extensional viscosity

{{short description|Polymer solution parameter}}

{{about|extensional viscosity||Rheology}}

Extensional viscosity (also known as elongational viscosity) is a viscosity coefficient when the applied stress is extensional stress.Barnes, H.A. "A handbook of elementary rheology", Institute of non-Newtonian Fluid Mechanics, 2000 It 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.

Extensional viscosity is defined as the ratio of the normal stress difference to the rate of strain. For uniaxial extension along direction $z$:Guyon, E., Hulin, JP. and Petit, L., Physical Hydrodynamics, Oxford University Press (2015), p113

:$\backslash eta\_e\; =\; \backslash frac\{\backslash sigma\_\{zz\}\; -\; \backslash frac\{1\}\{2\}\backslash sigma\_\{xx\}\; -\; \backslash frac\{1\}\{2\}\backslash sigma\_\{yy\}\}\{\backslash dot\{\backslash varepsilon\}\}\backslash ,\backslash !$

where

:$\backslash eta\_e\backslash ,\backslash !$ is the extensional viscosity or elongational viscosity

:$\backslash sigma\_\{nn\}\backslash ,\backslash !$ is the normal stress along direction n.

:$\backslash dot\{\backslash varepsilon\}\backslash ,\backslash !$ is the rate of strain: $\backslash dot\{\backslash varepsilon\}\; =\; \backslash frac\{\backslash partial\; v\_z\}\{\backslash partial\; z\}\backslash ,\backslash !$

The ratio between the extensional viscosity $\backslash eta\_e$ and the dynamic viscosity $\backslash eta$ is known as Trouton's Ratio, $\backslash mathrm\{Tr\}\; =\; \backslash eta\_e/\backslash eta$. For a Newtonian Fluid, the Trouton ratio equals three.