A Theoretical Investigation of the Behavior of Droplets in Axial Acoustic Fields

This paper describes a theoretical investigation of the behavior of small droplets in an acoustic field. It was motivated by the increasing interest in the use of pulsations to improve the performance of energy intensive, industrial processes which are controlled by rates of mass momentum and heat transfer. The acoustic field is expected to enhance heat and mass transfer to and from the droplets, probably because of the relative motion between the droplets and the gas phase. Relative motion is traditionally quantified by 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 alternate approach, these two quantities are combined into a single quantity called the “degree of opposition” (DOP), which is defined as the ratio of the amplitude of the relative velocity between the droplet and the gas phase to the amplitude of the acoustic velocity. The equation for the droplet motion is solved using two methods; by numerical integration and by using a spectral method. Despite the nonlinear nature of the problem, the results were found not to be sensitive to initial conditions. The DOP was predicted to 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 decreases with increasing acoustic velocity. Theoretical predictions were compared with experimental data and good agreement was observed.