On the analytical and numerical simulation of an oscillating drop in zero-gravity

•2D and 3D analytical solutions for surface oscillations of a drop including coupled effects of surface tension and viscosity, for finite viscous and potential forces.•Numerical framework for solving the unsteady Navier–Stokes equations for an incompressible two-fluid system separated by an interface described by the level set method.•Quantitative comparison of the analytical and numerical solutions for a system made of pure iron surrounded by air. The oscillation of a levitated drop is a widely used technique for the measurement of the surface tension and viscosity of liquids. Analyses are mainly based on theories developed in the nineteenth century for surface tension driven oscillations of a spherical, force-free, liquid drop. However, a complete analysis with both analytical and numerical approaches to study the damped oscillations of a viscous liquid drop remains challenging. We first propose in this work an extension of the theory that includes the coupled effects of surface tension and viscosity. The analytical solution permits derivation of both properties simultaneously, which is of interest for fluid with unknown viscosity. Then, the robustness of an Eulerian framework to simulate the fluid flow is discussed. Simulations of different oscillations modes for a liquid iron droplet immersed in a low-density gas and comparisons with the derived theory are detailed and presented.