Shape oscillations of a viscoelastic drop.

Small-amplitude axisymmetric shape deformations of a viscoelastic liquid drop in microgravity are theoretically analyzed. Using the Jeffreys constitutive equation for linear viscoelasticity, the characteristic equation for the frequency and decay factor of the shape oscillations is derived. Asymptotic analysis of this equation is performed in the low- and high-viscosity limits and for the cases of small, moderate, and large elasticities. Elastic effects are shown to give rise to a type of shape oscillation that does not depend on the surface tension. The existence of such oscillations is confirmed by numerical solution of the characteristic equation in various regimes. A method for determining the viscoelastic properties of highly viscous liquids based upon experimental measurements of the frequency and damping rate of such shape oscillations is suggested.