Rheology

Rheology is the study of the deformation and flow of matter under the influence of an applied extensional rheology. Shear rheology is much more widely used than extensional rheology. That is why it is often referred to as simply rheology without specfying type of the stress.

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 Heraclitus's famous expression panta rei, "everything flows".

Scope

In practice, rheology is principally concerned with extending the "classical" disciplines of polymers in solution or the particle size distribution in a solid suspension.

Rheology unites the seemingly unrelated fields of granular materials.

One of the tasks of rheology is to empirically establish the relationships between continuum mechanics.

Applications

Rheology has important applications in engineering, geophysics, paints in achieving paints that will level but not sag on vertical surfaces.

Elasticity, viscosity, solid- and liquid-like behaviour, and plasticity

One is used to associating liquid with viscous (a thick oil is a viscous liquid) as well as solid with elastic (an elastic string is an elastic solid). In fact, when one tries to deform a piece of material, some of the above properties appear at short times (relative to the duration of the experiment), others at long times.

Liquid and solid characters are long-time properties

Let us attempt to deform the material by applying a continuous, weak, constant stress:

• if the material, after some deformation , eventually resists further deformation, it is a solid ;
• if, by contrast, the material eventually flows, it is a liquid.

By contrast, elastic and viscous characters (or intermediate, viscoelastic behaviours) appear at short times

Again, let us attempt to deform the material by applying a weak stress varying in time:

• if the material deformation follows the applied force or stress, then the material is elastic;
• if the time-derivative of the deformation (deformation rate) follows the force or stress, then the material is viscous.

Plasticity appears at high stresses

Liquid, solid, viscous and elastic characters can be detected under weak applied stresses. If a high stress is applied, a material that behaves as a solid under low applied stresses may start to flow. It then reveals a plastic character: it is a plastic solid. Plasticity is thus characterised by a threshold stress (called plasticity threshold or yield stress) beyond which the material flows.

The term plastic solid is used when the 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 behaviour 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 behaviour), 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 Kelvin model) that are viscous on short time scales but solid on the long term.

Reynolds number

In 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 flowrates, have the same values for the relevant dimensionless numbers, they are said to be dynamically similar.

Typically it is given as follows:

where:

• v_s - mean fluid velocity, [m s^-1]
• L - characteristic length, [m]
• μ - (absolute) dynamic viscosity, [N s m^-2] or [Pa s]
• ν - kinematic fluid viscosity: ν = μ / ρ, [m² s^-1]
• ρ - fluid density, [kg m^-3].

• Applied Rheology
• Journal of Rheology
• Journal of the Society of Rheology, JAPAN
• Journal of Non-Newtonian Fluid Mechanics
• Korea-Australia Rheology Journal
• Rheologica Acta

Organizations concerned with the study of rheology

• The Society of Rheology
• The Society of Rheology, JAPAN
• The European Society of Rheology
• The British Society of Rheology
• Deutsche Rheologische Gesellschaft
• Groupe Français de Rhéologie
• Belgian Group of Rheology
• Swiss Group of Rheology
• Nederlandse Reologische Vereniging
• Società Italiana di Reologia
• Nordic Rheology Society
• Australian Society of Rheology

Rheology Conferences, Seminars, and Workshops

• Conferences on Rheology & Soft Matter Materials

Other Resources

• Application notes on the rheological characterization of polymers