# 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)