## surface shear viscosity

Also contains definitions of: area viscosity, surface dilatational viscosity
https://doi.org/10.1351/goldbook.S06189
For steady state deformations a surface @[email protected] $$\eta ^{\text{s}}$$, and an area viscosity or surface dilatational viscosity $$\zeta ^{\text{s}}$$ can be defined. In a Cartesian system with the x-axis normal to the surface, they are defined by the equations: $\eta ^{\text{s}} = \frac{\sigma _{xy}}{\frac{\partial \nu_{y}}{\partial \nu_{x}}}$ $\zeta ^{\text{s}}=\frac{\Delta \gamma }{\frac{\mathrm{d}(\ln A)}{\mathrm{d}t}}$ where $$\sigma _{xy}$$ is the shear component of the @[email protected] tensor, $$\nu_{x}$$ and $$\nu_{y}$$ are the $$x$$ and $$y$$ components of the surface velocity vector, respectively, $$A$$ is the surface area, $$t$$ is the time, and $$\Delta \gamma$$ is the difference between the (steady state) @[email protected] and the equilibrium surface tension.
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 1218 [Terms] [Paper]