# Laser-Inscribed Glass Microfluidic Device for Non-Mixing Flow of Miscible Solvents

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Methods

#### 2.2. Materials

## 3. Results

#### 3.1. Data Analysis

#### 3.2. Preliminary Considerations

^{3}and μ = 1.2 mPa·s. For Rhodamine 6G, D = 3 × 10

^{−}

^{10}m

^{2}/s [22]. The characteristic length of the rectangular channel was calculated to be 1.33 × 10

^{−4}m for h = 100 μm and 2.85 × 10

^{−4}m for h = 500 μm.

_{in}– P

_{out}) and the flow rate (Q) of pressure-driven flow [23]:

- cylindrical channel (tubings) with length L and internal radius r,$${R}_{\mathrm{tubing}}=\frac{8\mu L}{\pi {r}^{4}}$$
- rectangular channel (glass chip) with length L, height h, and width w,$${R}_{\mathrm{chip}}=\frac{12\mu L}{1-0.63\left(\frac{h}{w}\right)}\xb7\frac{1}{{h}^{3}w}$$

^{11}mbar∙s/m

^{3}for r = 75 μm and L = 11.5 cm. Assuming that the pressure given by the pump is equal to $\Delta {P}_{\mathrm{total}}$, we can calculate the flow rate and subsequently, the flow velocity of the chips with different h and varying pumping pressures, as reported in Table 1.

#### 3.3. The Effect of Pumping Pressure

#### 3.4. The Effect of Angle Between Inlets

#### 3.5. The Effect of Chamber Height

^{2}for the 100 μm high chamber and 1 mm

^{2}for the 500 μm.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Microfluidic chip geometry; image from optical microscope of the chip after (

**a**) femtosecond (fs) laser irradiation and subsequent; (

**b**) chemical etching; (

**c**) schematic of chip design, where h is the chamber height and θ is the separation angle.

**Figure 2.**Visual analysis technique of laser-fabricated microfluidic chip: (

**a**) reference image, (

**b**) colored image with the flowing dye solution; (

**c**) negative image obtained by subtracting (

**a**) from (

**b**). The red dashed line indicates the output of the chip position chosen to extract the intensity profile. Scale bar corresponds to 200 μm.

**Figure 3.**Intensity profile of the flow behavior processed with MATLAB algorithm. The x-axis represents the position in the image [pixels], while the y-axis is the fluorescence intensity in arbitrary units (a.u.). The red region indicates the diffusion zone between the two liquids. (

**a**) original, (

**b**) processed by a low-pass filter, and (

**c**) normalized intensity profile. The slope of the red line represents the diffusion behavior.

**Figure 4.**Diffusion behavior inside a microfluidic chip with 30° incident angle and h = 500 μm, at increasing pumping pressure (

**a**) ΔP = 25 mbar; (

**b**) ΔP = 75 mbar; (

**c**) ΔP = 200 mbar. Scale bars correspond to 500 μm. Arrow indicates the flow direction.

**Figure 5.**Slope of the linear interpolation of the intensity profile of the visual diffusion analysis (see Figure 3c) in the chip as a function of the pair inlet pressure at the different separation angles θ = 30°, 60°, and 80°.

**Figure 6.**Theoretical and experimental slope of the intensity profile in the diffusion region versus the pumping pressure for two different chamber heights: 100 μm and 500 μm.

**Table 1.**Calculated flow rates, velocities, Reynolds number (Re), and Peclet number (Pe) for different pumping pressures. ${\overline{\upsilon}}_{1}\mathrm{and}{\overline{\upsilon}}_{2}$ correspond to the flow velocity of glass chips with heights of 100 μm and 500 μm, respectively.

ΔP (mbar) | Q (μL/min) | ${\overline{\mathit{\upsilon}}}_{1}(\mathbf{mm}/\mathbf{s})$ | ${\overline{\mathit{\upsilon}}}_{2}(\mathbf{mm}/\mathbf{s})$ | Re | Pe |
---|---|---|---|---|---|

25 | 13.5 | 22.5 | 4.5 | 2 | 7507.5 |

50 | 27.0 | 45.0 | 9.0 | 3 | 15,015.0 |

100 | 54.1 | 90.0 | 18.0 | 6 | 30,030.0 |

200 | 108.1 | 180.0 | 36.0 | 12 | 60,060.0 |

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**MDPI and ACS Style**

Italia, V.; Giakoumaki, A.N.; Bonfadini, S.; Bharadwaj, V.; Le Phu, T.; Eaton, S.M.; Ramponi, R.; Bergamini, G.; Lanzani, G.; Criante, L.
Laser-Inscribed Glass Microfluidic Device for Non-Mixing Flow of Miscible Solvents. *Micromachines* **2019**, *10*, 23.
https://doi.org/10.3390/mi10010023

**AMA Style**

Italia V, Giakoumaki AN, Bonfadini S, Bharadwaj V, Le Phu T, Eaton SM, Ramponi R, Bergamini G, Lanzani G, Criante L.
Laser-Inscribed Glass Microfluidic Device for Non-Mixing Flow of Miscible Solvents. *Micromachines*. 2019; 10(1):23.
https://doi.org/10.3390/mi10010023

**Chicago/Turabian Style**

Italia, Valeria, Argyro N. Giakoumaki, Silvio Bonfadini, Vibhav Bharadwaj, Thien Le Phu, Shane M. Eaton, Roberta Ramponi, Giacomo Bergamini, Guglielmo Lanzani, and Luigino Criante.
2019. "Laser-Inscribed Glass Microfluidic Device for Non-Mixing Flow of Miscible Solvents" *Micromachines* 10, no. 1: 23.
https://doi.org/10.3390/mi10010023