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)