Satellite droplet velocities

Recently, Razumovskid441 studied the shape of drops, and satellite droplets formed by forced capillary breakup of a liquid jet. On the basis of an instability analysis, Teng et al.[442] derived a simple equation for the prediction of droplet size from the breakup of cylindrical liquid jets at low-velocities. The equation correlates droplet size to a modified Ohnesorge number, and is applicable to both liquid-in-liquid, and liquid-in-gas jets of Newtonian or non-Newtonian fluids. Yamane et al.[439] measured Sauter mean diameter, and air-entrainment characteristics of non-evaporating unsteady dense sprays by means of an image analysis technique which uses an instantaneous shadow picture of the spray and amount of injected fuel. Influences of injection pressure and ambient gas density on the Sauter mean diameter and air entrainment were investigated parametrically. An empirical equation for the Sauter mean diameter was proposed based on a dimensionless analysis of the experimental results. It was indicated that the Sauter mean diameter decreases with an increase in injection pressure and a decrease in ambient gas density. It was also shown that the air-entrainment characteristics can be predicted from the quasi-steady jet theory. 

Even if the jet velocity is low enough that just capillary forces need be accounted for, the hydrodynamic stability problem is relatively simple when only the jet stability to small disturbances is considered, that is, disturbances whose amplitudes are small compared with the jet radius. When this is not the case, nonlinear mechanisms enter, which are manifest in various phenomena, including the formation of satellite droplets, which are small spherules that form between the drops (Fig. 10.4.2B). For literature on these and other nonlinear effects of jet instability, see Bogy (1979). 

Fig. 1.1 Instability of a water jet with diameter of 0.27 mm and velocity of 3.3 m/s subject to a long wavelength periodic disturbance with wavelength to diameter ratio of 11.3 showing formation of satellite droplets [21, Fig. 16] (Courtesy of the Royal Society)...

A prerequisite for experimental investigations with colliding droplets is the controlled production of the colliding droplets, where the control concerns both the size and the velocity of the droplets. For controlled droplet production in the experiments, researchers employ droplet generators producing jets that are forced to break up into droplets of equal size due to a vibrational excitation. This process works properly - if satellite droplet formation can be suppressed - with Newtonian liquids, even of appreciable dynamic viscosities. Any non-Newtonian flow behavior of the liquids, in particular elasticity, however, makes a difference in this respect. Even small concentrations of, e.g., polymeric substances in Newtonian... 

The droplet velocity and the droplet frequency must be adjusted in a coupled way in order to generate a droplet train of adequate quality. At a certain droplet velocity, a too low droplet frequency leads to an excessively long tail behind the primary droplet, which leads to satellite droplets surrounding the primary droplet. On the contrary, a too high droplet frequency yields an insufficient distances between adjacent liquid pulses, which further results in random collisions and coalescence of primary droplets. Optimum combinations are droplet velocities from 2 to 3 m/s, and drop frequencies from 50 to 150 Hz. The resulting droplet diameters range from 1.4 to 2.0 mm. 

FIGURE 19.5 Nozzle shape channel geometry. Droplet breakup occurs at a fixed point due to the focused velocity gradient created by the nozzle shape geometry. The radius of the liquid thread decreases due to the perturbation caused by the extension of the thread. Initial balance of the pressure and shear forces at the interface of the thread determines the initial radius of the thread. The device also produces monodisperse submicron satellite drops. (Reprinted from Tan, Y.-C. et al. 2006. Sens. Actual. B 114 350-356. With permission.)... 

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