Numerical Study on the Role of Propagative Capillary Waves in Droplet Formation from a Ligament

摘要

A novel understanding of droplet formation mechanism from a ligament is presented. In the scaled-up microgravity experiment, it is observed that droplets are always created at the ligament tip at a shorter wavelength than that of Rayleighs analysis. In the new theoretical analysis by Umemura (1-6), the role of capillary waves from the tip is considered and it is shown that destabilization of these waves lead to pinch-off from the tip. In this report, a numerical study on this phenomenon is conducted to investigate the effects of ligament tip and internal liquid flow. It is shown that there is a short-wave self-sustained cycle of droplet breakup that is driven by the capillary force at the tip. Liquid jet elongation due to gas flow creates internal liquid flow and this modifies the characteristics of each region of the liquid column. This type of breakup mechanism is different from Rayleighs analysis. After a certain time, however, the liquid column length no longer increases and converges to an average value. At the same time with this change, longer waves appear on the liquid surface upstream of the tip. The wavelength corresponds to Rayleighs most unstable wave. It is observed that small-wavelength waves that have higher propagation speed have reached the nozzle exit and reflected. As the liquid column becomes longer, these perturbations have come to get enough time to grow to Rayleighs wave. Thus, the liquid breakup phenomenon from the tip is not a single phenomenon, but a combination of two mechanisms. This study gives a new insight into liquid atomization mechanism.