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.

This article is about extensional viscosity. For other uses, see Rheology.

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)

See also

• Rheology

References

1. Barnes, H.A. "A handbook of elementary rheology", Institute of non-Newtonian Fluid Mechanics, 2000