# Effect of Solid Particles on Droplet Size Applying the Time-Shift Method for Spray Investigation
## 4 Results and Discussion
### Spray Characterization  
The following section discusses measurements of droplet size obtained using the time-shift technique as well as laser diffraction. Every radial profile and integral measurement was performed three times to guarantee the reliability of the results. Reproducibility is given as standard deviation in the diagrams. The maximum deviation of local \(d_{32}\) is \(<10\)\(\upmu\)m. According to this small deviations, error bars are hardly visible for some measurement positions. After a full radial profile was measured and the rotational symmetry proven, two half-profiles of \(x\leq 0\) mm were carried out; the profiles were mirrored at radial position \(x=0\) mm. Therefore, the mirrored data points are shown as open symbols in the following diagrams. To obtain a reliable dataset at every radial position, the measuring options were set to either 20,000 droplets or a measuring time of at least 180 s. As mentioned above, the measuring plane was set to \(z=150\) mm for all measurements. For laser diffraction the measurement time was set to \(t=30\) s. The values of Sauter mean diameter detected by laser diffraction are given as \(d_{32,LDS}\) with a maximum deviation of \(\pm 9\)\(\upmu\)m.  
2.1 The Influence of Gas Velocity on the Radial Sauter Mean Diameter Distribution and Primary Breakup  
Figure 6 (left) shows the radial distribution of the Sauter mean diameter profiles for the ethylene glycol with \(\eta_{liq}=21\) mPa\(\cdot\)s at \(v_{gas}=60\) m\(\cdot\)s\({}^{-1}\) and \(v_{gas}=80\) m\(\cdot\)s\({}^{-1}\). For both gas velocities, a W-shaped radial profile was detected where the profile was more pronounced for the \(v_{gas}=80\) m\(\cdot\)s\({}^{-1}\). With increasing gas velocity (i.e., \(GLR\)), the droplet size decreased over the entire spray cone. The decrement of droplet size was around \(\Delta d_{32}=50\)\(\upmu\)m. The high-speed camera images in Figure 6 (right) also show an effect that had a clear influence on the droplet size. For \(v_{gas}=60\) m\(\cdot\)s\({}^{-1}\), smaller membranes and fibers leaving the detection area can be observed, whereas for \(v_{gas}=80\) m\(\cdot\)s\({}^{-1}\), the spray was highly homogenous in droplet size and without ligaments in the near field of the nozzle. The decrement in droplet size for the increased gas velocity has been confirmed by other researchers [9; 45; 46]. For both of the illustrated primary breakup images, the flapping instability (which is characterized by the non-axisymmetric oscillation of the liquid jet) was the predominant disintegration mode detected in the fiber-type regime according to [14]. In order to validate the tendencies revealed by the SpraySpy(r), additional measurements were performed with a commonly used laser diffraction system. The results for both gas velocities are shown in Figure 6 (left) as values. Due to the fact that the measurement systems differ, the results are only qualitatively compared in terms of their tendencies, as in [47]. As expected, the Sauter mean diameters detected by laser diffraction were smaller than those measured by the SpraySpy(r). This is in accordance to the comparison measurements of other local measurement techniques and laser diffraction [47; 48]. The present research is primarily focused on the influence of different process parameters on spray development. In this context both measurement techniques showed that with increasing gas velocity the droplet size decreased. For the LDS a decrease in droplet size of \(\Delta d_{32,LDS}=56.6\)\(\upmu\)m was detected, which \begin{table}
\begin{tabular}{l l l l l} \hline  & **Glycol** & **Glycerol/Water** & **Glycol/Ink/Glass** & **Glycol/Ink/Glass** \\ \hline \(\phi p\) in wt\(-\%\) & 0 & 0 & 30 & 50 \\ \(\rho\) in kg\(\cdot\)m\({}^{-3}\) & 1110 & 1215 & 1332 & 1537 \\ \(\eta\) in mPa\(\cdot\)s & 21 & 70 & 25 & 68 \\ \(\sigma\) in mN\(\cdot\)m\({}^{-1}\) & 48 & 65 & 48 & 48 \\ \(n_{real}\) in \(-\) & 1.432 & 1.445 & 1.432 & 1.432 \\ \(A\) in \(-\) & 0 & 0 & 0 & 0 \\ \(Oh\) & 0.064 & 0.176 & 0.070 & 0.178 \\ \hline \end{tabular}
\end{table}