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)
See also
Rheology
References
Barnes, H.A. "A handbook of elementary rheology", Institute of non-Newtonian Fluid Mechanics, 2000
Hellenica World - Scientific Library
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