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: \[\eta ^{\text{s}} = \frac{\sigma _{xy}}{\frac{\partial \nu_{y}}{\partial \nu_{x}}}\] \[\zeta ^{\text{s}}=\frac{\Delta \gamma }{\frac{\mathrm{d}(\ln A)}{\mathrm{d}t}}\] where 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.