For steady state deformations a surface shear viscosity ${\eta }^{\text{s}}$, 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: $${\eta }^{\text{s}}=\frac{{\sigma }_{xy}}{\frac{\partial {\nu }_y}{\partial {\nu }_x}}$$ $${\zeta }^{\text{s}}=\frac{\mathrm{\Delta }\gamma }{\frac{\mathrm{d}(\ln A)}{\mathrm{d}t}}$$ where ${\sigma }_{xy}$ is the shear component of the surface stress 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 $\mathrm{\Delta }\gamma$ is the difference between the (steady state) dynamic surface tension and the equilibrium surface tension.