Liquid breakup ejection

Al-Roub et all421 identified three basic modes of liquid breakup during droplet impingement onto a liquid film (1) rim breakup, (2) cluster breakup, and (3) column breakup. The rim breakup mode involves the breakup and ejection of one or a few small droplets at the outer edge of the film, while the cluster breakup mode involves the breakup of liquid into clusters of many small droplets at the outer edge of the film. In the column breakup mode, liquid breaks up into one or a few droplets from a column of liquid at the center of the spreading droplet as a result of the surface waves reflecting back to their source. The diameter and number of the... 

The spreading behavior of droplets on a non-flat surface is not only dependent on inertia and viscous effects, but also significantly influenced by an additional normal stress introduced by the curved surface. This stress leads to the acceleration-deceleration effect, or the hindering effect depending on the dimensionless roughness spacing, and causes the breakup and ejection of liquid. Increasing impact velocity, droplet diameter, liquid density, and/or... 

Atomization breakup is mainly characterized by a liquid high-speed jet which disperses into a fine spray of many single droplets directly behind the nozzle exit. A further characteristic is the arising spray cone so that the droplet trajectory is not inevitably in line with the nozzle. The ejected droplets usually exhibit a droplet size distribution rather than a constant droplet volume. The actuation is continuous and very strong which leads to very high velocities inside the nozzle. 

Droplet Dispensing, Fig. 7 Different breakup regimes represented by the relationship of the velocity v versus the droplet diameter D for water as ejected liquid... 

Rayleigh breakup is a continuous mode rather than an on-demand mode which means that a liquid jet is ejected out of a nozzle continuously. This jet disperses into single droplets due to the so-called Rayleigh instability after a certain distance from the nozzle. This Rayleigh instability is either caused by naturally occurring disturbances on the jet or by additionally applied external disturbances. In this case the droplet volume almost only depends on the nozzle diameter. The actuation has to be applied for much longer compared to the on-demand modes and can be relatively small. 

In order to discuss quantitatively the DoD droplet formation process, the positions of several representative points in the ejected liquid can be plotted as a function of time to produce the curves of the DoD droplet formation, as depicted in Figure 10. The axial distances of points 1-5 from the nozzle exit are denoted as Xi( ) to Xs( ), respectively, with measured from the first appearance of liquid from the nozzle. Initially, point 1 is the leading edge of the liquid ejected from the nozzle that later becomes the tip of the primary drop. Point 2 is the first pinch-off point of the liquid from the nozzle tip, and also the tail of the free liquid thread its first appearance corresponds to the initial breakup time bi. Points 3 and 4 are the lower and upper points produced by the second pinch-off, and the curves associated with these points initiated at the second breakup time b2) these curves form a closed loop if (in the case of a single satellite drop) the satellite recombines with the main drop (as is the case in Figure 10(a)) or may continue separately if the satellite survives as a discrete body of liquid. Later, point 3 becomes the tail of the primary drop, and point 4 becomes the head of the secondary free liquid thread or satellite. Between points 2 and 4, further pinch-off points may occur. Point 5 is the tip of liquid protruding from the nozzle orifice due to multiple reflections of the pressure wave inside the ink chamber. 

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