Extensional Viscosity
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Extensional viscosity (also known as elongational viscosity) is a
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
coefficient when applied
stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
is
extensional stress In continuum mechanics, stress is a physical quantity. It is a quantity that describes the magnitude of forces that cause deformation. Stress is defined as ''force per unit area''. When an object is pulled apart by a force it will cause elonga ...
. It is often used for characterizing polymer solutions. Extensional viscosity can be measured using rheometers that apply ''extensional stress''.
Acoustic rheometer An acoustic rheometer employs a piezo-electric crystal that can easily launch a successive wave of extensions and contractions into the fluid. It applies an oscillating extensional stress to the system. System response can be interpreted in terms ...
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 :\eta_e = \frac\,\! where :\eta_e\,\! is the extensional viscosity or elongational viscosity :\sigma_\,\! is the normal
stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
along direction n. :\dot\,\! is the rate of strain: \dot = \frac\,\! The ratio between the extensional viscosity \eta_e and the dynamic viscosity \eta is known as Trouton's Ratio Tr = \eta_e/\eta. For a
Newtonian Fluid A Newtonian fluid is a fluid in which the viscous stresses arising from its flow are at every point linearly correlated to the local strain rate — the rate of change of its deformation over time. Stresses are proportional to the rate of chang ...
, the Trouton ratio equals three.


See also

*
Rheology Rheology (; ) is the study of the flow of matter, primarily in a fluid ( liquid or gas) state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an appl ...


References

Fluid dynamics Viscosity {{fluiddynamics-stub