Influence of ambient air viscosity on the accuracy of measurements of liquid properties in a levitating drop

Abstract

In this paper, we consider low-amplitude capillary oscillations of a liquid droplet that has a spherical shape in equilibrium and is placed in an immobile light gas volume. In the approximation of low medium viscosity, and under the condition that the media differ greatly in density, a correction to natural frequency was determined and the viscous damping coefficient was estimated. Theoretical predictions were obtained analytically and verified by performing numerical calculations for water or mercury drops in the air. It is shown that the contributions of the viscosity and inertia of the gas to the real frequency of free oscillations of the system are insignificant. As regards the damping factor, the gas viscosity makes a contribution determined by the square root of its kinematic viscosity, which can no longer be neglected. The damping coefficient calculated relative to the liquid contribution linear in viscosity increases as the fourth root of the droplet size. For the water drop of 5 mm diameter, it is about ten percent, and for the mercury drop of the same size, the relative contribution reaches five percent. The results obtained are necessary for improving the "levitating" drop method, which is a variation of the dynamic capillary wave method used for non-contact measurement of viscosity coefficients and surface tension. A generalization of the Lamb formula for calculating liquid viscosity is proposed, which, in addition to the damping decrement of the quadrupole mode and the drop size, includes the density and viscosity of the gas, as well as the natural frequency of the system. The surface tension coefficient can be calculated using the Rayleigh formula, which, as it turns out, does not require a correction.