Everything about Rheology totally explained
Rheology is the study of the deformation and flow of
matter under the influence of an applied
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 synonomously with rheometry, particularly by experimentalists. Theoretical aspects of rheology are the relation of the flow/deformation behaviour of material and its internal structure (for example the orientation and elongation of polymer molecules), and the flow/deformation behaviour of materials that can't be described by classical fluid mechanics or elasticity. This is also often called
Non-Newtonian fluid mechanics in the case of fluids.
The term
rheology 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 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
elasticity and (
Newtonian)
fluid mechanics to materials whose mechanical behavior can't 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, for example the
molecular size and architecture of
polymers in solution or the particle size distribution in a solid suspension.
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 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
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 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's considered a solid
- if, by contrast, the material flows indefinitely, it's 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 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 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 (vsρ) to viscous forces (μ/L) and consequently it quantifies the relative importance of these two types of forces for given flow conditions. Thus, it's 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 flow rates, have the same values for the relevant dimensionless numbers, they're said to be dynamically similar.
Typically it's given as follows:
»
where:
vs - mean fluid velocity, [ms-1]
L - characteristic length, [m]
μ - (absolute) dynamic fluid viscosity, [Ns m-2] or [Pas]
ν - kinematic fluid viscosity: ν = μ / ρ, [m²s-1]
ρ - fluid density, [kgm-3].Further Information
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