Viscosity measurement by the "Oscillating Drop Method": The case of strongly damped oscillations

Abstract

By the measurement of the 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 linking these material properties to the corresponding measurement quantities are the Rayleigh and the Lamb formula. However, both these equations are derived under the assumption of undamped or very weakly damped oscillations. In the following the basic characteristic equation of the linear Navier-Stokes equation, representing a corresponding physical model for the whole damping range, is theoretically investigated. A comparison of its accurate results with those of Rayleigh and Lamb reveal, that the Rayleigh formula provides, even in the case of strongly damped oscillations, an approximation which is still good enough for most practical purposes, whereas the Lamb formula deviates by more than 10% from the accurate value. An improvement of the Lamb formula is derived from the characteristic equation which extends its practical applicability also to strongly damped oscillations.