# Influence of Nozzle Geometry and Scale-Up on Oil Droplet Breakup in the Atomization Step during Spray Drying of Emulsions

^{1}

^{2}

^{*}

## Abstract

**:**

_{90,3}values of the oil droplet size distribution decreasing from 5.29 to 2.30 µm with a decrease of the inlet area from 2.0 to 0.6 mm. Good scalability of the findings from pilot to industrial-scale was shown using larger nozzles. A simplified theoretical model, aiming to predict the ODS as a function of calculated shear rates, showed reasonable agreement to the experimental data for different atomization pressures with coefficients of determination of up to 0.99. However, it was not able to predict the impact of different nozzle dimensions, most likely due to changes in flow characteristics. These results suggest that the stress history of the oil droplets might have a larger influence than expected. Further studies will need to consider other zones of high stress in addition to the outlet orifice.

## 1. Introduction

^{−1}, the shear viscosity of the continuous phase ${\eta}_{\mathrm{c}}$ measured in Pa·s, the droplet radius x in m, and the interfacial tension σ measured in N/m at the oil-water-interface as influencing parameters (Equation (1)). The viscosity of the continuous phase is used here in place of the emulsion viscosity, as very low disperse phase fractions were worked with.

_{cr}is exceeded for a sufficiently long time period [13,17]. The value of Ca

_{cr}highly depends on the type of flow that is acting on the droplet, as well as the emulsion’s viscosity ratio $\lambda $. Grace [17] defined $\lambda $ as the ratio of the viscosity of the dispersed phase ${\eta}_{d}$ to the viscosity of the continuous phase ${\eta}_{c}$. Assuming a simple shear flow at quasi-steady state, Ca

_{cr}has a minimum of around 0.5 for a viscosity ratio in the range of 0.1 < $\lambda $ < 1 [17,22]. For higher values of $\lambda $, the critical capillary number increases, and it is generally assumed that at $\lambda $ > 4, drops rotate and do not break up anymore.

_{cr}for shear. The results showed increasing oil droplet breakup with increasing shear rates in the liquid lamella at the outlet orifice, and it was concluded that laminar shear stresses in the liquid lamella at the outlet orifice dominate the oil droplet breakup. Furthermore, the model was used in Taboada et al. [8] to estimate capillary numbers for different emulsion viscosities and viscosity ratios. The authors used Equation (2) to fit their experimental data, proving it to be effective in describing oil droplet sizes after atomization.

_{L}measured in L·min

^{−1}and the dimensionless discharge coefficient C

_{d}. The discharge coefficient is described by Equation (3), with d

_{o}being the nozzle outlet orifice diameter in m, $\rho $ the emulsion density in kg·m

^{−3}, and Δp the atomization pressure in Pa.

_{d}< 0.6 [15].

_{V}in which stresses are high enough for droplet disruption. As typically broad droplet size distributions result from droplet breakup in industrial emulsification machines, a characteristic value is used in the equation to describe the correlation between resulting droplet size and energy density applied. Very often the Sauter mean diameter SMD is used, simplistically as the mean value of the distribution. However, from the point of view of droplet size reduction theory, the maximum surviving diameter should be calculated. A suitable characteristic value would therefore rather be the x

_{90,3}value of the resulting distribution; see Equation (4):

- Oil droplet breakup decreases with smaller inlet port area at a constant pressure. This hypothesis is based on the assumption that a decrease in inlet port area leads to a decrease in volume flow rate, and consequently to smaller shear stresses in the nozzle outlet, as the liquid velocity decreases.
- Oil droplet breakup increases with smaller outlet orifice area. This hypothesis assumes that a smaller outlet orifice leads to increasing shear rates due to higher liquid velocities, as the cross-sectional flow area decreases.
- Based on the expectation that oil droplet size after atomization is solely dependent on the acting shear rates, it can be hypothesized that the proposed model should also hold up for changes in geometry, as long as geometrical similarity of the nozzles can be assumed and the residence time in the nozzle orifice is sufficient to reach equilibrium conditions.

## 2. Materials and Methods

#### 2.1. Model Emulsion

_{90,3}= 41.72 µm. The mass ratio of emulsifier to oil was set to 1:10. Subsequently, this concentrated emulsion was mixed with a maltodextrin solution to adjust the viscosity to 10 mPa·s at 20 °C. Taking the viscosity of the dispersed oil into account, this results in a viscosity ratio of 0.97 and a theoretical critical capillary number Ca

_{cr,th}of 0.7 according to Grace [17]. An oil concentration of 1 wt% was chosen, as it is documented in the literature that coalescence of oil droplets can be neglected at this concentration.

#### 2.2. Pilot-Scale Pressure-Swirl Nozzles

#### 2.3. Atomization Experiments at Pilot-Scale

^{−1}, meaning the maximum achievable pressure was limited. The liquid volume flow rates Q

_{L}were measured with a flow meter (VSE0, 04/16, VSE Volumentechnik GmbH, Neuenrade, Germany). Spray droplet size was measured inline by means of a laser diffraction spectroscope (Spraytec, Malvern Instruments GmbH, Herrenberg, Germany), which measures the spray droplet size 25 cm below the nozzle outlet perpendicular to the nozzle axis line. The measured values were time averaged over a period of 30 s for each atomization condition, with a measurement interval of 1 s. To investigate oil droplet breakup, samples of the atomized emulsions were taken with a beaker 20 cm below the spray. Atomization was done at all operating points three times, resetting the experimental setup between each trial. All samples were taken at room temperature in triplicate. Oil droplet size distributions (ODSDs) were measured offline using a laser diffraction spectroscope (HORIBA LA950, Retsch Technology GmbH, Haan, Germany). A refractive index of 1.4494 was used with an imaginary part of zero. Data points in the ODSDs were connected for readability. Rheological data were obtained with a rotational rheometer (Physica MCR 101, Anton Paar, Graz, Austria) using a double gap geometry (DG26.7) with shear rates in a range of 10

^{1}to 10

^{3}s

^{−1}at 25 °C. The software OriginPro 2020 (OriginLab Corporation, Northampton, MA, USA) was used to perform statistical analysis.

#### 2.4. Industrial-Scale Nozzle Design and Atomization Experiments

## 3. Results

#### 3.1. Influence of Nozzle Geometry on the Discharge Coefficient and Key Parameters for Throughput Characteristics in Pilot-Scale

_{d}) need to be determined for all nozzle configurations at 5–25 MPa. Under the assumption that a proper air core is formed, an increase in atomization pressure is expected to lead to higher tangential velocities, a thinner liquid lamella, and therefore a lower C

_{d}.

_{d}value at different atomization pressures for the examined nozzle geometries. Overall, C

_{d}decreases with increasing atomization pressure, showing good agreement with the expected results. This is also reflected in the values for liquid film thickness (Appendix A). A noticeable deviation from the expected trend of C

_{d}can be observed for the Mini SDX using inlet ports with an area of 2.0 mm

^{2}. An increase in atomization pressure from 5 to 10 MPa leads to an increase of C

_{d}. In addition, C

_{d}is above 0.7 for the investigated atomization pressures. These combined effects indicate that a stable air core was probably not fully developed, leading to an improper atomization process. This is further supported by the results for key parameters that describe the throughput characteristics for the atomization experiments at 10 MPa (Table 3). The characteristic spray droplet size x

_{90,3}is with 150.68 µm for an inlet port area of 2.0 mm

^{2}, considerably larger than for components with smaller inlet port areas.

_{L}, the mean liquid velocity $\overline{u}$, and the calculated liquid film thickness t are shown in Table 3, and are all in line with this expectation. With the knowledge of the liquid film thickness, the cross-sectional area of the liquid in the outlet orifice can be calculated. An increase in C

_{d}is observed with increasing inlet port area, thereby showing the expected trends. This correlation is evident for both the Mini SDX and the SK.

_{d}[5]. Looking at the results, the discharge coefficient decreases with larger orifice diameter according to the expectation based on the literature. Simultaneously, an increase of the volume flow rate from 0.35 to 0.70 L·min

^{−1}is observed for an increase from 0.4 to 1.2 mm

^{2}outlet orifice area (Table 3). This increase in volume flow rate in combination with slightly lower liquid velocities (107.84–100.18 m·s

^{−1}) leads to an increase in liquid film thickness. However, the influence of the film thickness is not of the same magnitude as that of the increase in orifice area, still leading to a proportionally larger air core and, therefore, an overall lower discharge coefficient. Complete results on the film thickness are shown in Appendix A, and volume flow rates in Appendix B.

#### 3.2. Influence of Nozzle Design Type and Geometric Dimensions on Oil Droplet Size

#### 3.2.1. Atomization Experiments at Pilot-Scale

_{90,3}at 5–25 MPa (right) for atomization with different inlet ports of the Mini SDX. Four different nozzle components with inlet port areas A

_{i}in the range of 0.6 to 2.0 mm

^{2}were investigated. The ODSDs are narrow and monomodal for all investigated nozzle components, a result that is consistent for all investigated nozzles (Appendix C). Analysing the results for the oil droplet size distribution at 10 MPa (Figure 5, left), a significant reduction of the ODS can be observed for all geometries. A clear trend for smaller oil droplets with smaller A

_{i}is evident, as indicated by the x

_{90,3}values decreasing from 5.29 to 2.30 µm with a decrease of the A

_{i}from 2.0 to 0.6 mm.

_{90,3}values for the different nozzle configurations. It is known from the literature [7] that ODS decreases with increasing atomization pressure, as the acting stresses on the oil droplets are expected to increase. This behavior can be observed across all investigated A

_{i}. Furthermore, the correlation of smaller oil droplet sizes when atomizing with smaller A

_{i}at constant pressure remains valid for all investigated atomization pressures of the Mini SDX.

_{L}, estimated values of film thickness t, and mean liquid velocity $\overline{u}$ (Table 3) were taken into account to calculate the acting shear rates $\dot{\gamma}$ according to Equation (4), assuming a linear shear profile in the liquid lamella. A comprehensive summary of the estimated shear rates for all nozzle geometries and atomization pressures is given in Appendix D.

_{90,3}for different inlet port areas of the Mini SDX (A and B), as well as different inlet port areas (C and D) and outlet orifice areas (E and F) of the SK for atomization pressures from 5 up to 25 MPa. In this analysis, the results for an inlet port area of 2.0 mm

^{2}were not taken into account, as the results of the discharge coefficient in Section 3.1 gave clear indication that no stable air core was formed. If no stable air core is present in the outlet orifice, the prerequisites for the model of Taboada et al. [7] are not fulfilled, and it cannot be applied.

_{90,3}plotted against the estimated shear rate for each investigated nozzle configuration, while Figure 6B,D,F depicts the x

_{90,3}plotted against the energy density E

_{V}. It can generally be observed for all nozzle configurations that ODS decreases with increasing atomization pressure Δp for constant inlet areas Ai or constant outlet areas A

_{o}. Additionally, an increase in shear rate with larger Δp can be seen across all configurations (Figure 6A,C,E). A closer examination of the impact of changes in nozzle geometry at constant Δp reveals different results. For changes in A

_{i}of the Mini SDX, the results display a reduction of ODS with smaller inlet ports at constant Δp, as was observed in Figure 5 (right), while the estimated shear rates are increasing. For changes in A

_{i}of the SK, the same trend of decreasing ODS with decreasing A

_{i}can only be observed for Δp = 5 MPa (Figure 6C,D). When atomizing at higher Δp, no consistent trend can be detected. Looking at different outlet areas A

_{o}of the SK at constant Δp, the ODS increases with decreasing A

_{o}(Figure 6E,F). Nonetheless, the estimated shear rates increase with smaller dimensions at a constant Δp for all investigated configurations of the SK (Figure 6A,C,E).

^{2}is between 0.83 and 0.97. A critical capillary number Ca

_{cr}based on the estimated shear rates was calculated according to Taboada et al. [7] using the slope of Equation (2). The results for Ca

_{cr}are overall in a range of 0.94 to 1.79. The highest values are observed for changes in the inlet area A

_{i}of the Mini SDX (1.61 to 1.79), with no discernible trend. For the SK, values of Ca

_{cr}are around 1.05 to 1.25 for changes in A

_{i}and 0.89 to 1.42 for different A

_{o}. In both cases, the Ca

_{cr}decreases with increasing inlet or outlet area.

^{2}for the fits are shown in Table 4, exhibiting excellent values in a range of 0.93 to 1. The values for b (Table 4) are in a range of 0.65 to 1.23. Looking at the Mini SDX, the exponent b decreases from 1.14 to 0.65 for an increase in A

_{i}. In the case of the SK, no clear trend can be observed with values ranging from 1.17 to 1.23 for changes in A

_{i}and from 0.94 to 1.14 for A

_{o}. Values for the slope C were observed for the Mini SDX nozzle from 1.54 × 10

^{7}to 2.47 × 10

^{7}, increasing with increasing A

_{i}. For the SK, no clear trend is discernible again, with C ranging from 1.02 × 10

^{+7}to 1.91 × 10

^{+7}. The Reynolds number Re was calculated according to Nonnenmacher et al. [19,20]. Values for different inlet areas of the Mini SDX range from approximately 2000 to 3000. Smaller differences with values from around 1500 to 2000 are estimated for changes in A

_{i}of the SK, while no significant changes were observed for different A

_{o}with relatively constant values of around 1550.

#### 3.2.2. Atomization Experiments at Industrial-Scale

_{L}, mean liquid velocity $\overline{u}$, film thickness t, and discharge coefficient C

_{d}all show similar trends compared to the pilot-scale experiments (Table 3) for changes in A

_{i}as well as A

_{o}.

_{90,3}plotted against the estimated shear rates and energy density for different inlet ports (A and B) and outlet orifices (C and D) at atomization pressures Δp from 5 to 20 MPa. Analysis of the data for each nozzle configuration of the SDX V reveals a reduction in ODS with increasing Δp. Looking at the results on the impact of different inlet ports (Figure 7A,B) at constant Δp, the ODS also decreases with decreasing A

_{i}. For changes in A

_{o}, the results are depicted in Figure 7C,D. Generally, no clear trend was observed. Additionally, changes in A

_{i}lead to overall larger differences in ODS compared to different A

_{o}.

^{2}, C, and b are presented in Table 6. The coefficients of determination are generally in a range of 0.87 to 0.97, with the exception of a lower R

^{2}value of 0.56 when atomizing with the largest inlet port of 9.4 mm

^{2}. The values of Ca

_{cr}increase from 0.36 to 0.60 with increasing A

_{i}, whereas they remain relatively constant at around 0.35 to 0.39 for different A

_{o}. The energy density model was also applied to analyse the scaled-up experimental data and to validate flow characteristics within the nozzle outlet channel. The data were fitted using Equation (4). The calculated fits are shown in Figure 7B,D), and the resulting R

^{2}, slope C, and exponent b are presented in Table 6. The fit matches the experimental data exceptionally well, as an R

^{2}of around 0.99 was obtained for most component combinations. Only the fit for an inlet port area of A

_{i}= 9.4 mm

^{2}exhibits a lower R

^{2}of 0.93. The slope C decreases from 1.38 × 10

^{+6}to 6.21 × 10

^{+2}for larger A

_{i}, and from 1.38 × 10

^{+7}to 4.76 × 10

^{+4}for larger A

_{o}. The Reynolds numbers Re were estimated to increase from approximately 4000 to 6000 for different A

_{i}. A change in A

_{o}had no impact on Re, with all values around 4150.

## 4. Discussion

_{90,3}of the droplet size distributions. Considering the individual nozzle configurations, the x

_{90,3}values decrease with increasing Δp and therefore increasing E

_{V}, as more energy is available for droplet breakup when atomizing at higher pressures. The coefficients of determination R

^{2}for all investigated nozzle configurations showed values from R

^{2}= 0.83 − 0.97 using the model of Taboada et al. [7]. Similar values for R

^{2}were reported in the literature [8] using the same model system containing MCT-oil. This confirms that the model describes the impact of changes in the atomization pressure on the ODS in a reasonable manner for all nozzle configurations.

**Hypothesis**

**1.**

_{i}on Oil Droplet Breakup.

_{90,3}values with decreasing A

_{i}(Figure 6A). This result implies an increase in shear rates, which is confirmed by the values for the shear rates estimated using the model of Taboada et al. [7]. As a smaller A

_{i}leads to larger shear rates and increased oil droplet breakup at a constant pressure, the expected trend from Hypothesis 1 is not observed for the Mini SDX. Nonetheless, the observed trend for the estimated shear rates fit to the data of the ODS. This is generally not the case for the SK. While an increase in estimated shear rates for smaller A

_{i}is observed for the SK as well (Figure 6C), the ODS does not correlate with the increased shear rates as expected. No clear trend for the ODS depending on the shear rates at constant atomization pressure can be observed. Given the fundamental differences in construction between the Mini SDX and SK, it is assumed that different flow characteristics in the nozzles are responsible for this observation.

^{2}(Table 4) already demonstrate the weakness and the strength of this model. The empirical determination of the values b and C compromises theoretical prediction potential, but enhances the model’s ability to fit the experimental data with a higher coefficient of determination R

^{2}. This reflects the higher degree of freedom of the energy density model with its two variables (Equation (4)) compared to the model of Taboada et al. [7]. For the Mini SDX, the values for b decrease from the smallest inlet port to the largest at almost constant values for C, potentially indicating a transition in flow characteristics from laminar flow to a more transitional flow (Table 4). This is corroborated by the estimated values for the Reynolds number Re, which also suggest a flow in the transitional regime. A shift in flow characteristics might contribute to the deviation of the Mini SDX results to the anticipated outcome according to Hypothesis 1. In contrast, the energy density model only provides limited additional insights for different A

_{i}of the SK. Only minor differences in b are observed between the different inlet ports at near constant C, in addition to the impact on Re being lower.

**Hypothesis**

**2.**

_{o}on Oil Droplet Breakup.

_{o}at constant Δp, as well as for increasing Δp at constant A

_{o}. Based on Hypothesis 2, the ODS would be anticipated to decrease with increasing shear rates. Contrary to this expectation, the ODS increases with increasing estimated shear rates for changes in A

_{o}at constant Δp. The model’s simplicity may hinder a reliable estimation of the main stresses responsible for oil droplet breakup. Critical effects such as viscous losses may be misrepresented, leading to shear rate trends not matching the experimental results. Additionally, the flow characteristics and stress profiles throughout the whole nozzle could play a more significant role for droplet breakup than previously anticipated, and should be considered for prediction of oil droplet breakup. The assumption that other zones besides the nozzle orifice influence oil droplet breakup contradicts common reports from the literature [19,20]. It is generally assumed that stresses in the outlet orifice are sufficiently high to override the impact of the rest of the nozzle. This assumption is also challenged by Ballesteros and Gaukel [34]. The authors investigated the local shear and elongation stress as well as stress histories in comparable geometries of the Mini SDX and SK by means of computational fluid dynamics simulation. The results showed that not only in the outlet region of a nozzle high shear rates can be expected, but also in the inlet area. As the oil droplets are larger when they pass the inlet area, a first breakup may happen at this point. In addition, the authors gave a detailed analysis of the stresses and found out that especially in the inlet region, elongational stresses can dominate the breakup. They proposed that oil droplet breakup may happen as a two-step process. A first droplet breakup happens in the inlet ports mainly due to elongational stresses, while another droplet breakup may occur due to shear stresses in the nozzle outlet orifice. This more complex breakup mechanism obviously cannot be properly captured by the simplified model from Taboada et al. [7].

_{o}of the SK at near constant values of C. This indicates similar breakup mechanisms in the outlet orifice, further supporting the assumption that it is an oversimplification to solely investigate the shear rates in the outlet orifice to describe and try to predict oil droplet breakup in pressure-swirl nozzles.

**Hypothesis**

**3.**

_{90,3}align with anticipation based on pilot-scale findings using the Mini SDX. The x

_{90,3}values decrease with higher shear rates. This indicates that the fundamental principles remain valid even for nozzles accommodating larger volume flow rates.

_{i}. To assess if the model applies to SDX-type nozzles at industrial volume flow rates as well, the experimental data of the SDX V was fitted according to the shear-rate-based model proposed by Taboada et al. (Equation (2)). The obtained values of R

^{2}showed generally similar results to the reported R

^{2}for model systems containing MCT oil of [8]. This confirms that the model describes the impact of changes in the atomization pressure on the ODS in a reasonable manner for all nozzle configurations.

_{cr,th}= 0.7. Using the estimated shear rate and measured x

_{90,3}values, a value for Ca

_{cr}was calculated and compared to Ca

_{cr,th}. These values would ideally coincide, assuming that the model correctly calculates the shear rates. This is not the case for the Mini SDX, as all values of Ca

_{cr}were above the theoretical value of Ca

_{cr,th}= 0.7, indicating that the model overestimates the acting shear rates. It is essential to note that the calculated shear rates are maximum shear rates and are neglecting any potential viscous losses that occur at these high-pressure applications, possibly leading to the overestimation of the shear rates. For the SDX V nozzle, the calculated critical capillary numbers Ca

_{cr}of 0.36 to 0.60 are lower than the expected theoretical value of 0.7, suggesting that shear rates were underestimated by the model. It has to be noted that the calculation of the capillary number assumes a spherical droplet in equilibrium conditions. This is likely not the case, as it was shown by Ballesteros and Gaukel [34] that oil droplets are already partially broken up in the inlet port of the nozzle. Another notable observation is in cases where larger oil droplets were observed despite larger estimated shear rates, both at pilot- and industrial-scale (Figure 6A). A possible explanation could be an insufficient residence time of the oil droplets in the high-stress zone of the nozzle orifice. Based on the results of Ballesteros and Gaukel [34], this is likely not the case, as the residence time in the nozzle orifice is expected to be much higher than the critical breakup time of oil droplets.

^{2}for the fitted data, with values of up to 0.99. Similar to the Mini SDX, a major decrease in b for decreasing A

_{i}can be observed for the SDX V. In case of the SDX V, the results show a change from droplet breakup in a relatively laminar flow b = 0.83 to a value of 0.31, which is commonly associated with droplet breakup in a more turbulent regime. These results alone do not allow the conclusion that droplet breakup occurs in a turbulent flow regime, a notion that is reinforced when taking the greatly varying results for the constant C into account. As the results using the energy density model are inconclusive, the calculated Reynolds numbers (Table 6) are considered as well. The results show a shift in the Reynolds numbers also indicating a change in flow characteristics. The impact of a change in A

_{o}on the key parameters b and Re is comparatively much smaller.

## 5. Conclusions

_{i}, and larger outlet areas A

_{o}. Notably, changes in the inlet port area significantly influenced final ODS for the Mini SDX, as the ODS decreases with smaller inlet port areas and higher shear rates in contrast to the anticipation of Hypothesis 1. In contrast to Hypothesis 2, a decrease of the outlet orifice area of the SK leads to an increase in ODS, even though the estimated shear rates increased. These findings suggest that the flow characteristics in high-stress zones besides the nozzle outlet orifice, such as the inlet ports, may play a crucial role in oil droplet breakup. Applying these principles to larger volume flow rates using the industrial-scale SDX V nozzle generally reflected the principles found in pilot-scale.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Overview of Liquid Film Thickness during Atomization Experiments

Mini SDX Inlet Port Area | 0.6 mm^{2} | 1.1 mm^{2} | 1.5 mm^{2} | 2.0 mm^{2} |
---|---|---|---|---|

5 MPa | 96.73 | 107.83 | 122.07 | 124.70 |

10 MPa | 91.75 | 102.77 | 120.85 | 127.54 |

15 MPa | 88.08 | 97.37 | 109.85 | - |

20 MPa | 82.50 | 91.63 | - | - |

25 MPa | 78.81 | - | - | - |

SK inlet port area | 0.2 mm^{2} | 0.3 mm^{2} | 0.6 mm^{2} | - |

5 MPa | 81.69 | 82.34 | 91.80 | - |

10 MPa | 78.38 | 82.76 | 88.41 | - |

20 MPa | 71.57 | 76.15 | 82.50 | - |

SK outlet port area | 0.4 mm^{2} | 0.5 mm^{2} | 0.8 mm^{2} | 1.2 mm^{2} |

5 MPa | 75.44 | 81.69 | 85.58 | 92.32 |

10 MPa | 73.09 | 78.38 | 82.88 | 91.71 |

15 MPa | 69.49 | 75.48 | 78.70 | 87.23 |

20 MPa | 66.88 | 71.57 | 76.22 | 83.55 |

25 MPa | 64.05 | 67.81 | 72.27 | 80.07 |

SDX V inlet port area | 4.6 mm^{2} | 6.5 mm^{2} | 9.4 mm^{2} | - |

5 MPa | 250.70 | 283.94 | 325.26 | - |

10 MPa | 245.61 | 280.39 | 319.48 | - |

20 MPa | 244.57 | 281.10 | 317.05 | - |

SDX V outlet port area | 2.4 mm^{2} | 2.7 mm^{2} | 3.0 mm^{2} | - |

5 MPa | 250.70 | 255.23 | 259.36 | - |

10 MPa | 245.61 | 252.84 | 257.52 | - |

20 MPa | 244.57 | 253.55 | 254.07 | - |

## Appendix B. Overview of Volume Flow Rate during Atomization Experiments

Mini SDX Inlet Port Area | 0.6 mm^{2} | 1.1 mm^{2} | 1.5 mm^{2} | 2.0 mm^{2} |
---|---|---|---|---|

5 MPa | 0.40 | 0.46 | 0.52 | 0.53 |

10 MPa | 0.53 | 0.61 | 0.73 | 0.78 |

15 MPa | 0.62 | 0.70 | 0.81 | - |

20 MPa | 0.66 | 0.75 | - | - |

25 MPa | 0.69 | - | - | - |

SK inlet port area | 0.2 mm^{2} | 0.3 mm^{2} | 0.6 mm^{2} | - |

5 MPa | 0.32 | 0.33 | 0.38 | - |

10 MPa | 0.43 | 0.47 | 0.51 | - |

20 MPa | 0.54 | 0.59 | 0.66 | - |

SK outlet port area | 0.4 mm^{2} | 0.5 mm^{2} | 0.8 mm^{2} | 1.2 mm^{2} |

5 MPa | 0.26 | 0.32 | 0.40 | 0.50 |

10 MPa | 0.35 | 0.43 | 0.54 | 0.70 |

15 MPa | 0.40 | 0.51 | 0.62 | 0.80 |

20 MPa | 0.45 | 0.54 | 0.68 | 0.87 |

25 MPa | 0.47 | 0.57 | 0.71 | 0.92 |

SDX V inlet port area | 4.6 mm^{2} | 6.5 mm^{2} | 9.4 mm^{2} | - |

5 MPa | 4.88 | 4.93 | 5.50 | - |

10 MPa | 5.33 | 6.40 | 7.63 | - |

20 MPa | 7.52 | 9.07 | 10.63 | - |

SDX V outlet port area | 2.4 mm^{2} | 2.7 mm^{2} | 3.0 mm^{2} | - |

5 MPa | 4.88 | 5.02 | 4.97 | - |

10 MPa | 5.33 | 5.72 | 6.08 | - |

20 MPa | 7.52 | 8.12 | 8.4 | - |

## Appendix C. Q3-Distributions of the ODS for Atomization Experiments

**Figure A1.**ODSD for the atomization with different inlet ports of the SK nozzle at a constant atomization pressure of 10 MPa.

**Figure A2.**ODSD for the atomization with different outlet ports of the SK nozzle at a constant atomization pressure of 10 MPa.

**Figure A3.**ODSD for the atomization with different inlet ports of the SDX V nozzle at a constant atomization pressure of 10 MPa.

**Figure A4.**ODSD for the atomization with different outlet ports of the SDX V nozzle at a constant atomization pressure of 10 MPa.

## Appendix D. Overview of Estimated Shear Rates during Atomization Experiments

Mini SDX Inlet Port Area | 0.6 mm^{2} | 1.1 mm^{2} | 1.5 mm^{2} | 2.0 mm^{2} |
---|---|---|---|---|

5 MPa | 1.85 × 10^{+6} | 1.76 × 10^{+6} | 1.66 × 10^{+6} | 1.64 × 10^{+6} |

10 MPa | 2.69 × 10^{+6} | 2.55 × 10^{+6} | 2.36 × 10^{+6} | 2.29 × 10^{+6} |

15 MPa | 3.35 × 10^{+6} | 3.20 × 10^{+6} | 3.03 × 10^{+6} | - |

20 MPa | 3.99 × 10^{+6} | 3.80 × 10^{+6} | - | - |

25 MPa | 4.55 × 10^{+6} | - | - | - |

SK inlet port area | 0.2 mm^{2} | 0.3 mm^{2} | 0.6 mm^{2} | - |

5 MPa | 1.86 × 10^{+6} | 1.83 × 10^{+6} | 1.71 × 10^{+6} | - |

10 MPa | 2.69 × 10^{+6} | 2.58 × 10^{+6} | 2.46 × 10^{+6} | - |

20 MPa | 3.96 × 10^{+6} | 3.79 × 10^{+6} | 3.59 × 10^{+6} | - |

SK outlet port area | 0.4 mm^{2} | 0.5 mm^{2} | 0.8 mm^{2} | 1.2 mm^{2} |

5 MPa | 2.06 × 10^{+6} | 1.86 × 10^{+6} | 1.68 × 10^{+6} | 1.54 × 10^{+6} |

10 MPa | 2.95 × 10^{+6} | 2.69 × 10^{+6} | 2.41 × 10^{+6} | 2.18 × 10^{+6} |

15 MPa | 3.69 × 10^{+6} | 3.35 × 10^{+6} | 3.01 × 10^{+6} | 2.74 × 10^{+6} |

20 MPa | 4.34 × 10^{+6} | 3.96 × 10^{+6} | 3.53 × 10^{+6} | 3.22 × 10^{+6} |

25 MPa | 4.94 × 10^{+6} | 4.53 × 10^{+6} | 4.04 × 10^{+6} | 3.67 × 10^{+6} |

SDX V inlet port area | 4.6 mm^{2} | 6.5 mm^{2} | 9.4 mm^{2} | - |

5 MPa | 1.48 × 10^{+4} | 1.04 × 10^{+4} | 7.91 × 10^{+3} | - |

10 MPa | 1.62 × 10^{+4} | 1.35 × 10^{+4} | 1.10 × 10^{+4} | - |

20 MPa | 2.28 × 10^{+4} | 1.91 × 10^{+4} | 1.53 × 10^{+4} | - |

SDX V outlet port area | 2.4 mm^{2} | 2.7 mm^{2} | 3.0 mm^{2} | - |

5 MPa | 1.48 × 10^{+4} | 1.52 × 10^{+4} | 1.51 × 10^{+4} | - |

10 MPa | 1.62 × 10^{+4} | 1.73 × 10^{+4} | 1.84 × 10^{+4} | - |

20 MPa | 2.28 × 10^{+4} | 2.46 × 10^{+4} | 2.55 × 10^{+4} | - |

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**Figure 1.**Schematic representation of pressure-swirl atomizers with (

**a**) axial inlet with helical slots and (

**b**) tangential inlet. Reproduced with the permission from Walzel and Musemic [15] in Chemie Ingenieur Technik, published by John Wiley and Sons, 2011.

**Figure 2.**Features of the examined pressure-swirl nozzles. (

**a**) The SK with the nozzle body (1), the orifice insert (2), and a slotted core with axial inlet slots (3). (

**b**) The Mini SDX with the nozzle body (1), the outlet orifice insert (2), and a core with a single tangential inlet port (3).

**Figure 3.**The atomization rig (

**left**) with an open view of the spray booth (

**right**). The following components are highlighted: the spray booth (1), sampling window (2), flow meter (3), laser diffraction spectrometer (4), feed container (5), water container (6), three piston pump (7), spray lance (8), funnel and keg to collect the emulsion after atomization (9).

**Figure 4.**Discharge coefficients C

_{d}for different inlet areas of the Mini SDX, and for different inlet and outlet areas of the SK at atomization pressures from 5 to 25 MPa.

**Figure 5.**ODSD for an atomization pressure of 10 MPa (

**left**) and values of x

_{90,3}for different inlet areas of the Mini SDX for 5–25 MPa (

**right**).

**Figure 6.**Values of x

_{90,3}against different estimated shear rates (

**A**,

**C**,

**E**) and energy density (

**B**,

**D**,

**F**) for different inlet ports of the Mini SDX (

**A**,

**B**) and different inlet ports (

**C**,

**D**) as well as outlet orifices (

**E**,

**F**) of the SK.

**Figure 7.**Values of x

_{90,3}against different estimated shear rates (

**A**,

**C**) and energy density (

**B**,

**D**) for different inlet ports (

**A**,

**B**) and outlet orifices (

**C**,

**D**) of the SDX V.

**Table 1.**Part numbers and cross-sectional area of the inlet ports of the Mini SDX and SK, as well as the outlet orifice of the SK. The dimensions for all nozzle components were either taken from the nozzle specifications or measured in-house. The components written in bold letters were used where it is not further specified.

Mini SDX—Inlet Area | SK—Inlet Area | SK—Outlet Area | |||
---|---|---|---|---|---|

32933-4 | 0.6 mm^{2} | SKY MFP 16 | 0.2 mm^{2} | M 80 | 0.4 mm^{2} |

32933-1 | 1.1 mm^{2} | SKY MFP 20 | 0.3 mm^{2} | M 78 | 0.5 mm^{2} |

32933-2 | 1.5 mm^{2} | SKY MFP 17 | 0.6 mm^{2} | M 76 | 0.8 mm^{2} |

32933-3 | 2.0 mm^{2} | - | - | M 72 | 1.2 mm^{2} |

**Table 2.**Part numbers and cross-sectional area of the inlet and outlet ports of the SDX V nozzle. The components written in bold letters were used where it is not further specified.

Inlet Area | Outlet Area | ||
---|---|---|---|

SD | 4.6 mm^{2} | 70 | 2.4 mm^{2} |

SE | 6.5 mm^{2} | 74 | 2.7 mm^{2} |

SF | 9.4 mm^{2} | 78 | 3.0 mm^{2} |

**Table 3.**Values of key parameters for throughput characteristics at an atomization pressure of 10 MPa for different nozzle geometries.

Mini SDX Inlet Port Area/mm^{2} | 0.6 | 1.1 | 1.5 | 2.0 |
---|---|---|---|---|

$\mathrm{Spray}\mathrm{droplet}\mathrm{size}{x}_{\mathrm{90,3}}$/µm | 89.47 | 84.30 | 97.08 | 150.68 |

Volume flow rate Q_{L}/L·min^{−1} | 0.53 | 0.61 | 0.73 | 0.77 |

$\mathrm{Mean}\mathrm{liquid}\mathrm{velocity}\overline{u}$/m·s^{−1} | 123.28 | 131.01 | 142.35 | 146.09 |

Film thickness t/µm | 91.75 | 102.77 | 120.85 | 127.75 |

Discharge coefficient C_{d} | 0.53 | 0.60 | 0.72 | 0.76 |

SK inlet port area/mm^{2} | 0.2 | 0.3 | 0.6 | - |

$\mathrm{Spray}\mathrm{droplet}\mathrm{size}{x}_{\mathrm{90,3}}$/µm | 83.95 | 84.09 | 87.52 | - |

Volume flow rate Q_{L}/L·min^{−1} | 0.43 | 0.47 | 0.51 | - |

$\mathrm{Mean}\mathrm{liquid}\mathrm{velocity}\overline{u}$/m·s^{−1} | 105.30 | 106.92 | 108.94 | - |

Film thickness t/µm | 78.38 | 82.76 | 88.52 | - |

Discharge coefficient C_{d} | 0.43 | 0.46 | 0.50 | - |

SK outlet port area/mm^{2} | 0.4 | 0.5 | 0.8 | 1.2 |

$\mathrm{Spray}\mathrm{droplet}\mathrm{size}{x}_{\mathrm{90,3}}$/µm | 83.95 | 84.19 | 89.09 | 103.01 |

Volume flow rate Q_{L}/L·min^{−1} | 0.35 | 0.43 | 0.54 | 0.70 |

$\mathrm{Mean}\mathrm{liquid}\mathrm{velocity}\overline{u}$/m·s^{−1} | 107.84 | 105.30 | 99.68 | 100.18 |

Film thickness t/µm | 73.17 | 78.38 | 82.88 | 91.71 |

Discharge coefficient C_{d} | 0.48 | 0.43 | 0.34 | 0.31 |

**Table 4.**Values for coefficients of determination and estimated Ca

_{cr}for the fit to Equation (2), as well as coefficients of determination, slope C, and exponent b for the fit to Equation (4) for all pilot-scale nozzle geometries.

Mini SDX Inlet Port Area/mm^{2} | 0.6 | 1.1 | 1.5 | 2.0 |
---|---|---|---|---|

R^{2} Taboada et al. model [7] | 0.88 | 0.91 | 0.86 | - |

Estimated Ca_{cr} | 1.61 | 1.79 | 1.63 | - |

R^{2} Energy density model | 0.99 | 0.93 | 0.99 | - |

C | 1.54 × 10^{+7} | 1.73 × 10^{+7} | 2.47 × 10^{+7} | - |

b | 1.14 | 0.98 | 0.65 | - |

Reynolds number Re | 2019 | 2403 | 3070 | - |

SK inlet port area/mm^{2} | 0.2 | 0.3 | 0.6 | - |

R^{2} Taboada et al. model [7] | 0.87 | 0.91 | 0.83 | - |

Estimated Ca_{cr} | 1.25 | 1.07 | 1.05 | - |

R^{2} Energy density model | 1.00 | 0.99 | 0.99 | - |

C | 1.47 × 10^{+7} | 1.30 × 10^{+7} | 1.91 × 10^{+7} | - |

b | 1.17 | 1.11 | 1.23 | - |

Reynolds number Re | 1581 | 1720 | 1909 | - |

SK outlet port area/mm^{2} | 0.4 | 0.5 | 0.8 | 1.2 |

R^{2} Taboada et al. model [7] | 0.97 | 0.87 | 0.89 | 0.85 |

Estimated Ca_{cr} | 1.49 | 1.22 | 1.02 | 0.89 |

R^{2} Energy density model | 0.99 | 0.99 | 0.99 | 0.98 |

C | 1.02 × 10^{+7} | 1.41 × 10^{+7} | 1.21 × 10^{+7} | 1.31 × 10^{+7} |

b | 1.03 | 1.14 | 1.13 | 0.94 |

Reynolds number Re | 1554 | 1581 | 1524 | 1613 |

**Table 5.**Values for key parameters for throughput characteristics at 10 MPa for all industrial-scale nozzle geometries.

SDX V Inlet Port Area/mm^{2} | 4.6 | 6.5 | 9.4 |
---|---|---|---|

Volume flow rate/L·min^{−1} | 5.33 | 6.40 | 7.63 |

Mean liquid velocity/m·s^{−1} | 85.15 | 91.60 | 98.48 |

Film thickness/µm | 245.61 | 280.39 | 319.48 |

Discharge Coefficient | 0.27 | 0.32 | 0.39 |

SDX V outlet port area/mm^{2} | 2.4 | 2.7 | 3.0 |

Volume flow rate/L·min^{−1} | 5.33 | 5.72 | 6.08 |

Mean liquid velocity/m·s^{−1} | 85.15 | 83.51 | 82.34 |

Film thickness/µm | 245.61 | 252.84 | 257.52 |

Discharge Coefficient | 0.27 | 0.26 | 0.25 |

**Table 6.**Values for coefficients of determination and estimated Ca

_{cr}for the fit to Equation (2), as well as coefficients of determination, slope C, and exponent b for the fit to Equation (4) for all industrial-scale nozzle geometries.

SDX V Inlet Port Area/mm^{2} | 4.6 | 6.5 | 9.4 |
---|---|---|---|

R^{2} Taboada et al. model [7] | 0.87 | 0.92 | 0.56 |

Estimated Ca_{cr} | 0.36 | 0.50 | 0.60 |

Reynolds number Re | 4124 | 5064 | 6204 |

R^{2} Energy density model | 0.99 | 0.99 | 0.93 |

C | 1.38 × 10^{+6} | 3.35 × 10^{+5} | 6.21 × 10^{+2} |

b | 0.83 | 0.72 | 0.31 |

SDX V outlet port area/mm^{2} | 2.4 | 2.7 | 3.0 |

R^{2} Taboada et al. model [7] | 0.87 | 0.89 | 0.97 |

Estimated Ca_{cr} | 0.36 | 0.39 | 0.35 |

Reynolds number Re | 4124 | 4163 | 4181 |

R^{2} Energy density model | 0.99 | 0.99 | 0.99 |

C | 1.38 × 10^{+6} | 8.63 × 10^{+5} | 4.76 × 10^{+4} |

b | 0.83 | 0.79 | 0.61 |

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**MDPI and ACS Style**

Höhne, S.; Taboada, M.L.; Schröder, J.; Gomez, C.; Karbstein, H.P.; Gaukel, V.
Influence of Nozzle Geometry and Scale-Up on Oil Droplet Breakup in the Atomization Step during Spray Drying of Emulsions. *Fluids* **2024**, *9*, 70.
https://doi.org/10.3390/fluids9030070

**AMA Style**

Höhne S, Taboada ML, Schröder J, Gomez C, Karbstein HP, Gaukel V.
Influence of Nozzle Geometry and Scale-Up on Oil Droplet Breakup in the Atomization Step during Spray Drying of Emulsions. *Fluids*. 2024; 9(3):70.
https://doi.org/10.3390/fluids9030070

**Chicago/Turabian Style**

Höhne, Sebastian, Martha L. Taboada, Jewe Schröder, Carolina Gomez, Heike P. Karbstein, and Volker Gaukel.
2024. "Influence of Nozzle Geometry and Scale-Up on Oil Droplet Breakup in the Atomization Step during Spray Drying of Emulsions" *Fluids* 9, no. 3: 70.
https://doi.org/10.3390/fluids9030070