shear viscosity

https://doi.org/10.1351/goldbook.S05642
For a @[email protected], the shear @[email protected] is often termed simply @[email protected] since in most situations it is the only one considered. It relates the shear components of stress and those of rate of @[email protected] at a point in the fluid by: \[\sigma _{xy}=\sigma _{yx}=\eta \ (\frac{\partial \nu_{x}}{\partial y}+\frac{\partial \nu_{y}}{\partial x})=2\ \eta \ \overset{\text{.}}{\gamma }_{yx}\] where \(\overset{\text{.}}{\gamma }_{yx}\), the shear component of rate of @[email protected] is defined as follows: \[\overset{\text{.}}{\gamma }_{yx}=\frac{1}{2}\ (\frac{\partial \nu_{x}}{\partial y}+\frac{\partial \nu_{y}}{\partial x})\] 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.
See also:
shear dependent viscosity
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 [Terms] [Paper]