Dynamics of oscillating viscous droplets immersed in viscous media

Damped oscillations of a viscous droplet immersed in a viscous medium are considered in detail. The characteristic equation is solved numerically for arbitrary, finite fluid properties. The cylinder functions in the characteristic equation are solved using an accurate continued fraction algorithm, and the complex decay factor is searched using a minimization scheme. Oscillation frequency and damping rate results are presented for the fundamental mode, for various cases of practical interest (liquid-gas, and liquid-liquid systems), and the effect of the external medium properties are discussed. Results are compared to exact solutions for limiting cases, and to existing experimental data for both the fundamental and higher order modes. It is shown that the theoretical frequency prediction matches well with the experimental observation. Damping rate predictions, however, underestimate experimental observation in some cases, and this is thought to be due to surface impurities. The application of these results to the measurement of surface tension and viscosity of liquid droplets from single-droplet levitation experiments is also discussed.