# Flow Analysis and Structural Optimization of Double-Chamber Parallel Flexible Valve Micropumps

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Simulation Methodology

#### 2.1. Principle of EWOD and Flow Domain

#### 2.2. Simulation Methodology

^{5}Pa, density is 850 kg/m

^{3}, length is 450 μm, width is 20 μm, inclined angle is 45°. The meshed geometry is shown in Figure 4.

#### 2.3. Validation and Grid Resolution

## 3. Results and Discussion

_{max}). The pumping volume (Q) is the cumulative volume of liquids at the micropump’s outlet, serving as an indicator of the pump’s transporting capacity, while the flow rate (q) is the measure of the volume of fluid transported by the micropump per unit of time [19]:

_{max}) mentioned later refers to the maximum pressure at the outlet compared to the pressure in the surrounding environment which is set to 0. P

_{max}indicates the potential energy that micropumps can achieve.

#### 3.1. Pumping Volume and Maximum Pressure

_{max}). As illustrated in Figure 7, the flow rate (q) at the outlet consistently maintains a positive value throughout the entire pumping cycle, albeit with some minor fluctuations. This steady flow contributes to a gradual increase in the pumping volume (Q), clearly demonstrating the micropump’s effectiveness in preventing significant backflow. Also, it is worth noting that the pumping volume at the outlet of the micropump fluctuates very little, and there is no sharp abrupt change.

#### 3.2. Internal Flow Field Analysis

_{1}B

_{2}section during the pumping process, while the microfluid in the A

_{1}A

_{2}section flows into the pump chamber concurrently. The extent of deformation in the flexible valve varies, leading to differing resistance levels for the microfluid. Consequently, more microfluid flows toward the B

_{2}end compared to the amount directed to the B

_{1}end. Similarly, more microfluid is extracted from the A

_{1}end than from the A

_{2}end. In Figure 9b, the microfluid within the pump chamber moves upwards as the KCL droplet ascends. During this phase, the microfluid flowing into the A

_{1}A

_{2}section from the pump chamber acts as a pumping flow, while the microfluid entering the pump chamber from the B

_{1}B

_{2}section serves as a supply. Under these conditions, the microfluid flowing towards the A

_{2}end from the pump chamber exceeds that directed to the A

_{1}end. Likewise, the microfluid flowing into the pump chamber from the B1 end surpasses that from the B

_{2}end.

#### 3.3. Flexible Valve Deformation

_{1}A

_{2}and B

_{1}B

_{2}sections experience discernible deformation, yet it is crucial to note that the degree of deformation in the flexible valve is somewhat limited. As a result, the disparity in resistance posed to the microfluid is relatively minor.

#### 3.4. Analysis of Velocity Distribution in the Micropump

_{ew}) of the KCL droplet during these moments. Consequently, when the electrowetting angle changes at 0.25 s and 0.35 s, the velocity at each end of the KCL droplet is significantly higher than in other regions. The KCL droplet’s motion primarily occurs within the pump chamber, which has a width of 300 μm that is narrower than the 500 μm width of the microchannel. This explains why the maximum velocity within the micropump is situated in the pump chamber for the rest of the time in Figure 11. Moreover, it is evident that the velocity at the inlet and outlet of the micropump is considerably lower than in other regions. This leads to the conclusion that the primary driver of the overall flow within the micropump is the result of the left and right internal circulation, along with the microfluid flow at the inlet and outlet of the micropump.

## 4. Optimization of the Parallel EWOD Flexible Valve Micropump

_{v}), the length of the flexible valve (L

_{V}) and the mechanical properties of flexible valves like the Young’s modulus (E) and the Poisson’s ratio (ν).

#### 4.1. Width of the Inlet and Outlet

_{max}) at 1 s for various widths of the micropump’s inlet and outlet. It is important to clarify that volume Q represents the accumulated pump volume within a 1 s interval. Notably, the micropump’s pumping volume demonstrates a continuous rise as the inlet and outlet widths increase. Conversely, the maximum pressure of the micropump exhibits a convex curve, with its lowest point occurring at a width of 700 μm. The trend is like the results of Ameri et al. [19], where the pumping volume increases with the increase in the maximum pressure for W > 700 μm.

_{4}to W

_{5}results in a notable shift in the position of the backflow, as indicated in Figure 17a. Vortices disappear, causing the backflow to relocate from the upper end of the outlet to the lower end. As a result, the microfluid flow near the outlet becomes smoother, with no vortices obstructing the microfluid’s passage. This is the underlying reason behind the increased flow rate of the micropump and the corresponding rise in backflow.

_{1}to W

_{4}, and conversely, it flows upward for widths ranging from W

_{5}to W

_{8}.

#### 4.2. Width of the Side Channel

#### 4.3. Influence of Microchannel Length on Micropump Performance

#### 4.4. Microchannel Fillet near the Inlet and Outlet

#### 4.5. Microchannel Angle

#### 4.6. Analysis of the Structural Parameters of the Flexible Valve

#### 4.6.1. Influence of the Placement Angle of the Flexible Valve

#### 4.6.2. Influence of the Width of the Flexible Valve

#### 4.6.3. Influence of the Length of the Flexible Valve

#### 4.6.4. Influence of the Material Properties of Flexible Valves

#### 4.7. Global Optimization of Structural Parameters

^{3}, the Young’s modulus is 5 × 10

^{5}Pa, and the Poisson’s ratio is 0.499.

^{3}(Figure 28a), which is approximately 3.5 times that of the original model. Additionally, the maximum pressure reaches 33.7513 Pa (Figure 28b), approximately 1.2 times that of the original model. As a result, the optimized micropump outperforms the original model in terms of both pumping volume and maximum pressure.

^{3}, with a voltage of 170 V [24]; Zeng et al.’ results are q = 318 mL/min, p = 4.05 kPa, and their structure size is 54 × 49 × 15 mm

^{3}, with a voltage of 130 V [25]).

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 6.**Interface sharpness by varying grid resolution, blue is KCL droplet, and red is silicon oil.

**Figure 9.**The flow field inside the micropump while the KCL droplet is moving down (

**a**) and up (

**b**) in the pump chamber. The gray line is a streamline, and the red arrow is flowing direction.

**Figure 10.**The magnified view of internal flow on the micropump inlet and outlet. The yellow dots indicate the core of the vortices at each time instant.

**Figure 11.**The magnified view of the internal flow and the corresponding deformation of the flexible valves, blue is upper wall and flexible valve, and green is bottom wall and flexible valve.

**Figure 16.**The pumping volume and the maximum pressure in the micropump at different widths of inlet and outlet.

**Figure 17.**The velocity distribution at different widths of the outlet, (

**a**) is X-direction, and (

**b**) is Y-direction.

**Figure 18.**The relationship of pumping volume and maximum pressure with different microchannel widths.

**Figure 19.**The vector velocity distribution at the outlet with different microchannel widths, (

**a**) is X-direction, and (

**b**) is Y-direction.

**Figure 20.**The relationship of pumping volume and maximum pressure with different microchannel lengths.

**Figure 22.**The vector velocity distribution at the outlet with a different fillet radius, (

**a**) is X-direction, and (

**b**) is Y-direction.

**Figure 23.**The relationship of pumping volume and maximum pressure with different microchannel angles.

**Figure 25.**The relationship of pumping volume and maximum pressure with different flexible valve angles.

**Figure 26.**The relationship of pumping volume and maximum pressure with different flexible valve width.

**Figure 27.**The relationship of pumping volume and maximum pressure with different flexible valve lengths.

**Figure 28.**The relationship of pumping volume and maximum pressure with different flexible valve material properties, (

**a**) the effect of flexible valve density on the performance of micropumps, (

**b**) the effect of flexible valve Young’s modulus on micropump performance, and (

**c**) the effect of flexible valve Poisson’s ratio on micropump performance.

**Figure 29.**The Pumping performance of in the optimized micropump, (

**a**) is the pumping volume and flow rate, (

**b**) is the maximum pressure.

Material | $\mathbf{Density}\mathbf{(}\mathbf{k}\mathbf{g}\mathbf{/}{\mathbf{m}}^{\mathbf{3}}\mathbf{)}$ | $\mathbf{Viscosity}(\mathbf{P}\mathbf{a}\xb7\mathbf{s})$ | $\mathbf{Tension}\mathbf{of}\mathbf{Contact}\mathbf{Surfaces}\mathbf{\left(}\mathbf{N}\mathbf{/}\mathbf{m}\mathbf{\right)}$ |
---|---|---|---|

KCL solution | 1000 | 0.87 $\times {10}^{-3}$ | 2 $\times {10}^{-2}$ |

Silicone oil | 1000 | 0.1 |

Items | W | H | L | R | β | α | W_{v} | Lv | E | ν |
---|---|---|---|---|---|---|---|---|---|---|

Value | 600 | 500 | 4000 | 0 | 79.61° | 45° | 20 | 450 | 3 × 10^{5} Pa | 0.499 |

Cases | ${\mathit{W}}_{\mathbf{1}}$ | ${\mathit{W}}_{\mathbf{2}}$ | ${\mathit{W}}_{\mathbf{3}}$ | ${\mathit{W}}_{\mathbf{4}}$ | ${\mathit{W}}_{\mathbf{5}}$ | ${\mathit{W}}_{\mathbf{6}}$ | ${\mathit{W}}_{\mathbf{7}}$ | ${\mathit{W}}_{\mathbf{8}}$ |
---|---|---|---|---|---|---|---|---|

Width ($\mathsf{\mu}\mathrm{m}$) | 300 | 400 | 500 | 600 | 700 | 800 | 900 | 1000 |

Cases | ${\mathit{H}}_{\mathbf{1}}$ | ${\mathit{H}}_{\mathbf{2}}$ | ${\mathit{H}}_{\mathbf{3}}$ | ${\mathit{H}}_{\mathbf{4}}$ | ${\mathit{H}}_{\mathbf{5}}$ | ${\mathit{H}}_{\mathbf{6}}$ | ${\mathit{H}}_{\mathbf{7}}$ |
---|---|---|---|---|---|---|---|

Width of Part I ($\mathsf{\mu}\mathrm{m}$) | 400 | 450 | 500 | 550 | 600 | 650 | 700 |

Width of Part II ($\mathsf{\mu}\mathrm{m}$) | 310 | 350 | 380 | 420 | 460 | 500 | 540 |

Cases | ${\mathit{L}}_{\mathbf{1}}$ | ${\mathit{L}}_{\mathbf{2}}$ | ${\mathit{L}}_{\mathbf{3}}$ | ${\mathit{L}}_{\mathbf{4}}$ | ${\mathit{L}}_{\mathbf{5}}$ | ${\mathit{L}}_{\mathbf{6}}$ | ${\mathit{L}}_{\mathbf{7}}$ |
---|---|---|---|---|---|---|---|

Length ($\mathsf{\mu}\mathrm{m}$) | 3600 | 3800 | 4000 | 4200 | 4400 | 4600 | 4800 |

Cases | ${\mathit{R}}_{\mathbf{1}}$ | ${\mathit{R}}_{\mathbf{2}}$ | ${\mathit{R}}_{\mathbf{3}}$ | ${\mathit{R}}_{\mathbf{4}}$ | ${\mathit{R}}_{\mathbf{5}}$ | ${\mathit{R}}_{\mathbf{6}}$ | ${\mathit{R}}_{\mathbf{7}}$ |
---|---|---|---|---|---|---|---|

Radius ($\mathsf{\mu}\mathrm{m}$) | 200 | 300 | 400 | 500 | 600 | 700 | 800 |

Cases | ${\mathit{\beta}}_{\mathbf{1}}$ | ${\mathit{\beta}}_{\mathbf{2}}$ | ${\mathit{\beta}}_{\mathbf{3}}$ | ${\mathit{\beta}}_{\mathbf{4}}$ | ${\mathit{\beta}}_{\mathbf{5}}$ | ${\mathit{\beta}}_{\mathbf{6}}$ | ${\mathit{\beta}}_{\mathbf{7}}$ |
---|---|---|---|---|---|---|---|

Angle ($\xb0$) | 65.32 | 69.56 | 74.29 | 79.61 | 85.59 | 92.34 | 99.94 |

Cases | ${\mathit{\alpha}}_{\mathbf{1}}$ | ${\mathit{\alpha}}_{\mathbf{2}}$ | ${\mathit{\alpha}}_{\mathbf{3}}$ | ${\mathit{\alpha}}_{\mathbf{4}}$ | ${\mathit{\alpha}}_{\mathbf{5}}$ | ${\mathit{\alpha}}_{\mathbf{6}}$ | ${\mathit{\alpha}}_{\mathbf{7}}$ |
---|---|---|---|---|---|---|---|

Angle ($\xb0$) | 35 | 40 | 45 | 50 | 55 | 60 | 65 |

Cases | ${\mathit{W}}_{\mathit{V}\mathbf{1}}$ | ${\mathit{W}}_{\mathit{V}\mathbf{2}}$ | ${\mathit{W}}_{\mathit{V}\mathbf{3}}$ | ${\mathit{W}}_{\mathit{V}\mathbf{4}}$ | ${\mathit{W}}_{\mathit{V}\mathbf{5}}$ | ${\mathit{W}}_{\mathit{V}\mathbf{6}}$ | ${\mathit{W}}_{\mathit{V}\mathbf{7}}$ |
---|---|---|---|---|---|---|---|

Width ($\mathsf{\mu}\mathrm{m}$) | 10 | 15 | 20 | 25 | 30 | 35 | 40 |

Cases | ${\mathit{L}}_{\mathit{V}\mathbf{1}}$ | ${\mathit{L}}_{\mathit{V}\mathbf{2}}$ | ${\mathit{L}}_{\mathit{V}\mathbf{3}}$ | ${\mathit{L}}_{\mathit{V}\mathbf{4}}$ | ${\mathit{L}}_{\mathit{V}\mathbf{5}}$ | ${\mathit{L}}_{\mathit{V}\mathbf{6}}$ |
---|---|---|---|---|---|---|

Length ($\mathsf{\mu}\mathrm{m}$) | 300 | 350 | 400 | 450 | 500 | 550 |

Cases | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

Density $\mathsf{\rho}$ (kg/${m}^{3}$) | 700 | 750 | 800 | 850 | 900 | 950 | 1000 |

Young’s modulus $E$ $(\mathrm{p}\mathrm{a}\xb7\mathrm{s})$ | ${2\times 10}^{5}$ | ${2.5\times 10}^{5}$ | ${3\times 10}^{5}$ | ${3.5\times 10}^{5}$ | ${4\times 10}^{5}$ | ${4.5\times 10}^{5}$ | ${5\times 10}^{5}$ |

Poisson’s ratio $v$ | 0.379 | 0.399 | 0.419 | 0.439 | 0.459 | 0.479 | 0.499 |

Cases | ${\mathit{W}}_{\mathbf{8}}$ | ${\mathit{H}}_{\mathbf{3}}$ | ${\mathit{L}}_{\mathbf{1}}$ | ${\mathit{R}}_{\mathbf{7}}$ | ${\mathit{\beta}}_{\mathbf{4}}$ | ${\mathit{\alpha}}_{\mathbf{5}}$ | ${\mathit{W}}_{\mathit{V}\mathbf{5}}$ | ${\mathit{L}}_{\mathit{V}\mathbf{3}}$ | ${\mathit{\rho}}_{\mathbf{4}}$ | ${\mathit{E}}_{\mathbf{7}}$ | ${\mathit{v}}_{\mathbf{7}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|

Valve | 1000 $\mathsf{\mu}\mathrm{m}$ | 500 $\mathsf{\mu}\mathrm{m},$380 $\mathsf{\mu}\mathrm{m}$ | 3600 $\mathsf{\mu}\mathrm{m}$ | 800 $\mathsf{\mu}\mathrm{m}$ | ${79.61}^{\xb0}$ | ${55}^{\xb0}$ | 25 $\mathsf{\mu}\mathrm{m}$ | 450 $\mathsf{\mu}\mathrm{m}$ | 850 kg/${\mathrm{m}}^{3}$ | 5 $\times {10}^{5}\mathrm{P}\mathrm{a}$ | 0.499 |

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## Share and Cite

**MDPI and ACS Style**

Jiang, F.; Wen, J.; Dong, T.
Flow Analysis and Structural Optimization of Double-Chamber Parallel Flexible Valve Micropumps. *ChemEngineering* **2023**, *7*, 111.
https://doi.org/10.3390/chemengineering7060111

**AMA Style**

Jiang F, Wen J, Dong T.
Flow Analysis and Structural Optimization of Double-Chamber Parallel Flexible Valve Micropumps. *ChemEngineering*. 2023; 7(6):111.
https://doi.org/10.3390/chemengineering7060111

**Chicago/Turabian Style**

Jiang, Fan, Jinfeng Wen, and Teng Dong.
2023. "Flow Analysis and Structural Optimization of Double-Chamber Parallel Flexible Valve Micropumps" *ChemEngineering* 7, no. 6: 111.
https://doi.org/10.3390/chemengineering7060111