Viscosity Measurement by the “Oscillating Drop” Method: Limits of the Linear Model

Abstract By the measurement of frequency and damping time of surface oscillations, excited by a short pulse on a freely floating liquid droplet, the surface tension and viscosity of the liquid can under certain conditions contactlessly be determined. The conventional physical models connecting these material properties with the corresponding measurement quantities are the well-known Rayleigh and Lamb formula. However, the use of these formulas in oscillating drop experiments does not always deliver physically reasonable results especially in the case of thin fluid liquids. Among others, this is due to the fact that both equations result from calculations of the fluid flow inside the oscillating liquid droplet which are based on the simplified linearized Navier–Stokes equation neglecting its substantially appertaining nonlinear convective term. In the following, the theoretical basis of the Rayleigh and Lamb formulae is investigated in more detail. Furthermore, criteria are derived to provide limits for the reasonable application of these equations.