# Effect of Solid Particles on Droplet Size Applying the Time-Shift Method for Spray Investigation
## 4 Results and Discussion
### Spray Characterization

Table 1: Summary of the measured fluid properties—the measurements were performed at \(T=20\)\({}^{\circ}\)C and \(p=1\) atm. implies good agreement and a validation of the tendencies attained with the time-shift technique leading to a decrease of around \(\Delta d_{32}=50\)\(\upmu\)m.  
.2.2 The Influence of Dynamic Viscosity on the Sauter Mean Diameter Distribution and Primary Breakup  
In Figure 7 (left), the radial distribution of the Sauter mean diameter is shown at \(v_{gas}=80\) m\(\cdot\)s\({}^{-1}\) for ethylene glycol with \(\eta_{liq}=21\) mPa\(\cdot\)s and the glycerol/water-mixture with \(\eta_{liq}=70\) mPa\(\cdot\)s. Here, both investigated liquids show a distinct W-shape radial profile. With increasing dynamic viscosity, the droplet size increases, which corresponds to [13; 14]. In the region of the spray axis, the increment in droplet size is more pronounced, whereas the size difference is reduced with increasing radial distance to the spray center. These results are confirmed by the high-speed camera images in Figure 7 (right). For increasing the dynamic viscosity, the disintegration process leads to the formation of large ligaments, leaving the field of view marked, finally leading to increased droplet sizes. Identical tendencies can also be found in the literature [13] and are typical for an increase in \(\eta_{liq}\). In the present case, this effect is even more pronounced due to the higher surface tension of the glycerol/water-mixture compared to ethylene glycol (see Table 1). As the surface tension increases, the secondary breakup of droplets is reduced for the same aerodynamic operating conditions. The fiber-type regime underpinned the primary breakup of both investigated liquids. Contrary to the flapping instability of low viscosity liquids, the predominant disintegration mode for the glycerol/water-mixture is a pulsating Kelvin-Helmholtz wave according to [14]. Laser diffraction measurements were performed to compare the tendencies observed with the SpraySpy\({}^{\circledR}\). The results for both dynamic viscosities are illustrated in Figure 7 (left). In the case of both measurement techniques, the droplet size increases with increasing dynamic viscosity. Here, the LDS detected an increase in droplet size of \(\Delta d_{32,LDS}=33.7\)\(\upmu\)m for increasing viscosity. The difference measured by the SpraySpy\({}^{\circledR}\) system was between \(\Delta d_{32}=15\)-\(30\)\(\upmu\)m dependent on the radial position, which implies good agreement and a validation of the results attained with the time-shift technique. Figure 6: Radial distribution of the Sauter mean diameter at \(z=150\) mm below the nozzle orifice as a function of gas velocity (i.e., \(GLR\)) for \(\eta_{liq}=21\) mPa\(\cdot\)s (dots: SpraySpy\({}^{\circledR}\), values: LDS) (left); High-speed camera images of the primary breakup for \(\eta_{liq}=21\) mPa\(\cdot\)s at (**a**) \(v_{gas}=60\) m\(\cdot\)s\({}^{-1}\) and (**b**) \(v_{gas}=80\) m\(\cdot\)s\({}^{-1}\) (right). 2.3 The Influence of Varying Particle Fractions on the Sauter Mean Diameter Distribution and Primary Breakup  
Figure 8 (left) shows the radial distribution of the Sauter mean diameter at \(v_{gas}=80\) m\(\cdot\)s\({}^{-1}\) for ethylene glycol with \(\eta_{liq}=21\) mPa\(\cdot\)s and the ethylene glycol/ink/glass-mixture with \(\eta_{sus}=25\) mPa\(\cdot\)s, \(\phi_{P}=30\) wt-%. As shown in the liquid and suspension properties (see Table 1), the particle mass fraction can be investigated isolated from other parameters influencing the atomization process such as dynamic viscosity or surface tension. Compared to the previous results, the suspension with \(\phi_{P}=30\) wt-% also shows a distinct W-shape profile. A comparison of the two fluids with similar viscosities but varying particle fractions reveals a significant increase in droplet size over the entire spray cone.