# Microstructure Adjustment of Spherical Micro-samples for High-Throughput Analysis Using a Drop-on-Demand Droplet Generator

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

#### 1.1. Droplet Motion

^{2}equal to that of the original correlation.

#### 1.2. Heat Transfer of a Sphere

#### 1.3. Experimental Generation and Analyses of Molten Metal Droplets

## 2. Materials and Methods

#### 2.1. Experimental Setup

#### 2.2. High Speed Imaging Analysis

#### 2.3. Microstructural Parameters

#### 2.4. Droplet Cooling Model

## 3. Results

#### 3.1. Initial Velocity

#### 3.2. Secondary Dendrite Arm Spacing and Experimentally Determined Cooling Rate

^{−1}for CuSn6 and from 80 to 100 Ks

^{−1}for AlCu4.5. This allowed us to compare data in a wide range of cooling rates at different temperature levels with the predictions from the cooling rate model.

#### 3.3. Modeling of Evolution of Particle Temperature and Velocity over Falling Distance/Time

_{p}= 800 µm). The cooling rate was calculated with an initial velocity of 0.2 ms

^{−1}and a superheat temperature of 100 K. The particles fell all along the tower and therefore had a maximum falling distance of 6.5 m. Inspection of the figure indicates that the CuSn6 droplets accelerate and fall faster due to the higher density and achieve a higher terminal velocity. Consequently, the velocity of the CuSn6 droplet still rises strongly, while the AlCu4.5 particle velocity slowly merges into the plateau. Accordingly, the fall time with CuSn6 was approximately 0.2 s shorter. The thermal history clearly showed the solidification between liquidus and solidus temperature. For both alloys, the solidification time was similar. While latent heat of AlCu4.5 was about double that of CuSn6 and its specific heat was almost three times higher than that of CuSn6, its density was about 3.5 times lower and the temperature level during solidification was much lower. This leads to a decreased driving temperature difference for both convection and radiation and a lower convective heat transfer coefficient due to changes in gas properties with temperature. Since droplet velocities were higher for CuSn6, their solidification distance was slightly lower.

#### 3.4. Comparison of Experimental and Modeling Data

## 4. Discussion

^{−1}for AlCu4.5 and 1.5 ms

^{−1}for CuSn6 (according to average velocities from Figure 4), and a melt superheat of 100 K. Based on these parameters, we determined the percental change in the cooling rate for AlCu4.5 and CuSn6 for individually varied parameters.

_{0}) affected the cooling rate by 2% for AlCu4.5 and 5% for CuSn6. This is because CuSn6 droplets have a much higher terminal velocity due to their higher density, while relative changes have less effect for AlCu4.5 particles which are slower. The convective heat transfer coefficient was not strongly affected by such small velocity changes. The same percental changes in melt superheat led to a change in the cooling rate of 2% for both alloys. Here, the effect is that for an increased melt superheat, solidification will start after the droplets have accelerated to a higher velocity, which again slightly increases the convective heat transfer coefficient.

## 5. Conclusions

^{−1}for AlCu4.5 and CuSn6. The validated model can be used for calculating the cooling rate of many other alloys in the melting ranges up to 1600 °C. Together with high reproducible droplet generation and individual droplet cooling, we developed a method to obtain fundamental data regarding the dependency of microstructure on the cooling rate of novel materials. Regarding the application of drop-on-demand droplet generation and solidification as a synthesis process for high-throughput methods, we showed that droplet diameter coupled with its initial velocity were the most influential parameters on the resulting microstructure. High reproducibility in droplet formation is the strength of droplet generators. We therefore conclude that this process is a versatile tool to produce thousands of samples in a short time from various alloys for analyses in high-throughput methods.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Greek Symbols | |

λ | Thermal conductivity of the fluid, W m^{−1} K^{−1} |

λ_{0} | Constant for determining the cooling rate using SDAS |

ρ_{F} | Density of the fluid, kg/m^{3} |

ρ_{P} | Density of the particle, kg/m^{3} |

Roman Symbols | |

A_{P} | Particle surface, m^{2} |

c_{P} | Heat capacity of the particle, J kg^{−1} K^{−1} |

d_{P} | Particle diameter, m |

F_{b} | Buoyancy force, N |

F_{g} | Weight force, N |

F_{i} | Inertia force, N |

F_{D} | Drag force, N |

g | Gravitational acceleration, m s^{−2} |

m_{P} | Mass of the particle, kg |

t | Time, s |

T_{F} | Fluid temperature, K |

T_{L} | Liquidus temperature, K |

T_{M} | Melt temperature, K |

T_{s} | Surface temperature, K |

T_{film} | Film temperature, K |

v | Velocity, m s^{−1} |

Non-dimensional numbers | |

$Nu=\frac{hd}{k}$ | Nusselt number |

Nu_{F} | Nusselt number at film temperature |

$Pr=\frac{\eta {c}_{p}}{\lambda}$ | Prandtl number |

Pr_{F} | Prandtl number at film temperature |

Pr_{∞} | Prandtl number at ambient temperature |

$Re=\frac{ud\rho}{\eta}$ | Reynolds number |

Re_{F} | Reynolds number at film temperature |

c_{D} | Drag coefficient |

n | Constant for determining the cooling rate using SDAS |

n_{arms} | Number of secondary dendrite arms |

Abbreviations: | |

fps | Frames per second |

SDAS | Average secondary dendrite arm spacing, µm |

CR | Cooling rate |

## Appendix A. Overview of Material Properties and Experimental Parameters During the Droplet Generation

Alloy | Specific Heat Capacity (J/gK) | Latent Heat (J/kg) | Density (g/cm^{3}) | Liquidus Temperature (°C) | Solidus Temperature (°C) |
---|---|---|---|---|---|

AlCu4.5 | 1.148 | 381.774 | 2350 | 644.8 | 571 |

CuSn6 | 0.394 | 187.890 | 7948 | 1050 | 900 |

Droplet Diameter µm | Initial Velocity m s ^{−1} | Measured SDAS µm | Standard Deviation of SDAS µm | Cooling Rate from SDAS K s ^{−1} | Cooling Rate Prediction from Model K/s | SDAS Prediction from Model µm |
---|---|---|---|---|---|---|

560 | 0.638 | 5.31 | 0.44 | 313.7 | 330.6 | 5.22 |

559 | 0.614 | 5.15 | 0.4 | 344.9 | 331.3 | 5.22 |

504 | 0.848 | 5.01 | 0.31 | 375.6 | 386.4 | 4.96 |

456 | 2.272 | 4.71 | 0.16 | 454.7 | 484.2 | 4.62 |

606 | 2.271 | 5.29 | 0.33 | 317.4 | 321.6 | 5.27 |

509 | 0.522 | 5.11 | 0.33 | 353.3 | 374.2 | 5.02 |

480 | 2.025 | 4.81 | 0.46 | 426.1 | 442.8 | 4.75 |

Droplet Diameter µm | Initial Velocity m s ^{−1} | Measured SDAS µm | Standard Deviation of SDAS µm | Cooling Rate from SDAS K s ^{−1} | Cooling Rate Prediction from Model K/s | SDAS Prediction from Model µm |
---|---|---|---|---|---|---|

802 | 1.295 | 10.84 | 0.65 | 98.1 | 93.9 | 11.02 |

945 | 0.249 | 11.40 | 0.41 | 84.4 | 78.3 | 11.71 |

923 | 0.15 | 11.5 | 0.51 | 82.2 | 75.3 | 11.86 |

877 | 0.054 | 11.13 | 0.66 | 90.8 | 85.5 | 11.37 |

843 | 0.136 | 10.95 | 0.63 | 95.1 | 90.3 | 11.16 |

908 | 0.207 | 11.36 | 0.5 | 85.2 | 82.0 | 11.52 |

917 | 0.142 | 11.55 | 0.71 | 81.0 | 79.2 | 11.66 |

949 | 0.132 | 11.61 | 0.61 | 79.9 | 77.3 | 11.75 |

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**Figure 1.**Schematic view of the droplet generator consisting of a droplet generation unit and a tower with movable particle collectors.

**Figure 2.**(

**a**) Image from a high-speed sequence showing a CuSn6 droplet after detachment. (

**b**) The measured droplet trajectory from image analysis.

**Figure 3.**Polished and etched particle of AlCu4.5 at two different magnifications of 5× (left) and 10× (right). Particle diameter: 978 µm.

**Figure 4.**Measured initial velocities for both alloys. A minimum velocity is achieved at the change from ejection to jetting droplet formation mode.

**Figure 5.**(

**a**) Measured secondary dendrite arm spacing (SDAS) and (

**b**) the resulting cooling rate as a function of droplet diameter.

**Figure 6.**Evolution of particle temperature and velocity as a function of (

**a**) falling time and (

**b**) falling distance for a droplet diameter of 800 µm.

**Figure 7.**Comparison of the theoretical and experimental determination of (

**a**) cooling rate and (

**b**) secondary dendrite arm spacing.

**Figure 8.**Sensitivity of the cooling rate based on process parameters (initial velocity, melt superheat, and droplet diameter) for (

**a**) CuSn6 and (

**b**) AlCu4.5.

Alloy | Etchant | Etching Time (s) |
---|---|---|

AlCu4.5 | 10 g NaOH + 90 g H_{2}O | 40 |

CuSn6 | 10 g (NH_{4})_{2}S_{2}O_{8} + 100 g H_{2}O | 90 |

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**MDPI and ACS Style**

Imani Moqadam, S.; Mädler, L.; Ellendt, N.
Microstructure Adjustment of Spherical Micro-samples for High-Throughput Analysis Using a Drop-on-Demand Droplet Generator. *Materials* **2019**, *12*, 3769.
https://doi.org/10.3390/ma12223769

**AMA Style**

Imani Moqadam S, Mädler L, Ellendt N.
Microstructure Adjustment of Spherical Micro-samples for High-Throughput Analysis Using a Drop-on-Demand Droplet Generator. *Materials*. 2019; 12(22):3769.
https://doi.org/10.3390/ma12223769

**Chicago/Turabian Style**

Imani Moqadam, Saeedeh, Lutz Mädler, and Nils Ellendt.
2019. "Microstructure Adjustment of Spherical Micro-samples for High-Throughput Analysis Using a Drop-on-Demand Droplet Generator" *Materials* 12, no. 22: 3769.
https://doi.org/10.3390/ma12223769