# Effect of Solid Particles on Droplet Size Applying the Time-Shift Method for Spray Investigation
## 4 Results and Discussion
### Rheological Characterization  
Initially, the flow behavior concerning liquid viscosity and its dependence on the shear rate was investigated. All of the measurements were performed at least twice. As expected, for both liquids (ethylene glycol & the glycerol/water-mixture) a Newtonian flow behavior was detected; see Figure 5 (left). Due to the fact that no segregation effects or particle sedimentation could occur, the increment of the shear rate was set as linear. The dynamic viscosity of ethylene glycol was \(\eta_{liq}=21\) mPa\(\cdot\)s, whereas the glycerol/water-mixture with \(\phi_{W}=19.5\) wt-% featured \(\eta_{liq}=70\) mPa\(\cdot\)s.  
Figure 4: Signal of scattered light from a transparent (n = 1.333) (left) and an opaque (right) droplet in \(\theta_{S}=165^{\circ}\) while passing the laser beams. Detector D1 is shown in gray with dotted lines, detector D2 in black. At the beginning of the rheological characterization of the suspensions, investigations of suspension viscosity over time at a constant shear rate were performed for \(\Delta t=30\) min. These investigations revealed first effects of sedimentation on the suspension viscosity after \(t=2\) min. To capture the entire range of the shear rate, the increment was set to logarithmic, which allows for the investigation of a large shear rate range with negligible sedimentation influence. To guarantee for an adequate data rate with the SpraySpy(r) system in opaque operation mode, a constant amount of black ink (Pelikan A17 black ink) \(\phi_{ink}=0.13\) wt-% was added to the suspensions. The addition of ink had three effects: (i) The data rate increased significantly, even with a small amount of ink. As a result, the ink mass fraction increased until no further data rate increase was achieved, leading to \(\phi_{ink}=0.13\) wt-%. (ii) The ink enabled the detection of pure liquid droplets even smaller than the glass particles that resulted from the solid-liquid separation, in the opaque mode of the SpraySpy(r). (iii) Ink did not affect the resulting dynamic viscosity, as shown in Figure 5. Here, the dynamic viscosity of pure ethylene glycol (Figure 5 (left)) and the ethylene glycol/ink-mixture (Figure 5 (right)) was similar. As can be seen from the measurements shown, both suspensions exhibited Newtonian flow behavior (see Figure 5 (right)). This effect can be explained by several reasons: (i) the particles used are spherical and not deformable, which avoids an alignment in shear direction or deformation, typically leading to non-Newtonian flow behavior; (ii) the particle size distribution shows a narrow span without formed agglomerates as often found in non-Newtonian suspensions. The Sauter mean diameter of the glass beads with \(\mathrm{wt}-d_{32,P}=40\)-\(70\)\(\mathrm{\SIUnitSymbolMicro m}\) (density: \(\rho_{P}=2500\) kg\(\cdot\)m\({}^{-3}\)) (according to the manufacturer [44]) was checked in an extra set of experiments by means of laser diffraction, which revealed a particle diameter of \(d_{32,P}=69\pm 0.91\)\(\mathrm{\SIUnitSymbolMicro m}\). An increase in the glass mass fraction from \(\phi_{P}=0\) wt-% to \(\phi_{P}=30\) wt-% led to an increase in the viscosity from \(\eta_{liq}=21\) mPa\(\cdot\)s to \(\eta_{sus}=25\) mPa\(\cdot\)s, as shown in Figure 5 (right). The difference between the viscosities mentioned is therefore negligible. A further increase in the glass mass fraction from \(\phi_{P}=30\) wt-% to \(\phi_{P}=50\) wt-% resulted in a significant increase in the viscosity to \(\eta_{sus}=68\) mPa\(\cdot\)s, which is nearly identical to the \(\eta_{liq}=70\) mPa\(\cdot\)s of the glycerol/water-mixture. The refractive index of the glass particles was \(n=1.52\) as given by the manufacturer [44].