ABSTRACT
The free oscillation of liquid droplet is one of the classical questions in science
research, liquid drops play important role in a lot of engineering applications. Theory
study of droplet oscillation mainly based on the linear method, this method is only
adapted to the small-amplitude oscillatory motion of drops. Except the linear method
used in this study, numerical method have been successfully applied in simulation of
the free oscillation of liquid droplet. To date, the literature on simulation of oscillation
of viscoelastic drops is quite sparse.
In this paper, the finite element method is used to investigate numerically the
influence of viscoelasticity on the small-amplitude oscillation of drops of polymer
solutions. A spatial discretization is accomplished by the finite element method, the
time descretization is carried by the Crank-Nicolson method, and the arbitrary
Lagangian-Eulerian (ALE) method is used to track the change of the interface.
Numerical results are compared with the ones of linear theory. the behaviors of
oscillation are found to depend on the viscosity and the stress relaxation time of
viscoelastic fluid, the results of numerical simulation and linear theory are identical,
moreover, extension to large-amplitude non-linear oscillation is discussed.