Viscous Effect on the Frequency Shift of an Oscillating-Rotating Droplet

For an inviscid, spherical, infinitesimal-amplitude oscillating droplet, the surface tension is obtained by the oscillation frequency based on the linear theory. In reality, however, it is not fully applicable due to the severe presuppositions and frequency shift appears which introduces non-ignorable measurement errors in surface tension. In this work, a series of three-dimensional simulations were conducted to investigate the influence of property ratio, oscillation amplitude, viscous effect as well as rotation rate on frequency shift of an oscillating droplet. With the increase of oscillation amplitude, negative frequency shift was observed while positive frequency shift appears with increasing rotation rate, during which the viscous dissipation played role of hindering it. An empirical formula was proposed to determine the frequency shift of an oscillating-rotating droplet and it is in good agreement with experimental results. With this work, it was expected that the measurement accuracy of surface tension of droplet can be further enhanced by considering the frequency shift induced by amplitude, rotation and viscous effect.