# Effect of Solid Particles on Droplet Size Applying the Time-Shift Method for Spray Investigation
## 2 Theoretical Background
Two external-mixing twin-fluid atomizers with central liquid jet and a concentric annular gap for the fast gas stream were used. The regimes were classified as either Rayleigh-type, fiber-type or atomization (which corresponds to the fiber-type supersulsating sub-mode) in the parametric space of \(We_{aero}\) and \(Oh\). Due to the particle loading, membrane formation was significantly reduced, although the viscosity of the suspension was increased, which typically leads to an increase in membrane formation for pure liquids. Additionally, [PERSON] et al. [28] determined a dimensionless correlation for the breakup length in accordance with the Kelvin-Helmholtz--Rayleigh-Taylor hybrid model. Periodic structures as shear waves for low \(\eta_{liq}\) and high \(v_{liq}\), as well as jet oscillation for low \(v_{liq}\) and high \(\eta_{liq}\) were identified, leading to a significant change in the spray angle. In 2016, [PERSON] et al. [29] presented the stabilizing effect of capillary suspensions by adding small amounts of octanol to a beechwood coke slurry, leading to a significant increase in \(\eta_{liq,0}\) and enhanced storage stability. Applying these capillary suspensions for atomization to an external-mixing twin-fluidnozzle, the increased octanol fraction led to a decrease in the spray angle, droplet size and a change in the primary instability. This effect was attributed to a decrease in the surface tension, with increasing octanol content. To conclude the literature review, previous studies provide a wide overview of suspension atomization processes. In particular, the early investigations of model suspensions by [PERSON] et al. [24] lead to a major insight into the disintegration process. Furthermore, the studies presented here emphasize the importance of isolating the influence of spray parameters, as well as fluid properties. This knowledge can be deepened through the application of new image evaluation methods [30] and measurement techniques [31], such as the measurement of local droplet sizes instead of integral measurement, as commonly performed by means of laser diffraction. Thus, this work investigates the influence of solid particles on spray formation and the resulting local droplet size distributions for constant dynamic viscosity. Primary breakup was detected by a high-speed camera, whereas the local drop size was analyzed with a SpraySpy(r) system, which allows for the measurement of local drop size distributions in opaque suspension sprays and is based on the time-shift method. Finally, a conventional laser diffraction-based measurement system was used to confirm and validate the measured tendencies. Ethylene glycol (\(\eta_{liq}=21\) mPa\(\cdot\)s) and a glycerol/water-mixture (\(\eta_{liq}=70\) mPa\(\cdot\)s) were used as pure liquids. The suspensions were composed of mixtures of ethylene glycol and spherical glass particles with size fractions of \(D_{p}=40\)-\(70\) um. Solid mass fractions of \(\phi_{P}=30\) wt-% and \(\phi_{P}=50\) wt-% were used for the suspensions, resulting in \(\eta_{liq}=25\) mPa\(\cdot\)s and \(\eta_{liq}=70\) mPa\(\cdot\)s, respectively. This setup allows for separation of the influence of particles on spray formation independent of the fluid viscosity.