Abstract:When a liquid drop is periodically excited by an external radial oscillation force, the instability of standing wave mode will be formed on its surface, which is known as the spherical Faraday instability problem. The oscillation frequency of the instability surface wave will render as a harmonic or sub-harmonic mode according to the different fluid physical parameters and the forced excitation conditions. Based on the linear small perturbation theory, this paper studies the instability behavior of the viscoelastic droplet surface wave subjected to the radial oscillating force. The oscillating radial force causes the momentum equations to be Mathieu equations which included time period coefficients. Therefore, the system becomes a parametric instability problem, which can be solved by Floquet theory. In this model, the characteristics of viscoelasticity are treated as an effective viscosity which related to the rheological model of the fluid, which simplifies the solving process of the problem. Based on the analysis of the neutral stability curve and growth rate of the surface wave, the influence of viscoelastic parameters on the stability of droplets were studied. The results showed that the increase of zero-shear viscosity ( μ ₀) as well as deformation retardation time ( λ ₂) can inhibit the growth of droplet surface wave, therefore increased the excitation amplitude which made the droplet unstable at a harmonic mode.With the increase of oscillation amplitude, the regions of unstable growth rate decrease, and as the oscillation frequency increase, the value of droplet surface wave growth rate decrease. Through the analysis of the growth rate, it can be concluded that the increase of the stress relaxation time ( λ ₁) increases the growth rate, thereby promoting the growth of surface wave on the droplet.