# Experiments on Liquid Flow through Non-Circular Micro-Orifices

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{3}/s and 1.1–11.1 cm

^{3}/s spans) that were calibrated end-to-end online prior to the tests (accuracy within ±1%). The water temperature inside the autoclave was measured (to within ±1 K) using direct immersion type-J thermocouples (not shown in Figure 2).

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## References

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**Figure 2.**Schematic representation of the flow loop (

**left**) and 3D representation and drawing of the flow cell test section (

**right**).

**Figure 4.**Dimensionless pressure drop as a function of Reynolds number for the micro-orifices tested.

**Figure 5.**(

**a**) Dimensionless pressure drop as a function of Reynolds number for the micro-orifices tested in this study and from the literature; (

**b**) parity plot of measured dimensionless pressure drop vs. prediction of Equation (3) (the dashed lines are ±30% bounds).

Reference | ${\mathit{d}}_{\mathit{h}\mathit{y}\mathit{d}}\left(\mathsf{\mu}\mathbf{m}\right)$ | ${\mathit{d}}_{\mathit{h}\mathit{y}\mathit{d}}/\mathit{D}$ | $\mathit{t}/{\mathit{d}}_{\mathit{h}\mathit{y}\mathit{d}}$ | Fluid | Reynolds | Cross-Section |
---|---|---|---|---|---|---|

Johansen [26] | 704; 1634 | 0.09; 0.209 | 0.083 | Oil | 0.1–150 | Circular |

Kojasoy et al. [27] | 1000; 2000 | 0.057; 0.114 | 1.0; 2.0 | R113 | 560–14,000 | Circular |

Wang et al. [28] | 150; 370 | NA | NA | Water | 800–4500 | Square |

Mishra and Peles [29] | 11.5 | 0.114 | 1.7 | Water | 160–550 | Square |

Phares et al. [30] | 81.7–59.2 | 0.008–0.016 | 2.65–5.16 | Water | 2.5–120 | Circular |

Tu et al. [31] | 31.0; 52.0 | 0.007; 0.012 | 2.5; 4.2 | R134a | 1600–6500 | Circular |

Ushida et al. [32] | 100; 400 | NA | 0.05; 0.2 | Water | 1.3–1300 | Circular |

Cioncolini et al. [33] | 150–600 | 0.015–0.06 | 1.87–6.93 | Water | 6000–26,000 | Circular |

Cioncolini et al. [34] | 300; 600 | 0.0306; 0.0612 | 1.67; 3.33 | Water | 18,000–220,000 | Circular |

Szolcek et al. [35] | 200 | 0.02 | 4.25–27.0 | Water | 5–4500 | Circular |

Cioncolini et al. [36] | 150; 300 | 0.015–0.03 | 3.53–6.93 | Water | 3425–30,043 | Circular |

This study | 326–510 | 0.05–0.08 | 2.29–3.62 | Water | 5883–212,030 | Square Rectangular |

Sample No. | ${\mathit{P}}_{\mathit{w}\mathit{e}\mathit{t}}\left(\mathsf{\mu}\mathbf{m}\right)$ | ${\mathit{A}}_{\mathit{f}\mathit{l}\mathit{o}\mathit{w}}\mathbf{\xb7}{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{\left(}\mathsf{\mu}{\mathbf{m}}^{2}\right)$ | ${\mathit{d}}_{\mathit{h}\mathit{y}\mathit{d}}\left(\mathsf{\mu}\mathbf{m}\right)$ | $\mathit{t}$ (mm) | $\mathit{t}/{\mathit{d}}_{\mathit{h}\mathit{y}\mathit{d}}$ | $\mathit{A}\mathit{R}{}^{\mathbf{a}}$ | Cross-Section |
---|---|---|---|---|---|---|---|

1 | 927 ± 40 | 68.3 ± 4.6 | 295 ± 24 | 1.05 ± 0.01 | 3.56 | NA | Circular |

2 | 1210 ± 40 | 98.6 ± 6.0 | 326 ± 23 | 1.18 ± 0.01 | 3.62 | 1.06 | Square |

3 | 1209 ± 40 | 99.7 ± 6.0 | 330 ± 23 | 1.19 ± 0.01 | 3.61 | 1.05 | Square |

4 | 1958 ± 40 | 249.6 ± 9.8 | 510 ± 23 | 1.17 ± 0.01 | 2.29 | 1.00 | Square |

5 | 1571 ± 40 | 153.7 ± 7.8 | 391 ± 22 | 1.16 ± 0.01 | 2.97 | 1.58 | Rectangular |

6 | 1586 ± 40 | 155.6 ± 7.9 | 392 ± 22 | 1.24 ± 0.01 | 3.16 | 1.58 | Rectangular |

7 | 1946 ± 40 | 209.1 ± 9.7 | 430 ± 22 | 1.06 ± 0.01 | 2.46 | 2.23 | Rectangular |

8 | 1993 ± 40 | 221.9 ± 9.9 | 445 ± 22 | 1.11 ± 0.01 | 2.49 | 2.26 | Rectangular |

^{a}Aspect ratio of the micro-orifice cross-section: ratio of the long side length to the short side length.

Property | 298 K | 503 K |
---|---|---|

$\rho $ (kg/m^{3}) | 1002 | 835.9 |

$\mu $ (µPa s) | 891.6 | 118.7 |

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**MDPI and ACS Style**

Cassineri, S.; Cioncolini, A.; Smith, L.; Curioni, M.; Scenini, F.
Experiments on Liquid Flow through Non-Circular Micro-Orifices. *Micromachines* **2020**, *11*, 510.
https://doi.org/10.3390/mi11050510

**AMA Style**

Cassineri S, Cioncolini A, Smith L, Curioni M, Scenini F.
Experiments on Liquid Flow through Non-Circular Micro-Orifices. *Micromachines*. 2020; 11(5):510.
https://doi.org/10.3390/mi11050510

**Chicago/Turabian Style**

Cassineri, Stefano, Andrea Cioncolini, Liam Smith, Michele Curioni, and Fabio Scenini.
2020. "Experiments on Liquid Flow through Non-Circular Micro-Orifices" *Micromachines* 11, no. 5: 510.
https://doi.org/10.3390/mi11050510