# 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.

${\displaystyle \eta _{e}={\frac {\sigma _{n}}{\dot {\varepsilon }}}\,\!}$

where

${\displaystyle \eta _{e}\,\!}$ is the extensional viscosity or elongational viscosity
${\displaystyle \sigma _{n}\,\!}$ is the normal stress: ${\displaystyle \sigma _{n}={\frac {F}{A}}\,\!}$
${\displaystyle {\dot {\varepsilon }}\,\!}$ is the rate of strain: ${\displaystyle {\dot {\varepsilon }}={\frac {1}{L}}{\frac {dL}{dt}}\,\!}$

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.

${\displaystyle \eta _{e}=3\eta \,\!}$ (Trouton's Ratio)