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S. Y. Lee^{a},
D. Wee^{a},
J. R. Youn*^{a} and
Y. S. Song*^{b}
^{a}Research Institute of Advanced Materials (RIAM), Department of Materials Science and Engineering, Seoul National University, Seoul 08826, Korea. E-mail: jaeryoun@snu.ac.kr
^{b}Department of Fiber System Engineering, Dankook University, Gyeonggi-do 16890, Korea. E-mail: ysong@dankook.ac.kr

Received
29th April 2017
, Accepted 11th July 2017

First published on 19th July 2017

An optofluidic microlens was investigated in this study by using a gas–liquid interface, and the underlying physics of the microlens formation was exploited by considering fluid parameters that control the shape of the microlens. A microfluidic device was designed and fabricated to secure a stable multiphasic interface in the channel. A theoretical model based on the coupled Stokes–Cahn–Hilliard equations was proposed to understand the characteristics of the lens formation in the device. The results show that nonlinear flow behavior near the gas–liquid interface affects the interface shape due to the effect of surface tension, and the extent of the lens symmetry is inversely proportional to the product of the capillary number (Ca) and Reynolds number (Re).

In this letter, a tunable optofluidic microlens that utilizes the gas–liquid flow in a symmetric expansion chamber is reported. The characteristics of the lens are analyzed by controlling the inlet pressures of the liquid flow and gas flow. Moreover, numerical and theoretical analyses are conducted to figure out the formation mechanism of asymmetric and symmetric lens surfaces and relevant physics governing the interface formation. For the theoretical model, the Stokes–Cahn–Hilliard equation is non-dimensionalized, and material and operational parameters, such as the average flow rate (u_{avg}), dynamic viscosity (μ), density (ρ), surface tension coefficient (σ), and characteristic length (L), are analyzed based on the theoretical evaluation. In addition, the lens characteristics such as the lens curvature, thickness, and focal length in the microfluidic device are examined by performing optical observation and ray-tracing simulation. The schematic configuration of the microfluidic set-up is shown in Fig. 1.

0 = ∇·[−pI + μ(∇u + (∇u)^{T}] + F_{st}
| (1) |

F_{st} = G∇ϕ
| (2) |

(3) |

(4) |

(5) |

ψ = −∇·ε^{2}∇ϕ + (ϕ^{2} − 1)ϕ
| (6) |

(7) |

(8) |

Material | Property | |||
---|---|---|---|---|

Dynamic viscosity (μ, × 10^{−3} Pa s) |
Density (ρ, kg m^{−2}) |
Surface tension (σ, mN m^{−1}) |
Refractive index (n) | |

N_{2} |
0.01747 | 1.2754 | — | 1.0003 |

IPA | 1.96 | 786 | 23 | 1.3776 |

BA | 5.474 | 1044 | 39 | 1.5396 |

EG | 16.2 | 1110 | 47 | 1.43 |

PDMS | — | — | — | 1.4 |

Fig. 3 (a) Measured average velocities, (b) Reynolds numbers, (c) capillary numbers, and (d) product values of capillary numbers and Reynolds numbers for three liquids with respect to pressures. |

The enhancement factor, defined as the ratio of the peak intensity of a focused beam (B′) to the intensity of an unfocused beam (B), is measured to be 4.07.^{6} The characteristics of the optofluidic lens obtained from the experimental and numerical results are illustrated in Fig. 5. The curvature (1/R) and the lens thickness (t) were determined by fitting a circle to the gas–liquid interface acquired from the experiment and simulation. The curvature has a maximum value at P_{main} = 24 kPa, and then declines as the pressure increases because the lens interface approaches the wall of the expansion chamber at above 24 kPa (see Fig. S1† in the ESI).^{6,9} The experimental results showed that the tunable focal length between 1.60 mm and 3.15 mm could be manipulated in the microfluidic device fabricated in this study, as presented in Fig. 5(c). A ray-tracing code was developed based on MATLAB®, and the curvature and lens thickness obtained from the simulation results were employed to predict the focal length numerically (see Fig. S2† in the ESI). The overall trends of the experimental and simulation results were similar, but a slight discrepancy was observed in the case of the focal length at lower inlet pressure because aspherical microlens shape was obtained in the experiment unlike the spherical shape calculated in the simulation. The aspherical microlens leads to decrease in the refraction of light and then increase in the focal length (see Fig. S1 and S3† in the ESI).

Fig. 5 Comparison of the lens characteristics obtained from simulation and experimental results: (a) curvatures, (b) lens thickness, and (c) focal lengths as a function of the pressure of mainstream. |

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## Footnote |

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7ra04828a |

This journal is © The Royal Society of Chemistry 2017 |