Title: shear viscosity
Long Title: IUPAC Gold Book - shear viscosity
DOI: 10.1351/goldbook.S05642
Status: current

Definition
For a Newtonian fluid, the shear viscosity is often termed simply viscosity since in most situations it is the only one considered. It relates the shear components of stress and those of rate of strain at a point in the fluid by: \[\sigma _{xy}=\sigma _{yx}=\eta \ (\frac{\partial \nu_{x}}{\partial y}+\frac{\partial \nu_{y}}{\partial x})=2\ \eta \ \overset{\rm{.}}{\gamma }_{yx}\] where \(\overset{\rm{.}}{\gamma }_{yx}\), the shear component of rate of strain is defined as follows: \[\overset{\rm{.}}{\gamma }_{yx}=\frac{1}{2}\ (\frac{\partial \nu_{x}}{\partial y}+\frac{\partial \nu_{y}}{\partial x})\] Corresponding relations hold for \(\sigma _{xz}\) and \(\sigma _{yz}\); \(\sigma _{xy}\) is the component of stress acting in the \(y\)-direction on a plate normal to the \(x\)-axis; \(\nu_{x}\), \(\nu_{y}\), \(\nu_{z}\) are the components of velocity.

Related Terms
- Newtonian fluid: https://dev.goldbook.iupac.org/terms/view/N04138
- shear dependent viscosity: https://dev.goldbook.iupac.org/terms/view/S05634
- strain: https://dev.goldbook.iupac.org/terms/view/S06037
- viscosity: https://dev.goldbook.iupac.org/terms/view/V06627

Source
- PAC, 1979, 51, 1213. 'Terminology and Symbols in Colloid and Surface Chemistry Part 1.13. Definitions, Terminology and Symbols for Rheological Properties' on page 1216 (https://doi.org/10.1351/pac197951051213)

Other Outputs
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- json: https://dev.goldbook.iupac.org/terms/view/S05642/json
- xml: https://dev.goldbook.iupac.org/terms/view/S05642/xml

Citation: Citation: 'shear viscosity' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.S05642
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Accessed: 2025-12-13T22:45:24+00:00