Numerical simulation to study the impact of gravity on viscosity determination through the aerodynamic levitation of a metal drop

This communication deals with the simulation of metal droplet deformation to establish the relationship between gravity and the damping of an oscillating drop. A 2D axisymmetric multiphysics simulation is developed in the finite element code Comsol Multiphysics® to represent both liquid metal and levitation gas. The A.L.E. method is employed to describe the moving mesh and the dynamic behavior of the liquid-gas interface. Viscosity is assumed to be well-known as the initial radius, density, and surface tension because they are inputs of the model. Simulations are performed at different viscosities ranging from 3 to 100 mPa.s and for gravity values between 0 and 2 (Earth = 1). The amplitude of numerical radial oscillations shows that, as gravity increases, oscillations dampen more rapidly. In zero gravity, Lamb’s formula is used successfully to determine dynamic viscosity from the characteristic time of the exponential decrease of oscillations. For other gravity values, and for each viscosity, the error between the real viscosity and the one predicted by Lamb’s formula is quantified. As the viscosity decreases below 100 mPa·s, the associated error progressively increases, exceeding 50% when the viscosity falls below 12 mPa·s, thereby rendering Lamb’s formula unsuitable. A relationship for the time evolution of the radius, depending on viscosity and gravity, is established and tested for a viscosity of 9 mPa.s. This relation can reduce the viscosity error by a factor of two compared to that obtained using Lamb’s formula but limitation remains.