Extensional viscosity (also known as elongational viscosity) is a

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

coefficient when applied stress is extensional stress. It is often used for characterizing polymer solutions. Extensional viscosity can be measured using rheometers that apply ''extensional stress''.

Acoustic rheometer An acoustic rheometer employs a piezo-electric crystal that can easily launch a successive wave of extensions and contractions into the fluid. It applies an oscillating extensional stress to the system. System response can be interpreted in terms ...

is one example of such devices. Extensional viscosity is defined as the ratio of the normal stress difference to the rate of strain. For uniaxial extension along direction

z

:Guyon, E., Hulin, JP. and Petit, L., Physical Hydrodynamics, Oxford University Press (2015), p113 :

\eta_e = \frac\,\!

where :

\eta_e\,\!

is the extensional viscosity or elongational viscosity :

\sigma_\,\!

is the normal stress along direction n. :

\dot\,\!

is the rate of strain:

\dot = \frac\,\!

The ratio between the extensional viscosity

\eta_e

and the dynamic viscosity

\eta

is known as Trouton's Ratio

Tr = \eta_e/\eta

. For a

Newtonian Fluid A Newtonian fluid is a fluid in which the viscous stress tensor, viscous stresses arising from its Fluid dynamics, flow are at every point linearly correlated to the local strain rate — the derivative (mathematics), rate of change of its deforma ...

, the Trouton ratio equals three.

References

Fluid dynamics Viscosity {{fluiddynamics-stub

See also

References