# Experimental and Numerical Investigations on the Flow Characteristics within Hydrodynamic Entrance Regions in Microchannels

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Description

#### 2.1. Microchannel Fabrication

#### 2.2. Experimental Setup

#### 2.3. Experimental Uncertainty

^{th}of a seed particle image. The image diameter for a particle in the object plane can be estimated by

## 3. Experimental Results and Discussion

#### 3.1. Developing Velocity Profiles

#### 3.2. Velocity Development Along Centerline

#### 3.3. Correlations of Hydraulic Entrance Length

## 4. Numerical Simulation

#### 4.1. Investigation Method

#### 4.2. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Images of actual microchannels. (

**a**) Microchannels etched on silicon wafer. (

**b**) Microscope view of one of the microchannels (D

_{h}= 100 μm).

**Figure 4.**Image of particles and velocity vectors. (

**a**) Particles illuminated by laser. (

**b**) Velocity vectors in microchannel.

**Figure 5.**Profiles at different locations along the microchannel length in a 200 μm microchannel (Re = 20). (x/D

_{h}is the dimensionless distance away from the inlet).

**Figure 6.**Developing velocity profiles for the 100 μm channel at Re of (

**a**) 0.5, (

**b**) 5, (

**c**) 20, and (

**d**) 50.

**Figure 7.**Developing velocity profiles for the 150 μm channel at Re of (

**a**) 0.5, (

**b**) 5, (

**c**) 20, and (

**d**) 50.

**Figure 8.**Developing velocity profiles for the 200 μm channel at Re of (

**a**) 0.5, (

**b**) 5, (

**c**) 20, and (

**d**) 50.

**Figure 9.**Centerline velocity development for the 100 μm channel at Re of (

**a**) 0.5, (

**b**) 5, (

**c**) 20, and (

**d**) 50.

**Figure 10.**Centerline velocity development for the 150 μm channel at Re of (

**a**) 0.5, (

**b**) 5, (

**c**) 20, and (

**d**) 50.

**Figure 11.**Centerline velocity development for the 200 μm channel at Re of (

**a**) 0.5, (

**b**) 5, (

**c**) 20, and (

**d**) 50.

**Figure 12.**Dimensionless hydraulic entrance length comparison between experimental data and proposed correlations.

**Figure 13.**Dimensionless hydraulic entrance length comparison between experimental data and modified correlations.

**Figure 14.**Test-section microchannel inlet configuration of Ahmad et al. [31]: (

**a**) Isometric view of the microchannel entrance with the reservoir walls and (

**b**) separation zone at section A-A for the microchannel entrance due to the asymmetric vena contracta effect.

**Figure 16.**Comparison of entrance length from experiments and simulations for (

**a**) 100 μm, (

**b**) 150 μm, and (

**c**) 200 μm.

**Figure 17.**Comparison of developing velocity profiles near and downstream of the inlet for Model 1 and Model 2. (

**a**) Re = 0.5 for 100 μm, (

**b**) Re = 20 for 100 μm, (

**c**) Re = 0.5 for 150 μm, (

**d**) Re = 20 for 150 μm, (

**e**) Re = 0.5 for 200 μm, and (

**f**) Re = 20 for 200 μm.

**Figure 18.**Comparison of entrance length from experiments and simulations for (

**a**) 100 μm, (

**b**) 150 μm, and (

**c**) 200 μm.

**Figure 19.**Comparison of developing velocity profiles near and downstream the inlet for Model 1 and Model 3. (

**a**) Re = 0.5 for 100 μm, (

**b**) Re = 20 for 100 μm, (

**c**) Re = 0.5 for 150 μm, (

**d**) Re = 20 for 150 μm, (

**e**) Re = 0.5 for 200 μm, and (

**f**) Re = 20 for 200 μm.

Correlations | A | B | C |
---|---|---|---|

Atkinson et al. [19] | |||

Tube | 0.590 | 0.056 | – |

Parallel plates | 0.625 | 0.044 | – |

Chen [20] | |||

Tube | 0.600 | 0.035 | 0.056 |

Parallel plates | 0.630 | 0.035 | 0.044 |

**Table 2.**Conclusions of some previous experimental research on entrance region in microchannels with microscopic particle image velocimetry (micro-PIV).

Reference | Size of Microchannel | Range of Re Number | Conclusions |
---|---|---|---|

Zhang et al. [27] | 50–254 μm in diameter | $~{10}^{-5}\u2013{10}^{-2}$ | Velocity distribution measured by micro-PIV was in strong agreement with the value calculated by the Navier–Stokes equation. |

Lee et al. [28] | 690 μm in height 260 μm in width | $~$250–2100 | Fluid had been pre-developed in pipe before entering the microchannel, causing a shorter entrance length. |

Lee and Kim [29] | 58 μm in depth 100 μm in width | 1 | Entrance length for microchannels is much smaller compared with conventional channels. |

Hao et al. [30] | 237 μm in hydraulic diameter | $~$50–1200 | $\frac{{L}_{e}}{{D}_{h}}=0.08\u20130.09Re$ |

Ahmad and Hassan [31] | 100, 200, and 500 μm in hydraulic diameter | $~$0.5–200 | $\frac{{L}_{e}}{{D}_{h}}=\frac{0.6}{0.14Re+1}+0.0752Re$ |

Mesh No. | Nodes | Elements | $\Delta \mathit{p},\text{}\mathbf{Pa}$ | r | ε |
---|---|---|---|---|---|

1 | 1147384 | 1066770 | 2270.29 | - | - |

2 | 1582848 | 1485551 | 2269.04 | 1.39 | −0.059% |

3 | 2025528 | 1918673 | 2267.84 | 1.29 | −0.079% |

4 | 2518888 | 2401230 | 2266.97 | 1.25 | −0.068% |

5 | 3242004 | 3126872 | 2266.28 | 1.30 | −0.043% |

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**MDPI and ACS Style**

Li, H.; Huang, B.; Wu, M.
Experimental and Numerical Investigations on the Flow Characteristics within Hydrodynamic Entrance Regions in Microchannels. *Micromachines* **2019**, *10*, 317.
https://doi.org/10.3390/mi10050317

**AMA Style**

Li H, Huang B, Wu M.
Experimental and Numerical Investigations on the Flow Characteristics within Hydrodynamic Entrance Regions in Microchannels. *Micromachines*. 2019; 10(5):317.
https://doi.org/10.3390/mi10050317

**Chicago/Turabian Style**

Li, Haiwang, Binghuan Huang, and Min Wu.
2019. "Experimental and Numerical Investigations on the Flow Characteristics within Hydrodynamic Entrance Regions in Microchannels" *Micromachines* 10, no. 5: 317.
https://doi.org/10.3390/mi10050317