing applied stress, then the material is viscous in the Newtonian sense. These materials are characterized due to the time delay between the applied constant stress and the maximum strain.

if the materials behaves as a combination of viscous and elastic components, then the material is viscoelastic. Theoretically such materials can show both instantaneous deformation as elastic material and a delayed time dependent deformation as in fluids.

Plasticity is the behaviour observed after the material is subjected to 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. However, there is no fundamental difference between the two concepts.

References

1.a b c W. R. Schowalter (1978) Mechanics of Non-Newtonian Fluids Pergamon ISBN 0-08-021778-8

2.J. F. Steffe (1996) Rheological Methods in Food Process Engineering 2nd ed ISBN 0-9632036-1-4 page 1

3.The Deborah Number

4.Barnes, Jonathan (1982). The presocratic philosophers. ISBN 978-0-415-05079-1.

5.R. B. Bird, W. E. Stewart, E. N. Lightfoot (1960), Transport Phenomena, John Wiley & Sons, ISBN 0-471-07392-X

6.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

7.Faith A. Morrison (2001), Understanding Rheology, Oxford University Press, ISBN 0-19-514166-0 and 978-0195141665

8.William N. Findley, James S. Lai, Kasif Onaran (1989), Creep and Relaxation of Nonlinear Viscoelastic Materials, Dover Publications