# Effect of Solid Particles on Droplet Size Applying the Time-Shift Method for Spray Investigation
## 4 Results and Discussion
### Spray Characterization
To confirm that the result cannot be attributed to a change in the measuring mode from transparent to opaque, the same results for the low-viscosity liquid were identified using a mixture with ethylene glycol and ink in the opaque mode of the SpraySpy\({}^{\textregistered}\) (see Section 3). As already discussed in the previous chapter, a maximum increment in the droplet size was achieved in the center of the spray. With regard to the high-speed camera images, the primary breakup of the pure liquid and suspension only shows small deviations. The detected droplets for \(\phi_{P}=30\) wt-% were larger compared to the pure liquid, with some remaining fragments of the primary breakup in the far field of the nozzle. For both investigated fluids, the fiber-type regime with flapping instability was the predominant disintegration mode according to [14]. For a comparison of the tendencies observed with the SpraySpy\({}^{\textregistered}\), laser diffraction measurements were performed. The results are illustrated in Figure 8 (left) for both solid mass fractions at low viscosity (\(\eta_{liq/sus}=21\)-\(25\) mPa\(\cdot\)s). For both of these measurement techniques, the droplet size increased in conjunction with increasing solid mass fraction and constant viscosity. The LDS showed an increment of \(\Delta d_{32,LDS}=26.3\)\(\upmu\)m, whereas the SpraySpy\({}^{\textregistered}\) system detected an increment of \(\Delta d_{32}=50\)-\(60\)\(\upmu\)m depending on radial position. Figure 7: Radial distribution of the Sauter mean diameter at \(z=150\) mm below the nozzle orifice as a function of the dynamic viscosity for \(v_{gas}=80\) m\(\cdot\)s\({}^{-1}\) (dots: SpraySpy\({}^{\textregistered}\), values: LDS) (left); High-speed camera images of the primary breakup for \(v_{gas}=80\) m\(\cdot\)s\({}^{-1}\) at (a) \(\eta_{liq}=21\) mPa\(\cdot\)s and (b) \(\eta_{liq}=70\) mPa\(\cdot\)s (right). Considering the secondary breakup of suspension fragments and droplets, as presented by [PERSON] et al. [24], the difference in droplet size at \(z=150\) mm can be explained using the tensile strength approach. For disintegration of a liquid droplet, the surface tension force must be overcome, whereas the tensile force of a suspension droplet is significantly higher [27]. Therefore, the dynamic pressure of the gas phase required for the disintegration of a suspension droplet is increased significantly compared to that for a pure liquid droplet. This effect is explained in the following example:  
With a force balance between the surface tension force and dynamic pressure of the gas phase, an ethylene glycol droplet with \(d_{32}=300\) um requires a relative gas velocity of \(v_{gas}>12.5\) m\(\cdot\)s\({}^{-1}\) for further breakup [25]. Against this, applying Equation (5) and assuming a pendular state of the suspension droplet, according to [PERSON] [27], a relative gas velocity of \(v_{gas}>21.9\) m\(\cdot\)s\({}^{-1}\) is needed to induce further breakup. Due to the fact that the gas velocity decreases with increasing distance from the nozzle orifice, the disintegration process of the suspension droplets is halted at larger droplet sizes compared to the case of pure liquids for identical operating conditions at the nozzle. Comparing the results of low viscosity (\(\eta_{liq/sus}=21\)-\(25\) mPa\(\cdot\)s) with those revealed for the increased viscosity of \(\eta_{liq}=70\) mPa\(\cdot\)s, similar conclusions can be drawn. In Figure 9 (left), the radial distribution of the Sauter mean diameter profiles is shown at \(v_{gas}>80\) m\(\cdot\)s\({}^{-1}\) for the glycerol/water-mixture with \(\eta_{liq}=70\) mPa\(\cdot\)s, \(\phi_{P}=0\) wt-% and the ethylene glycol/ink/glass-mixture with \(\eta_{sus}=68\) mPa\(\cdot\)s, \(\phi_{P}=50\) wt-%. For an increase in the glass mass fraction from \(\phi_{P}=0\) wt-% to \(\phi_{P}=50\) wt-%, a significant increase in the droplet size was detected. The W-shaped profile is revealed with both media. The high-speed camera images in Figure 9(right) show the fiber-type breakup for both fluids.