Rheology is the science of flow and deformation of matter and describes the interrelation between force, deformation and time. The term comes from Greek rheos meaning to flow. Rheology is applicable to all materials, from gases to solids.
The science of rheology is only about 70 years of age. It was founded by two scientists meeting in the late '20s and finding out having the same need for describing fluid flow properties. The scientists were Professor Marcus Reiner and Professor Eugene Bingham.
The Greek philosopher Heraclitus described rheology as panta rei - everything flows. Translated into rheological terms by Marcus Reiner this means everything will flow if you just wait long enough.
Fluid rheology is used to describe the consistency of different products, normally by the two components viscosity and elasticity. By viscosity is usually meant resistance to flow or thickness and by elasticity usually stickiness or structure.

Classification of materials

Fluids are normally divided into three different groups according to their flow behaviour:
Newtonian fluids
Non-Newtonian fluids, time independent
Non-newtonian fluids, time dependent

Flow curves 

Flow curves are normally use for the graphical description of flow behaviour.

Kinematic and dynamic viscosity

Kinematic viscosity is measured with kinematic instruments , normally different types of cups which means that the knowledge and control of shear rates is limited or non-existent. Therefore kinematic viscosity values are of little or no use for design of equipment for non-Newtonian fluids.
Dynamic viscosity takes into account the effect of shear rate and time and is therefore the only type of viscosity relevant for non-Newtonian design purposes. Dynamic viscosity is measured with dynamic instruments, either rotating (shearing) or oscillating.
An instrument only capable of measuring shearing viscosities is called a viscometer and the oscillating type is called a rheometer.

Basic constitutive equations

Various models for approximation of rheological data have been presented. One of the most widely spread models is the so-called power law for approximation of viscosity data. The main reason for the power law being so popular is that the shearing rheological behaviour of a fluid is represented simply by a straight line in a log-log shear rate/shear stress graph. Another reason is that the shearing behaviour of most fluids lends itself to a good approximation applying the power law.


All materials, from gases to solids, can be divided into the following three categories of rheological behaviour:
Viscous materials: in a purely viscous material all energy added is dissipated into heat
Elastic materials: in a purely elastic material all energy added is stored in the material
Viscoelastic materials: a viscoelastic material exhibits viscous as well as viscoelastic behaviour

Typical examples of viscoelastic materials are bread dough, polymer melts and artificial or natural gels.
Note: in the rheological sense water is a "viscous" fluid. Normally, however, the term "viscous" is used for fluids with high viscosity.
In most cases of viscoelastic behaviour the time factor has a significant impact on the flow properties observed. A measure of the influence of time is the so-called Deborah Number, D:
D = (response time) / (observation time)
An example of a system having a large Deborah Number is a normal glass window. If old enough, e.g. an old church window, a difference in thickness at the top and at the bottom can be easily measured. Although the viscosity of glass is high, about 1040 Pas, it is still a liquid and consequently it flows. However, the observation time has to be long, perhaps a couple of centuries, to observe the movement.
When shearing a viscoelastic fluid so-called normal stresses will appear. These normal stresses can result in flow behaviour quite different from that of Newtonian fluids.

Viscosity and elasticity measurements

Rheological measurements are normally performed in kinematic instruments in order to get quantitative results useful for design and development of products and process equipment. For design of products, e.g. in the food, cosmetic or paint industry, rheometric measurements are often performed to establish the elastic properties, such as gel strength and yield value, both important parameters affecting e.g. particle carrying ability and spreadability. For design of process equipment the properties during shearing of the product is of prime interest. Those properties are established in a normal viscosity measurement.
A rheometric measurement normally consists of a strain (deformation) or a stress analysis at a constant frequency (normally 1 Hz) combined with a frequency analysis, e.g. between 0.1 and 100 Hz. The strain sweep gives information of the elastic modulus G', the viscous modulus G'' and the phase angle d. A large value of G ' in comparison of G '' indicates pronounced elastic (gel) properties of the product being analysed. For such a product the phase angle is also small, e.g. 20º (a phase angle of 0º means a perfectly elastic material and a phase angle of 90º means a perfectly viscous material). The frequency sweep gives information about the gel strength where a large slope of the G ' curve indicates low strength and a small slope indicates high strength.

G* = Stress*/Strain
G* = G’ + iG”

A viscometric measurement normally consists of a shear rate analysis. The shear rate sweep should preferably cover the range applied in the intended equipment. For liquid foods a shear rate range from around 1 to 1,000 s-1 covers the needs for a low-viscous product, e.g. milk or juice, and a shear rate range from around 1 to 100s-1 covers the needs for a high-viscous product, e.g. tomato paste or quark.
Below a number of examples from measurements on some fermented dairy products are found. The fermented cream has a fat content of about 35%, the fermented milk "type 1" has a fat content of 0.5% and the fermented milk "type 2" has a fat content of 1.5%. Note that despite the difference in the elastic modulus G ' between the two fermented milk types being significant, the viscosity curves are nearly identical. The practical implication of this is that when the two products are sitting in a cup the "type 2" fermented milk seems to have appreciably higher viscosity than the "type 1" milk, but when subjected to shear, e.g. when being pumped through a pipe, the pressure drop will be much the same for both products. What is observed in the "cup analysis" is instead the more pronounced elastic properties of the "type 2" milk giving the impression of a higher viscosity.
For the youghurt a significant degree of thixotropy can be seen in that the "up curve", i.e. the curve obtained when increasing the shear rate from zero and upwards, is appearing above the "down curve", i.e. the curve obtained when going back in shear rate to zero. For comparison of the degree of thixotropic behaviour the distance or area between the two curves can be calculated, applied to either the shear stress curves or the apparent viscosity curves.

Read more at the rheology page by Prof Ulf Bolmstedt