A theoretical investigation of the behavior of droplets in axial acoustic fields

This paper describes a theoretical investigation of the behavior of small d roplets in an acoustic field. It was motivated by the increasing interest i n the use of pulsations to improve the performance of energy intensive, ind ustrial processes which are controlled by rates of mass momentum and heat t ransfer. The acoustic field is expected to enhance heat and mass transfer t o and from the droplets, probably because of the relative motion between th e droplets and the gas phase. Relative motion is traditionally quantified b y an entrainment factor which is defined as the ratio between the amplitude of the droplet and the gas phase oscillations, and a phase delay. In an al ternate approach, these two quantities are combined into a single quantity called the "degree of opposition" (DOP), which is defined as the ratio of t he amplitude of the relative velocity between the droplet and the gas phase to the amplitude of the acoustic velocity. The equation for the droplet mo tion is solved using two methods; by numerical integration and by using a s pectral method. Despite the nonlinear nature of the problem, the results we re found not to be sensitive to initial conditions. The DOP was predicted t o increase with increasing droplet diameter and frequency. In other words, larger diameters and higher acoustic frequencies reduce the ability of the droplets to follow the gas phase oscillations. The DOP also decreases with increasing acoustic velocity. It was shown that the amplitude of the higher harmonics are very small and that the droplet mean terminal velocity decre ases with increasing acoustic velocity. Theoretical predictions were compar ed with experimental data and good agreement was observed.