Haiwang
Li
a,
Chaolong
Song
b,
Trung
Dung Luong
a,
Nam-Trung
Nguyen
*a and
Teck
Neng Wong
a
aSchool of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang, Avenue, Singapore 639798. E-mail: mntnguyen@ntu.edu.sg
bSchool of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371
First published on 24th May 2012
This paper numerically and experimentally investigates and demonstrates the design of an optofluidic in-plane bi-concave lens to perform both light focusing and diverging using the combined effect of pressure driven flow and electro-osmosis. The concave lens is formed in a rectangular chamber with a liquid core-liquid cladding (L2) configuration. Under constant flow rates, the performance of the lens can be controlled by an external electric field. The lens consists of a core stream (conducting fluid), cladding streams (non-conducing fluids), and auxiliary cladding streams (conducting fluids). In the focusing mode, the auxiliary cladding stream is introduced to sandwich the biconcave lens to prevent light rays from scattering at the rough chamber wall. In the diverging mode, the auxiliary cladding liquid has a new role as the low refractive-index cladding of the lens. In the experiments, the test devices were fabricated in polydimethylsiloxane (PDMS) using the standard soft lithography technique. Ethanol, cinnamaldehyde, and a mixture of 73.5% ethylene glycol and 26.5% ethanol work as the core stream, cladding streams and auxiliary cladding streams. In the numerical simulation, the electric force acts as a body force. The governing equations are solved by a finite volume method on a Cartesian fixed staggered grid. The evolution of the interface was captured by the level set method. The results show that the focal length in the focusing mode and the divergent angle of the light beam in the diverging mode can be tuned by adjusting the external electric field at fixed flow rates. The numerical results have a reasonable agreement with the experimental results.
Currently, most L2 lenses can only focus light along the optical axis. The single function of these micro-lenses cannot satisfy the requirement of fluorescence excitation and detection. Mao et al.19 designed a gradient refractive-index lens to swing a focused light beam, based on the diffusion interface, between two miscible fluids. Song et al.2 reported a liquid-core liquid-cladding prism to continuously deflect light. Xiong et al.9 presented another prism to deflect light using only two laminar flow streams of different refractive indices. These works provided different ways of modifying the in-plane light, by which the area out of the optical axis can also be selectively illuminated, thus exciting the local fluorescent sample. Song et al.8 integrated the focusing and diverging function into a single bi-concave lens, where the focal length or the divergent angle of the light beam can be tuned by adjusting the flow rate ratio between core and cladding streams.
The light properties of focused length, location of light beam or divergent degree depend on the interfacial shape between the streams. The majority of previous micro optofluidic lenses tune the interfacial shape by adjusting flow rates.2,3,8,11,12,19 The results showed that the relationship between the interfacial shape and the flow rate ratio of the core stream and the cladding streams is a complex parabola.8 In order to achieve the ideal optical performance, the flow rate ratio has to be manually adjusted. Electro-osmosis is another popular actuating method in microfluidics for the control of the interfacial shape and location.21–25 When the electric field is used to adjust the interfacial shape, a direct relationship between the interfacial shape and the electric field can be established.4,26,27
This paper presents the design and demonstration of an optofluidic bi-concave lens that can tune a light beam from focused to divergent using the combined effect of pressure and electro-osmosis. The functions are achieved by adjusting the applied external electric field under fixed flow rates. This lens consists of a core stream, cladding streams and auxiliary cladding streams. These streams have various roles in both the focusing mode and the diverging mode. Fig. 1(a) schematically describes the focusing mode of the lens. In this mode, the core stream is a conducting fluid with a low refractive index, and the cladding streams are non-conducting fluids, each with a high refractive index. The flow rates of the core stream and cladding stream are kept constant throughout practical operation. The external electric field is added to the core stream. Following the concept reported by Song et al.,8 an auxiliary cladding stream with a very low flow rate and a refractive index matching that of PDMS can prevent the light beam from scattering. Although no external electric field is added to the auxiliary cladding stream, the auxiliary cladding streams are electrically conducting in order to tune the lens from focusing mode to diverging mode conveniently. The effect of the auxiliary cladding stream is negligible due to the low flow rate and refractive index. The light emitted from the optical fibre can be highly focused and the focal length can be tuned by adjusting the electric field applied to the conducting core stream. The diverging mode is described in Fig. 1(b). In the diverging mode, the roles of the streams are changed. Table 1 indicates these changes. The core stream in the focusing mode is blocked, the cladding streams in the focusing mode become the core stream, and the auxiliary cladding streams act as cladding streams. In the diverging mode, the core stream is non-conducting and the cladding streams are conducting, thus, the external electric field is applied to the cladding stream. The divergence of the light beam is achieved via the higher refractive index of the core stream and the tuneable lens interface. The expansion of the light beam can be adjusted by the external electric field.
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Fig. 1 Schematics: (a) bi-concave lens in the focusing mode. The light beam in the ray-tracing chamber propagates through the bi-concave lens in the focusing mode. The liquids for the core, cladding, and auxiliary cladding streams are ethanol, cinnamaldehyde, and the mixture of 73.5% ethylene glycol and 26.5% ethanol, respectively. The voltage applied to the core stream is −5000 V. (b) Bi-concave lens in the diverging mode. The light beam in the ray-tracing chamber propagates through the bi-concave lens in the diverging mode. The liquids for the core and cladding streams are cinnamaldehyde, and the mixture of 73.5% ethylene glycol and 26.5% ethanol, respectively. |
Liquids | Focusing | Diverging |
---|---|---|
Ethanol | Core stream | — |
Cinnamaldehyde | Cladding stream | Core stream |
Mixture of 73.5% ethylene glycol and 26.5% ethanol | Auxiliary cladding stream | Cladding stream |
Compared to the micro optofluidic lenses previously reported in the literature, our lens combines the functions of both focusing and diverging in a single design. In addition, the width of the light beam can be tuned across a larger range.
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Fig. 2 Numerical model of the lens: (a) domain calculated in numerical simulation, (b) velocity profile in the rectangular chamber for the diverging mode. The flow rates of the core and cladding streams are fixed at same value of 0.5 ml h−1. The voltage applied to the cladding stream is 5000 V. (c) Numerical ray-tracing results. The flow rates of the core and cladding streams are fixed at the same value of 0.5 ml h−1. The voltage applied to the core stream is −3000 V. |
E = −∇φ | (1) |
where ∇ is the del operator. In a dielectric medium, the electrical scalar potential φ is governed by:
∇ (ε∇φ) = 0 | (2) |
![]() | (3) |
The multi-phase microfluidic system can be described by the Navier–Stokes equation coupled with the electric force.
∇·(ρivv)−∇·[μi(∇v + ∇vT)] = −∇p + Eρe | (4) |
where ρi is the initial fluid density, v is the flow velocity, μi is the dynamic viscosity, and p is the pressure. Gravity is neglected in this model. An incompressible media is assumed:
∇·(ρiv) = 0 | (5) |
The jumps of the properties near the interface were smoothed with Heaviside function over the whole computational domain 28
![]() | (6) |
![]() | (7) |
Since the thickness of the microchannel (120 μm) is small compared to the other dimension (1 mm), the depth average method30 was used in this work to reduce the three-dimensional model to a two-dimensional model.
![]() | (8) |
v·∇θ = 0 | (9) |
A reinitialization procedure is employed to maintain the level set function as a signed distance function to the interface with some degree of accuracy
![]() | (10) |
ς(r,0) = θ(r) | (11) |
For numerical purposes, it is useful to smooth the signed function as
![]() | (12) |
(a) Guess the locations of the interfaces,
(b) Calculate the value of θ for all nodes for the interface,
(c) Calculate the properties for all nodes using eqn (6) and (7),
(d) Solve the distribution of electric potentials using eqn (1) and (2),
(e) Solve the continuity and momentum equations given by eqn (4) and (5) according the electric field and boundary conditions,
(f) Calculate the value of θ using eqn (9) according to the velocity distribution from step (5),
(g) Calculate the value of ζ according to eqn (10) and the solution of step (6),
(h) Set θ(r) = ζ(r) and
(i) Repeat steps (3)–(8) until the solution converges.
In the experiments, all liquids were kept in 10 ml glass syringes (10 ml gastight, Hamilton). The syringes were driven by syringe pumps (KDS230, KD Scientific Inc, USA, 0.2 μl h−1 to 500 l h−1, accuracy of 0.5%) to deliver the fixed flow rates. The greyscale images were captured using a sensitive CCD camera (HiSense MKII) attached to the microscope. A digital camera (DCRDVD803E, SONY) was used to record the colour images. Laser light (200 mW, 532 nm) was coupled into a multimode optical fibre (AFS105/125Y, THORLABS Inc) with a numerical aperture NA = 0.22. The optical fiber was inserted into a pre-fabricated microchannel with a width of 130 mm to act as a point light source. Stainless steel tips (EFD, 5123PC-B, USA) were used to connect the inlet port and hard Teflon tubing. The inner and outer surfaces of the tips were covered with polytetrafluoroethylene. Platinum wires (Sigma-Aldrich, 0.1 mm diameter) were used as electrodes. The electric fields were provided by a high voltage DC power supply (Model PS350, Stanford Research System, Inc).
In the focusing mode, the core stream is ethanol (n = 1.36; μ = 1.2 × 10−3 N s m−2). In order to add the electric field to ethanol, NaCl was diluted in ethanol with a concentration of 7 × 10−4 M. The cladding stream is cinnamaldehyde (n = 1.62; μ = 5.7 × 10−3 N s m−2). The auxiliary cladding stream is a mixture of 73.5% ethylene glycol and 26.5% ethanol (n = 1.412; μ = 9.8 × 10−3 N s m−2). This mixture has the same refractive index as PDMS (n = 1.412). Similar to ethanol, NaCl was diluted in ethanol with a concentration of 7 × 10−4 M. During the experiments, the flow rates of the core stream and cladding stream were fixed at 0.5 ml h−1 and the flow rate of the auxiliary cladding stream was fixed at 0.05 ml h−1. To tune the lens curvature, an electric field was applied to the core stream. In the diverging mode, the core flow was stopped to allow cinnamaldehyde from the cladding inlets to become the new core stream, therefore changing the role of the auxiliary cladding liquid from light-scattering prevention to providing an alternative refractive index for the refraction of the light rays. In this mode, the flow rates of two streams were fixed at 0.5 ml h−1, and an electric field was added to the new cladding stream. A mixture of 73.5% ethylene glycol and 26.5% ethanol (n = 1.412) with fluorescence dye Rhodamine B (Sigma Aldrich, excitation wavelength 540 nm, emission wavelength 625 nm, 1 g L−1) was pumped into the ray-tracing chamber to visualize the light rays refracted by the concave lens.
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Fig. 3 The interfacial shape of the micro optofluidic bi-concave lens in focusing mode at different electric fields and fixed flow rates. The flow rates of the core stream and the cladding stream are all 0.5 ml h−1: (a) −5000 V; (b) −4000 V; (c) −3000 V; (d) 0 V. |
The optical performance of the optofluidic concave lens in the focusing mode was carried out experimentally and numerically using the ray-tracing method. Fig. 4 shows the experimental ray-tracing results for the focusing mode under various electric fields in the cladding streams and fixed flow rates of core fluid and cladding fluids. In the experiment, the fluorescence dye in the ray-tracing chamber is excited by the green laser from a fibre with a wavelength of 532 nm and recorded as a grayscale image. In the numerical simulation, a custom Matlab program based on Snell's law8 was implemented to trace the ray. Due to the refractive index of the core liquid (ethanol, n = 1.36) being lower than that of the cladding liquid (cinnamaldehyde, n = 1.62), the optofluidic concave lens possesses a light focusing effect. In order to measure the focal length of the optofluidic concave lens, the grayscale images of the light rays in the ray-tracing chamber were captured. The flow rates of the cladding stream and the core stream are fixed at 0.5 ml h−1.
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Fig. 4 The experimental ray-tracing results for focusing mode under various electric fields in the cladding streams and fixed flow rates of core fluid and cladding fluids: (a) 0 V; (b) −2000 V; (c) −5000 V. |
Fig. 5(a) shows the manipulation of the lens interface by adjusting the electric field added to the core stream under the fixed flow rates for the focusing mode of the optofluidic bi-concave lens. The error bars in Fig. 5 indicate the effect of flow fluctuation inside the lens chamber. In the experiments, the flow rates of the core stream and the cladding streams were fixed at 0.5 ml h−1, and the auxiliary cladding stream was fixed at 0.05 ml h−1. The voltage added to the core stream was varied from −5000 to 1000 V. When the voltage was 0 V, the core stream wass purely pressure driven. Under the same flow rates, the cladding stream (μ = 5.7 × 10−3 N s m−2) with high viscosity occupied a large part. The curvature of the interface between the core and the cladding stream was approximately 1.96 mm−1. If a negative electric field is applied to the core stream, the core stream flows slower and occupies a larger part of the channel. The curvature of the interface decreases. The effect of electro-osmosis becomes stronger with the increasing magnitude of the negative electric field. The curvature of the interface decreases with the increasing field magnitude. For the smooth curved interface, the curvature of the interface can be calculated according the radius of the interface using the relationship of κ = 1/R where R is the radius of interface. The curvature reduces to 1.62 mm−1 when V = 5000 V. A positive electric field drives the core stream flowing faster. The smaller core stream increases the curvature of the interface. The sensitivity of electro-osmosis becomes low under a highly positive electric field.
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Fig. 5 Focusing mode: (a) relationship between the external electric filed and the curvature of the interface under fixed flow rates in the focusing mode of the optofluidic bi-concave lens; (b) relationship between the external electric filed and the focal length under fixed flow rates in the focusing mode of the optofluidic bi-concave lens. The flow rates of core stream and cladding streams are fixed at 0.5 ml h−1. |
Fig. 5(b) shows the numerical and experimental focal length over a range of voltages with a fixed flow rate of 0.5 ml h−1. The intersection position of the rays and the optical axis is regarded here as the focal point. The focal point is calculated according the angular aperture of a light-ray in the image space. The results show that a negative electric field increases the focal length while a positive electric field decreases the focal length. Fig. 5 indicates that the numerical results have a good agreement with the experimental results.
Fig. 6 shows a series of lens interfaces on adjustment of the electric field applied to the cladding streams under a fixed flow rate of 0.5 ml h−1. Similar to the previous case of focusing, under a positive electric field, the positively charged ions within the cladding stream move and drag the cladding stream flow along the electric field. Thus, the cladding stream flows faster. Under the fixed flow rate, the cladding stream with the higher velocity will occupy a smaller part of channel. The core stream occupies a larger part of the channel and the curvature of the interface decreases. If a negative electric field is added to the cladding streams, the positive ions move and drag the cladding liquid to flow against the pressure. As a result, the cladding stream flows slower. Under the fixed flow rate, the cladding stream with the slower velocity occupies a larger part of the channel. The core fluid occupies a smaller part of the channel and the curvature of the interface increases. Fig. 6 clearly shows that the curvature of the interface at 4500 V is smaller than the curvature at 0 V.
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Fig. 6 The interfacial shape of the optofluidic bi-concave lens in diverging mode based on the different applied voltages and fixed flow rates. The flow rates of core stream and cladding stream are all 0.5 ml h−1: (a) 4500 V; (b) 4000 V; (c) 3000 V; (d) 0 V. |
In the diverging mode, the light beam from the optical fibre will expand because the refractive index of the core liquid is higher than that of the cladding stream. The similar experimental and numerical methods of ray-tracing are used in the focusing mode to investigate the optical performance of the diverging lens. The rays with an angular aperture in the image space were extracted from the recorded images. The divergent angle is the angle of the outer rays. Fig. 7 shows the experimental results with flow rates fixed at 0.5 ml h−1. The results show that the divergent angle can be altered using an electric field with a fixed flow rate. If the electric field is 0 V, the divergent angle is approximately 37.5°, Fig. 7(a). The divergent angle reduces to approximately 28° if the applied voltage increases to 5000 V, Fig. 7(b).
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Fig. 7 The experimental ray-tracing results for the diverging mode with an electric field in the cladding stream and a fixed flow rate of core fluid and cladding fluids: (a) 0 V; (b) 5000 V. |
Fig. 8(a) shows the relationship between the electric field and the curvature of the interface under fixed flow rates for the diverging mode. In the experiments, the flow rates of the core stream and the cladding streams are fixed at 0.5 ml h−1. The voltage applied on the cladding stream changes from −1000 to 5000 V. If the voltage is 0 V, the core and cladding streams are purely pressure driven. The curvature of the interface between the core and the cladding stream is approximately 1.9 mm−1. When a negative electric field is applied to the cladding stream, the stream becomes slower and occupies a larger part of the channel. Thus, the curvature of the interface increases. For instance, the curvature is 1.96 mm−1 at −1000 V. The curvature of the interface increases with the increasing negative electric field. In contrast, the positive electric field drives the cladding stream faster and decreases the curvature of the interface. For instance, the curvature is only about 1.57 mm−1 at 5000 V.
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Fig. 8 Diverging mode: (a) relationship between the external electric filed and the curvature of the interface under fixed flow rates in the diverging mode of the optofluidic bi-concave lens; (b) relationship between the external electric filed and the focal length under fixed flow rates in the diverging mode of the optofluidic bi-concave lens. The flow rates of core stream and cladding streams are fixed at 0.5 ml h−1. |
Fig. 8(b) shows a comparison between the experimental results and the numerical simulation of the divergent angle. The results were obtained when the flow rates of the core stream and the cladding streams were fixed at 0.5 ml h−1 and the voltage along the cladding stream changed from −1000 to 5000 V. If the positive electric field is very high, the curvature of the interface is small. The impact of the interface on the refraction of the light ray is small. Owing to the aperture, the opening angle of the light beam originating from the fibre is approximately 6°. The divergent angle then expands to 28° when the voltage reaches its highest value of 5000 V. The divergent angle increases monotonously as the positive electric field decreases, and reaches 38° at 1000 V.
The radiant flux and the size of the illumination area can be controlled using the lens in diverging mode by adjusting the electric field. Moreover, this tuneable diverging lens may be useful for the correction of spherical aberration in optofluidic lens systems.
Footnote |
† Published as part of a themed issue on optofluidics. |
This journal is © The Royal Society of Chemistry 2012 |