Absence of surface mode in a viscoelastic material with surface tension

The surface waves in the viscoelastic media with the surface tension are studied using the Voigt-Kelvin model of the viscoelasticity. It is shown that the surface mode of oscillation does not exist in the parameter region where the effect of surface tension is larger than that of the elastic stress at the surface unless the viscous stress masks the elastic stress in the bulk. In the region, the surface oscillation is suppressed and the oscillation beneath the surface diffuses after the pulse goes into the bulk. The experimental relevance of the present results is also discussed.