Linear shape oscillations and polymeric time scales of viscoelastic drops

We study small-amplitude axisymmetric shape oscillations of viscoelastic drops in a
gas. The Jeffreys model is used as the rheological constitutive equation of the liquid,
which represents a liquid with a frequency-dependent dynamic viscosity. The analysis
of the time-dependent deformations caused by the oscillations yields the characteristic
equation for the complex frequency, which describes the oscillation frequency and
damping rate dependence on the viscous liquid behaviour and the stress relaxation
and deformation retardation time scales λ1 and λ2 involved in the viscoelastic material
law. The aim of this study is to quantify the influences of the two time scales on the
oscillation behaviour of the drop and to propose an experimental method to determine
one of the time scales by measuring damped oscillations of a drop. A proof-of-concept
experiment is presented to show the potential and limitations of the method. Results
show that values of λ2/λ1 from these measurements are orders of magnitude smaller
than typical values used in simulations of viscoelastic flows