surface shear viscosity

For steady state deformations a surface shear viscosity $η s$ , and an area viscosity or surface dilatational viscosity $ζ s$ can be defined. In a Cartesian system with the x-axis normal to the surface, they are defined by the equations:

$η s = σ x y ∂ v y ∂ v x$

$ζ s = Δ γ d ( ln A ) d t$

where $σ x y$ is the shear component of the surface stress tensor, $v x$ and $v y$ are the $x$ and $y$ components of the surface velocity vector, respectively, $A$ is the surface area, $t$ is the time, and $Δ γ$ is the difference between the (steady state) dynamic surface tension and the equilibrium surface tension.

Source:

PAC, 1979, 51, 1213 (Manual of symbols and terminology for physicochemical quantities and units. Appendix II: Definitions, terminology and symbols in colloid and surface chemistry. Part 1.13. Selected definitions, terminology and symbols for rheological properties) on page 1218

surface shear viscosity

Also contains definitions of: area viscosity, surface dilatational viscosity