For steady state deformations a surface shear viscosity \(\eta ^{\rm{s}}\), and an area viscosity or surface dilatational viscosity \(\zeta ^{\rm{s}}\) can be defined. In a Cartesian system with the x-axis normal to the surface, they are defined by the equations: \[\eta ^{\rm{s}} = \frac{\sigma _{xy}}{\frac{\partial \nu_{y}}{\partial \nu_{x}}}\] \[\zeta ^{\rm{s}}=\frac{\Delta \gamma }{\frac{\mathrm{d}(\ln A)}{\mathrm{d}t}}\] 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 \(\Delta \gamma \) is the difference between the (steady state) dynamic surface tension and the equilibrium surface tension.