Extensional viscosity (also known aselongational viscosity) is aviscosity coefficient when the appliedstress isextensional stress.^[1] It is often used for characterizing polymer solutions.Extensional viscosity can be measured using rheometers that applyextensional stress.Acoustic rheometer 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${\displaystyle z}$:^[2]

${\displaystyle {\eta }_e=\frac{{\sigma }_{zz}-\frac{1}{2}{\sigma }_{xx}-\frac{1}{2}{\sigma }_{yy}}{\dot{\epsilon }}}$

where

${\displaystyle {\eta }_e}$ is theextensional viscosity orelongational viscosity

${\displaystyle {\sigma }_{nn}}$ is thenormalstress along direction n.

${\displaystyle \dot{\epsilon }}$ is therate of strain:${\displaystyle \dot{\epsilon }=\frac{\mathrm{\partial }{v}_z}{\mathrm{\partial }z}}$

The ratio between the extensional viscosity${\displaystyle {\eta }_e}$ and the dynamic viscosity${\displaystyle \eta }$ is known asTrouton's Ratio,${\displaystyle \mathrm{T}\mathrm{r}={\eta }_e/\eta }$. For aNewtonian Fluid, the Trouton ratio equals three.

• Rheology

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