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]