# An Experimental Setup to Investigate Non-Newtonian Fluid Flow in Variable Aperture Channels

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## Abstract

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## 1. Introduction

## 2. Theory

## 3. Numerical Model

- the Reynolds number is sufficiently low, so that no recirculation regions are produced between asperities;
- the fracture is sufficiently smooth. The ratio between the standard deviation of the aperture, ${\sigma}^{\prime}$, and the shortest wavelength of the aperture variation, ${\lambda}_{min}$, must be below 1/5 (${\lambda}_{min}>5{\sigma}^{\prime}$).

## 4. Experiments

#### 4.1. Test Schedule

#### 4.2. Uncertainty Quantification

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Constant aperture fracture (i.e., smooth parallel plates). (

**a**) Fracture sketch with applied pressure gradient; (

**b**) fracture profile in the y direction.

**Figure 2.**Variable aperture fracture. (

**a**) Channels arrangement; (

**b**) boundary conditions; (

**c**) fracture profile in the y direction.

**Figure 3.**Experimental apparatus to reproduce a variable aperture fracture: (

**a**) overview; (

**b**) photo of the assembly during a preliminary test.

**Figure 4.**Experimental setup: (

**a**) distance between the two plates as a function of x; (

**b**) Q–Q plot: actual distribution of $ln\left(b\right)$ vs. Gaussian distribution.

**Figure 5.**Comparison between experiments, numerical model and theory. Experimental results (

**a**–

**e**) for Newtonian fluid, and (

**f**–

**h**) for non-Newtonian shear-thinning fluid. Filled symbols are the experimental data, empty symbols are the numerical model and curves are the theory. Dashed lines are the 95% confidence limits, error bars refer to two standard deviations. All the experimental parameters are listed in Table 1.

**Figure 6.**Percentage deviation difference between the experimental/numerical results and the theoretical values (

**a**) for Newtonian fluids, and (

**b**) for non-Newtonian shear-thinning fluids. Filled symbols refer to the experiments, empty symbols refer to the numerical model. Error bars refer to two standard deviations.

Exp. | n | $\mathit{\mu}$ $\mathbf{Pa}\phantom{\rule{0.166667em}{0ex}}{\mathbf{s}}^{\mathbf{n}}$ | $\mathbf{\Theta}$ ${}^{\mathbf{\circ}}\mathbf{C}$ | $\mathit{\rho}$ $\mathbf{g}\phantom{\rule{0.166667em}{0ex}}{\mathbf{cm}}^{\mathbf{-}\mathbf{1}}$ | |
---|---|---|---|---|---|

1 | 1 | 0.054 | 23 | 1206 | water-glyc |

2 | 1 | 0.075 | 24 | 1213 | water-glyc |

3 | 1 | 0.14 | 24 | 1232 | water–glyc |

4 | 1 | 0.20 | 27 | 1234 | water–glyc |

5 | 1 | 0.21 | 25 | 1234 | water–glyc |

6 | 0.14 | 6.6 | 27 | 1005 | water–Xanth |

7 | 0.32 | 0.84 | 25 | 1005 | water–Xanth |

8 | 0.46 | 0.85 | 24 | 1005 | water–carbomer |

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**MDPI and ACS Style**

Lenci, A.; Chiapponi, L.
An Experimental Setup to Investigate Non-Newtonian Fluid Flow in Variable Aperture Channels. *Water* **2020**, *12*, 1284.
https://doi.org/10.3390/w12051284

**AMA Style**

Lenci A, Chiapponi L.
An Experimental Setup to Investigate Non-Newtonian Fluid Flow in Variable Aperture Channels. *Water*. 2020; 12(5):1284.
https://doi.org/10.3390/w12051284

**Chicago/Turabian Style**

Lenci, Alessandro, and Luca Chiapponi.
2020. "An Experimental Setup to Investigate Non-Newtonian Fluid Flow in Variable Aperture Channels" *Water* 12, no. 5: 1284.
https://doi.org/10.3390/w12051284