# Effect of Solid Particles on Droplet Size Applying the Time-Shift Method for Spray Investigation
## 3 Experimental Setup and Measurement Techniques
Two laser beams from laser diodes with wavelengths of \(\lambda_{L1}\) = 405 nm and \(\lambda_{L2}=450\) nm each with a constant laser power of about 5 mW, a beam distance of \(\Delta s\), as well as four detectors in fixed angle of \(\vartheta_{S}=165^{\circ}\) to the measuring plane are mounted, see Figure 2.  
Figure 1: Schematic view of the atmospheric spray test rig (ATMO) with the applied twin-fluid nozzle. As a result of the passage of a transparent droplet through the measurement volumes of laser L1 and laser L2, each of the two detector pairs (D1 & D2 as well as D3 & D4) received the typical measurement signal consisting of different scattering orders at several time steps. According to Figure 3, at \(t_{1}\) and \(t_{6}\), second order refraction in the second mode occurs, whereas for \(t_{2}\) and \(t_{5}\), the first mode is detected. When the laser beam is located close to the horizontal axis of the droplet (\(t_{3}\) & \(t_{4}\)), the reflection at the droplet surface is recorded [40]. When performing the same measurement with an opaque droplet, the scattered light can solely be described by the time steps \(t_{3}\) and \(t_{4}\). For the reason the droplet's opacity, the refraction cannot be observed due to the scattering of light at the particles within the droplet. As two laser beams were used, the measurement signals shown in Figure 4 were acquired twice. Figure 4 (left) illustrates the signal scattered from a transparent droplet at \(\vartheta_{S}=165^{\circ}\) as peaks over time for one laser beam and two detectors. The different time-shift periods can be detected between the signals \(p=2.2\) (second order, second mode refractions) as \(\Delta t_{22,22}\), \(p=2.1\) (second order, first mode refractions) as \(\Delta t_{21,21}\) and \(p=0\) (reflections) as \(\Delta t_{0,0}\). When applying an opaque suspension droplet, the detected signal in \(\vartheta_{S}=165^{\circ}\) can be illustrated as shown in Figure 4 (right). Here, the region of scattered light around the signal peak of the reflection for the respective detector can be attributed to the scattering of the particles within the droplet. The time-shift periods are then reduced to \(\Delta t_{0,0}\) for \(p=0\). Through a comparison of different redundant time-shift period ratios, a validation can be performed, as described in further detail by [PERSON] et al. [40]. Further experiments and simulations concerning the time-shift signal of colloidal suspensions can be found in [PERSON] et al. [41]. Figure 3: Schematic view of a scattered laser beam exiting a transparent droplet with n = 1.333 at \(\vartheta_{S}=165^{\circ}\) for different times \(t_{1}\) to \(t_{6}\) as a function of droplet velocity \(v_{z}\). The predominant scattering mode at the presented time step is shown as the thick line. Figure 2: Schematic view of the SpraySpy® system in the x,z-plane. With the SpraySpy\({}^{\textregistered}\) system, a transparent and an opaque measuring mode can be chosen for a maximum droplet diameter of \(d_{max}=1000\)\(\upmu\)m. Furthermore, the time-shift constant is needed for transparent mode, which is a function of the refractive index. Three different sensitivity levels can be set; increased sensitivity leads to higher data rate but lower signal validation and vice versa. In the following experiments, the sensitivity was always set to the optimal level between signal validation and data rate. Depending on the applied fluid, the associated opacity mode was used. For the integral droplet size measurement, the Spraytec\({}^{\textregistered}\) STP5342 [42] was used; a state-of-the-art laser diffraction system (LDS) with a Fourier lens with focal length of \(f_{LDS}\) = 750 mm, a He-Ne laser with a diameter of \(d_{LDS}\) = 10 mm and a wavelength of \(\lambda_{LDS}\) = 632.8 nm.