Numerical Study for Shape Oscillation of Free Viscoelastic Drop Using the Arbitrary Lagrangian-Eulerian Method

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. In this paper, the finite element method is used to investigate numerically the influence of viscoelasticity on the small-amplitude oscillation of drop 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.