Extensional viscosity

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

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.

\eta_e = \frac{\sigma_n}{\dot{\varepsilon}}\,\!


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

\eta_e = 3\eta\,\! (Trouton's law)

See also[edit]


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