Nonnegative rank (linear algebra)

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

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 elongational viscosity is three times the shear viscosity which can be derived using the continuity equation for incompressible fluids.

$\eta _{e}=3\eta \,\!$

References

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See also

• Rheology
• Viscosity
• Trouton's ratio

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