Extensional viscosity

Extensional viscosity (also known as elongational viscosity) is a viscosity coefficient when applied stress is extensional stress.^[1]

This parameter is often used for characterizing polymer solutions.

Extensional viscosity can be measured using rheometers that apply extensional stress. Acoustic rheometer is one example of such devices.

$\eta_e = \frac{\sigma_n}{\dot{\varepsilon}}\,\!$

where

$\eta_e\,\!$ is the extensional viscosity or elongational viscosity

$\sigma_n\,\!$ is the normal stress: $\sigma_n = \frac{F}{A}\,\!$

$\dot{\varepsilon}\,\!$ is the rate of strain: $\dot{\varepsilon} = \frac{1}{L}\frac{dL}{dt}\,\!$

For a Newtonian Fluid, the uniaxial elongational viscosity is three times the shear viscosity which can be derived using the continuity equation for incompressible fluids.

$\eta_e = 3\eta\,\!$ (Trouton's law)

See also

• Rheology
• Viscosity
• Trouton's ratio

References

1. Barnes, H.A. "A handbook of elementary rheology", Institute of non-Newtonian Fluid Mechanics, 2000