  Experiments over the last 50 years have suggested a tentative correlation
between the surface (shear) viscosity and the stability of a foam or emulsion.
We examine this link theoretically using small-amplitude capillary waves in the
presence of a surfactant solution of dilute concentrations where the associated
Marangoni and surface viscosity effects are modelled via the Boussinesq-Scriven
formulation. The resulting integro-differential initial value problem is solved
analytically and surface viscosity is found to contribute an overall damping
effect on the amplitude of the capillary wave with varying degrees depending on
the lengthscale of the system. Numerically, we find the critical damping
wavelength to increase for increasing surface concentration but the rate of
increase remains different for both the surface viscosity and the Marangoni
effect.
