spectroscopic techniques
Characterization of Liquid-Core/Liquid-Cladding Optical Waveguides of a Sodium Chloride Solution/Water System by Computational Fluid Dynamics Junya Kamiyama,a Soto Asanuma,a Hiroyasu Murata,a Yasuhiko Sugii,b Hiroki Hotta,c Kiichi Sato,a Kin-ichi Tsunodaa,* a b c
Gunma University, Department of Chemistry and Chemical Biology, 1-5-1 Tenjin-cho, Kiryu 376-8515, Japan University of Tokyo, Department of Applied Chemistry, 7-3-1, Hongo, Bunkyo, Tokyo 113-8656, Japan Nara University of Education, Department of Chemistry, Takabatake, Nara 630-8528, Japan
A stable liquid/liquid optical waveguide (LLW) was formed using a sheath flow, where a 15% sodium chloride (NaCl) solution functioned as the core solution and water functioned as the cladding solution (15% NaCl/water LLW). The LLW was at least 200 mm in length. The concentration distributions of the liquid core and liquid cladding solutions in the LLW system were predicted by computational fluid dynamics (CFD) to validate the characteristics of the waveguide. The broadening of the region of the fluorescence of Rhodamine B excited by the guided light and the increase in the critical angle of the guided light with the increase in the contact time of the core and the cladding solutions were well explained by CFD calculations. However, no substantial leakage of the guided light was observed despite the considerably large change in the refractive index profile of the LLW; thus, a narrower and longer waveguide was realized. Index Headings: Liquid-core/liquid-cladding optical waveguide; Computational fluid dynamics; Sodium chloride solution; Critical angle; Far-field pattern.
INTRODUCTION Liquid/liquid optical waveguides (LLWs), which have a liquid-core/liquid-cladding structure, were first proposed by our group.1–5 Liquid/liquid optical waveguides have been formed using a sheath flow of liquids from concentric glass capillaries into an outer glass capillary. Both immiscible solvent systems (e.g., toluene/water and diethyl ether/water) and miscible solvent systems (e.g., tetrahydrofuran [THF]/water) can be used to form LLWs. We have been using these LLWs as new tools for studying liquid–liquid interfaces. A THF/water LLW system was used to observe an ion-pair extraction of 1-anilino-8-naphthalene sulfonate (ANS) and hexadecyltrimethylammonium ion (CTA) from the water phase to the THF phase.4 Moreover, a 50% ethanol/water LLW system was employed to observe the complexation reaction between aluminum(III) and lumogallion.5 In addition, the concept of LLW has recently been extended to microchip development by other researchers, and it has become one of the key elements in the new field of optofluidics, where it Received 3 April 2013; accepted 8 August 2013. * Author to whom correspondence should be sent. E-mail: tsunoda@ gunma-u.ac.jp. DOI: 10.1366/13-07096
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is used to manipulate light in microchips (e.g., as an optical switch and an evanescent coupler).6–11 In this work, an LLW that uses a 15% sodium chloride (NaCl) solution for the core solution and water for the cladding solution (15% NaCl/water LLW) was formed, and its characteristics were studied by means of computational fluid dynamics (CFD). The computational results were then compared with the experimental results.
EXPERIMENTAL Reagents. All the reagents, including NaCl and Rhodamine B (RhB), were purchased (Wako Pure Chemical Industries, Japan). All aqueous solutions were prepared using water purified by a Milli-QII system (Millipore, USA). Apparatus. The experimental setup for the LLW system is shown in Fig. 1. The inner capillary was a stainless capillary (internal diameter [ID] 0.13 mm, outer diameter [OD] 0.31 mm) with a tapered tip, whereas the outer capillary was a square glass capillary (inner side, 1.2 3 1.2 mm; outer side, 1.7 3 1.7 mm; length, 200 mm). The source light, a water-cooled Arþ laser (488 nm; Model 95, from Lexel Laser Inc., USA), was introduced into the inner flow through an optical fiber (ultraviolet [UV] metalcoated optical fiber, OD 70 lm; numerical aperture [N.A.], 0.2; A.R.T. Photonics, Germany). A 15% aqueous NaCl solution (core solution) was introduced into the inner capillary under pressure from a nitrogen cylinder, and pure water (cladding solution) was sent into the outer capillary using a gravity-driven method. When necessary, 1 lmol dm3 RhB was added to both the core and cladding solutions to avoid the effects of diffusion. The fluorescence of RhB was monitored using a microscope system (custom-made system; Olympus Co., Ltd., Japan) equipped with a charge-coupled device (CCD) camera (Ratiga 2000R; QImaging Co., Ltd., Canada) or a multichannel CCD detector (PMA-11; Hamamatsu Photonics Co., Ltd.,). The microscope system was moved manually along the long axis of the LLW. Measurement. Formation Conditions of the Stable 15% Sodium Chlorde/Water Liquid/Liquid Optical Waveguide. Because the cross section of the outer capillary was much
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FIG. 1. Experimental setup of the 15% NaCl solution/water LLW.
FIG. 2. Attenuation of RhB fluorescence with the increase in distance from the tip of the inner capillary (the starting point): dotted line, experimental results; solid line, calculation result. Rhodamine B (1 lmol dm3) was added to both core and cladding solutions. An average linear velocity of 2.0 cm s1 and a ratio of the average linear velocities of the inner flow and outer flow of 2.0 were used. For the calculation, only the absorption due to RhB was taken into account.
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larger than that of the inner capillary, the average linear velocity of the sheath flow was mainly determined by that of the cladding solution. When the average linear velocity of the sheath flow and the ratio of the average linear velocities of the inner flow and outer flow at the tip of the inner capillary were set at ;0.5–10 cm s1 and ;1.5–10 cm s1, respectively, a stable 15 % NaCl/water LLW was formed. In Fig. 2, the attenuation curve of the RhB fluorescence is compared with the calculated one, where only the attenuation of the guided light due to the absorption of RhB molecules was postulated. In this experiment, 1 lmol dm3 RhB was added to both the core and cladding solutions to avoid the change in the concentration of RhB in the core solution due to its diffusion to the cladding solution. As shown in this figure, the experimental and calculated curves coincided with each other very well. This result indicated that there was almost no other reason, except for the absorption of RhB, for the attenuation of the guided light. In other words, the leakage of the guided light from the LLW at 488 nm throughout the length of the LLW should be the minimum. Moreover, Fig. 3 reinforces this observation (as discussed later). Thus, an average linear velocity of 2.0 cm s1 and a ratio of the average linear velocities of the inner flow and the outer flow of 2.0 were used throughout the experiments, unless otherwise indicated.
FIG. 3. Dependence of the intensity of the guided light on the contact time. The average linear velocity was varied from 0.6 to 9.3 cm s1. The same experimental set-up as that of Fig. 8 (far-field experiment) was applied.
Computational Fluid Dynamics Simulation of the 15% Sodium Chloride/Water Liquid/Liquid Optical Waveguide. The waveguide structures of the LLW—the distribution of NaCl concentration (refractive index) and the velocity distribution of the flow in the LLW—were predicted using CFD. The CFD software, STAR-CD (CD-adapco, USA), which is based on a finite-volume method, was used. To describe the mixing of the core and cladding liquids, a threedimensional Navier–Stokes equation and a convection–diffusion equation based on Fick’s law with laminar flow under steady state were chosen. The physical data used in the calculation were diffusion coefficient of NaCl in water, 1.52 3 109 m2 s1; kinematic viscosity of water, 1.56 3 106 m2 s1; and Schmidt number, 416.5.12 The dimensions of the LLW used for the simulation were the same as those for the experiments, except that the outer capillary was cylindrical (ID 1.2 mm) and not square-shaped. Details of the calculation are shown in the Appendix.
RESULTS AND DISCUSSION Computational Fluid Dynamics Simulation of the Waveguide Structure of the Liquid/Liquid Optical Waveguide. Figure 4 shows the velocity distribution of the sheath flow calculated by the CFD simulation. The flow shown in Fig. 4a developed after the core and cladding flows merged, becoming the Hagen–Poiseuille flow, which is a theoretical solution for a laminar flow. In the downflow region from the tip of the inner capillary, defined as the starting point for Fig. 4b, the core fluid was observed to flow toward the outside and the cladding fluid was observed flow toward the inside; in addition, the x components of velocity gradually decreased to zero at about 2 mm from the starting point, signifying that fluid mixing occurred in the downflow region of the starting point. However, the shape of the tapered inner capillary suppressed the mixing to stabilize the waveguide. Figure 5 shows the NaCl concentration profiles at several cross sections in the LLW calculated by the CFD simulation.
FIG. 4. Velocity distribution in the LLW calculated by the CFD simulation. a) The y-component of velocity vector. b) The x-component of velocity vector.
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FIG. 6. Concentration profiles for NaCl calculated based on Fick’s law. The same physical constants and dimensions of the LLW in Fig. 5 were postulated. FIG. 5. Concentration profiles for NaCl calculated by the CFD simulation.
The distance from the starting point (d, in centimeters) was converted into the contact time of the core and the cladding solutions. Because the average linear velocity of the sheath flow was 2.0 cm s1, the contact time is expressed as d/2 s. It was observed that NaCl diffused to the cladding region and the NaCl concentration at the center of the core deceased with an increase in contact time. The simulation results showed that the NaCl concentration profile was dependent on the contact time. That is, the contact time is useful for comparing LLWs that have the same ratio of the average linear velocities of the core solution and the cladding solution at the initial point but have different average linear velocities. This CFD simulation of the NaCl concentration (Fig. 5) was compared with the calculation (Fig. 6), where only Fickian diffusion of NaCl was taken into account and the effect of flow was not. As shown in these figures, the apparent diffusion of NaCl is faster and the distribution profiles of NaCl concentration are broader for the Fickian diffusion than for the CFD simulation. Careful observation of these figures reveals that the difference in the NaCl profiles occurred at an earlier stage of the LLW and was maintained throughout the LLW, implying that the tapered shape of the inner capillary possibly affects the flow, after which diffusion is the dominant process that determines the NaCl profile. This result suggests the necessity
of using CFD calculations to describe the LLW because the effect of flow is taken into account. Characterization of the Liquid/Liquid Optical Waveguide Using Experiments. Figure 7b shows the changes in the RhB fluorescence profile along with the outer capillary of the LLW. To make comparison easier, the results of the calculation of the NaCl distribution profiles are also shown in Fig. 7a. In Fig. 7b, the intensity of the fluorescence was corrected with consideration of the attenuation of the guided light due to RhB absorption. As shown in the figure, almost no attenuation of the guided light was observed despite the change in the NaCl profile (see Fig. 7a). On the other hand, the region of fluorescence became broader with an increase in contact time (Fig. 7b). This result is in good agreement with that of the calculation (compare Figs. 7a and 7b). Because the light energy can be distributed in the region that has a higher refractive index (RI) than that of the cladding (water, n = 1.333), the fluorescence profile should reflect the RI profile of the LLW (i.e., the NaCl concentration profile). To evaluate the change in the NaCl concentration experimentally, the far-field pattern of the out-coupled guided light was analyzed.13 The experimental setup is shown in Fig. 8a. The critical angle (hc) in the LLW was determined by measuring the radius of the far-field pattern and expressed by hc ¼
p tan1 ar 2 ncore
ð1Þ
FIG. 7. (a) A CFD simulation of the NaCl concentration. (b) Fluorescence intensity profile of RhB. Rhodamine B (1 lmol dm3) was added to both core and cladding solutions. The fluorescence intensity was corrected using the calculation data in Fig. 2.
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FIG. 8. (a) Experimental setup for measurements of far-field pattern of the guided light. The far-field pattern of the guided light was monitored to measure the radius (r) of the pattern. To calculate the radius, the effect of RI changes due to the experimental setup (e.g., the dish and the solution at the outlet) was carefully corrected for. (b) Dependence of critical angle of the LLW on the contact time. The square marks show the experimental results, and the solid line shows the calculation result. The average flow rate was varied from 1.0 to 10 cm s1.
where a denotes the distance between the screen and the outlet of the LLW, r denotes the radius of the far-field pattern in Fig. 8a, and ncore is the maximum RI value of the core at the outlet of the LLW. On the other hand, the critical angle hc should be hc ¼ sin1
nclad ncore
problem. Tentatively, we estimate that a large portion of the guided light had an incident angle much larger than hc; therefore, leakage of the guided light was minimal.
CONCLUSION ð2Þ
where nclad is the RI value of the cladding, water (1.333). Thus, we can calculate hc from the results of the simulation because the RI values of the NaCl solutions can be determined from the NaCl concentrations. Figure 8b demonstrates the relationship between hc and contact time. In this experiment, the average linear velocity (i.e., the contact time) was changed instead of the length of the LLW. The square marks show the experimental result, and the solid line shows the calculation result. As shown in the figure, they were in good agreement with each other, although the experiment gave slightly greater hc values than the calculation. This may be caused by the vagueness of the outlines of the farfield patterns in the experiment. As discussed, the CFD simulation is in good agreement with the actual LLW in terms of NaCl concentration distribution. However, it is unclear why there was no observable leakage of the guided light, as shown in Figs. 2 and 7b, despite the considerable decrease in NaCl concentration in the core of the LLW. In the farfield experiment, the light intensity was also monitored (Fig. 3), and the results confirmed that there was almost no significant change in the light intensity when the contact time was increased. Based on the results of the CFD simulation, we believe that it may be necessary to calculate the light energy distribution in the LLW using electromagnetic field theory to further understand this
A stable LLW was formed using sheath flow where 15% NaCl solution functioned as the core solution and water functioned as the cladding solution (15% NaCl/water LLW). The LLW was at least 200 mm long and yielded no substantial leakage of the guided light. This study demonstrates the usefulness of CFD simulations of LLWs via its ability to characterize and aid in the future designs of LLWs; however, further studies, especially on the distribution of light energy in the LLW, are necessary. This LLW has unique features that are discussed thoroughly in this paper, and it may be a new tool for analytical chemistry, for example, in liquid/liquid interface studies. ACKNOWLEDGMENTS This work was supported in part by a grant-in-aid for exploratory research (No. 16655026) and a grant-in-aid for scientific research (B) (No. 20350033) from Japan Society for the Promotion of Science. The authors thank Takuro Yoshii for his help with the experiments. 1. H. Takiguchi, T. Odake, T. Umemura, K. Tsunoda. ‘‘Development of Liquid/ Liquid Optical Waveguide Using a Two Phase Sheath Flow and its Application to Fluorescent Determination of Rhodamine B’’. In: Y. Baba, S. Shoji, A. van den Berg, editors. Micro Total Analysis Systems 2002. Proceedings of the lTAS 2002 Symposium, held in Nara, Japan, 3-7 November 2002. Dordrecht, Netherlands: Kluwer Academic. Vol. 1. Pp. 278-280. 2. H. Takiguchi, T. Odake, M. Ozaki, T. Umemura, K. Tsunoda. ‘‘A Liquid/ Liquid Optical Waveguide Using Sheath Flow as a New Tool for Liquid/ Liquid Interfacial Measurement’’. Appl. Spectrosc. 2003. 57(8): 1039-1041. 3. H. Takiguchi, T. Odake, T. Umemura, H. Hotta, K. Tsunoda. ‘‘Characteristics of Liquid/Liquid Optical Waveguide Using Sheath Flow
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4.
5.
6. 7.
8.
and Its Application to Detect Molecules at Liquid/Liquid Interface’’. Anal. Sci. 2005. 21(11): 1269-1274. H. Takiguchi, S. Asanuma, H. Hotta, T. Odake, K. Tsunoda. ‘‘Development of Liquid/Liquid Optical Waveguide with Miscible Solvents and its Application to the Observation of 1-Anilino-8-Naphtalene Sulfonate at the Tetrahydrofuran/Water Interface’’. In: T. Kitamori, H. Fujita, S. Hasebe, editors. Micro Total Analysis Systems 2006. Proceedings of the Tenth International Conference on Miniaturized Systems for Chemistry and Life Sciences (lTAS 2006). Tokyo: Chemical and Biological Microsystems Society, 2006. Vol. 2. Pp. 1318-1320. H. Murata, J. Kamiyama, S. Asanuma, K. Sato, K. Tsunoda, H. Hotta, Y. Sugii. ‘‘A Liquid/Liquid Optical Waveguide with Miscible Solvents to Observe Complexation Reaction’’. In: T. Fujii, A. Hibara, S. Takeuchi, T. Fukuba, editors. Proceedings of the 16th International Conference on Miniaturized Systems for Chemistry and Life Sciences (lTAS 2012). Okinawa, Japan: October 28-November 1, 2012. Pp. 1783-1785. D.B. Wolfe, R.S. Conroy, P. Garstecki, M.A. Fischbach, K.E. Paul, G.M. Whitesides. ‘‘Dynamic Control of Liquid-Core/Liquid-Cladding Optical Waveguides’’. Proc. Natl. Acad. Sci. U.S.A. 2004. 101(34): 12434-12438. B.T. Mayers, D.V. Vezenov, V.I. Vullev, G.M. Whitesides. ‘‘Arrays and Cascades of Fluorescent Liquid-liquid Waveguides: Broadband Light Sources for Spectroscopy in Microchannels’’. Anal. Chem. 2005. 77(5): 1310-1316. X.C. Li, J. Wu, A.Q. Liu, Z.G. Li, Y.C. Soew, H.J. Huang, K. Xu, J.T. Lin. ‘‘A Liquid Waveguide Based Evanescent Wave Sensor Integrated onto a Microfluidic Chip’’. Appl. Phys. Lett. 2008. 93(19): 193901. doi:10.1063/ 1.2988648.
9. K.S. Lee, S.B. Kim, K.H. Lee, H.J. Sung, S.S. Kim. ‘‘Three-Dimensional Microfluidic Liquid-Core/Liquid-Cladding Waveguide’’. Appl. Phys. Lett. 2010. 97(2): 021109. doi:10.1063/1.3460279. 10. J.M. Lim, J.P. Urbanski, J.H. Choi, T. Thorsen, S.M. Yang. ‘‘Liquid Waveguide-Based Evanescent Wave Sensor That Uses Two Light Sources with Different Wavelengths’’. Anal. Chem. 2011. 83(2): 585-590. 11. X.-D. Fan, I.M. White. ‘‘Optofluidic Microsystems for Chemical and Biological Analysis’’. Nat. Photonics. 2011. 5(10): 591-597. 12. I. Okada. ‘‘Transport Phenomena’’. In: Chemical Society of Japan, editor. Kagaku Binran, Kiso-Hen [Chemistry Handbook, Fundamentals]. Tokyo: Maruzen, 1984. 3rd ed. Vol. 2, pp. 38-70. 13. S. Kawakami. Hikari Doharo [Optical Waveguides]. Tokyo: Asakura, 1980. Pp. 269-272.
APPENDIX Figure A1 shows the model used for the CFD calculation. The mesh consisted of three different widths of grid in the x direction, as shown in the figure. In addition, the length of the grid in the y direction was varied as described in the figure caption. The core and the area near the core portion were divided into smaller grids. The shape of tapered inner capillary tubing was used in the model, as shown in the figure. Calculations were performed using an algebraic multi-grid method. The maximum calculation number was 105, and the convergence condition was 5.0 3 106.
FIG. A1. The mesh for the CFD simulation. The lengths of the grid (y-direction) are as follows. Upstream of the tip of inner capillary: 0–2.5 mm, 500 lm; 2.5–3.5 mm, 167 lm; 3.5–4.0 mm, 100 lm. Downstream of the tip of inner capillary: 0–0.5 mm, 25 lm; 0.5–1.0 mm, 50 lm; 1.0–2.0 mm, 100 lm; 2.0–3.0 mm, 167 lm; 3.0–60 mm, 500 lm; 60–160 mm, 1000 lm.
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Characterization of Liquid-Core/Liquid-Cladding Optical Waveguides of a Sodium Chloride Solution/Water System by Computational Fluid Dynamics Junya Kamiyama,a Soto Asanuma,a Hiroyasu Murata,a Yasuhiko Sugii,b Hiroki Hotta,c Kiichi Sato,a Kin-ichi Tsunodaa,* a b c
Gunma University, Department of Chemistry and Chemical Biology, 1-5-1 Tenjin-cho, Kiryu 376-8515, Japan University of Tokyo, Department of Applied Chemistry, 7-3-1, Hongo, Bunkyo, Tokyo 113-8656, Japan Nara University of Education, Department of Chemistry, Takabatake, Nara 630-8528, Japan
A stable liquid/liquid optical waveguide (LLW) was formed using a sheath flow, where a 15% sodium chloride (NaCl) solution functioned as the core solution and water functioned as the cladding solution (15% NaCl/water LLW). The LLW was at least 200 mm in length. The concentration distributions of the liquid core and liquid cladding solutions in the LLW system were predicted by computational fluid dynamics (CFD) to validate the characteristics of the waveguide. The broadening of the region of the fluorescence of Rhodamine B excited by the guided light and the increase in the critical angle of the guided light with the increase in the contact time of the core and the cladding solutions were well explained by CFD calculations. However, no substantial leakage of the guided light was observed despite the considerably large change in the refractive index profile of the LLW; thus, a narrower and longer waveguide was realized. Index Headings: Liquid-core/liquid-cladding optical waveguide; Computational fluid dynamics; Sodium chloride solution; Critical angle; Far-field pattern.
INTRODUCTION Liquid/liquid optical waveguides (LLWs), which have a liquid-core/liquid-cladding structure, were first proposed by our group.1–5 Liquid/liquid optical waveguides have been formed using a sheath flow of liquids from concentric glass capillaries into an outer glass capillary. Both immiscible solvent systems (e.g., toluene/water and diethyl ether/water) and miscible solvent systems (e.g., tetrahydrofuran [THF]/water) can be used to form LLWs. We have been using these LLWs as new tools for studying liquid–liquid interfaces. A THF/water LLW system was used to observe an ion-pair extraction of 1-anilino-8-naphthalene sulfonate (ANS) and hexadecyltrimethylammonium ion (CTA) from the water phase to the THF phase.4 Moreover, a 50% ethanol/water LLW system was employed to observe the complexation reaction between aluminum(III) and lumogallion.5 In addition, the concept of LLW has recently been extended to microchip development by other researchers, and it has become one of the key elements in the new field of optofluidics, where it Received 3 April 2013; accepted 8 August 2013. * Author to whom correspondence should be sent. E-mail: tsunoda@ gunma-u.ac.jp. DOI: 10.1366/13-07096
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is used to manipulate light in microchips (e.g., as an optical switch and an evanescent coupler).6–11 In this work, an LLW that uses a 15% sodium chloride (NaCl) solution for the core solution and water for the cladding solution (15% NaCl/water LLW) was formed, and its characteristics were studied by means of computational fluid dynamics (CFD). The computational results were then compared with the experimental results.
EXPERIMENTAL Reagents. All the reagents, including NaCl and Rhodamine B (RhB), were purchased (Wako Pure Chemical Industries, Japan). All aqueous solutions were prepared using water purified by a Milli-QII system (Millipore, USA). Apparatus. The experimental setup for the LLW system is shown in Fig. 1. The inner capillary was a stainless capillary (internal diameter [ID] 0.13 mm, outer diameter [OD] 0.31 mm) with a tapered tip, whereas the outer capillary was a square glass capillary (inner side, 1.2 3 1.2 mm; outer side, 1.7 3 1.7 mm; length, 200 mm). The source light, a water-cooled Arþ laser (488 nm; Model 95, from Lexel Laser Inc., USA), was introduced into the inner flow through an optical fiber (ultraviolet [UV] metalcoated optical fiber, OD 70 lm; numerical aperture [N.A.], 0.2; A.R.T. Photonics, Germany). A 15% aqueous NaCl solution (core solution) was introduced into the inner capillary under pressure from a nitrogen cylinder, and pure water (cladding solution) was sent into the outer capillary using a gravity-driven method. When necessary, 1 lmol dm3 RhB was added to both the core and cladding solutions to avoid the effects of diffusion. The fluorescence of RhB was monitored using a microscope system (custom-made system; Olympus Co., Ltd., Japan) equipped with a charge-coupled device (CCD) camera (Ratiga 2000R; QImaging Co., Ltd., Canada) or a multichannel CCD detector (PMA-11; Hamamatsu Photonics Co., Ltd.,). The microscope system was moved manually along the long axis of the LLW. Measurement. Formation Conditions of the Stable 15% Sodium Chlorde/Water Liquid/Liquid Optical Waveguide. Because the cross section of the outer capillary was much
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FIG. 1. Experimental setup of the 15% NaCl solution/water LLW.
FIG. 2. Attenuation of RhB fluorescence with the increase in distance from the tip of the inner capillary (the starting point): dotted line, experimental results; solid line, calculation result. Rhodamine B (1 lmol dm3) was added to both core and cladding solutions. An average linear velocity of 2.0 cm s1 and a ratio of the average linear velocities of the inner flow and outer flow of 2.0 were used. For the calculation, only the absorption due to RhB was taken into account.
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larger than that of the inner capillary, the average linear velocity of the sheath flow was mainly determined by that of the cladding solution. When the average linear velocity of the sheath flow and the ratio of the average linear velocities of the inner flow and outer flow at the tip of the inner capillary were set at ;0.5–10 cm s1 and ;1.5–10 cm s1, respectively, a stable 15 % NaCl/water LLW was formed. In Fig. 2, the attenuation curve of the RhB fluorescence is compared with the calculated one, where only the attenuation of the guided light due to the absorption of RhB molecules was postulated. In this experiment, 1 lmol dm3 RhB was added to both the core and cladding solutions to avoid the change in the concentration of RhB in the core solution due to its diffusion to the cladding solution. As shown in this figure, the experimental and calculated curves coincided with each other very well. This result indicated that there was almost no other reason, except for the absorption of RhB, for the attenuation of the guided light. In other words, the leakage of the guided light from the LLW at 488 nm throughout the length of the LLW should be the minimum. Moreover, Fig. 3 reinforces this observation (as discussed later). Thus, an average linear velocity of 2.0 cm s1 and a ratio of the average linear velocities of the inner flow and the outer flow of 2.0 were used throughout the experiments, unless otherwise indicated.
FIG. 3. Dependence of the intensity of the guided light on the contact time. The average linear velocity was varied from 0.6 to 9.3 cm s1. The same experimental set-up as that of Fig. 8 (far-field experiment) was applied.
Computational Fluid Dynamics Simulation of the 15% Sodium Chloride/Water Liquid/Liquid Optical Waveguide. The waveguide structures of the LLW—the distribution of NaCl concentration (refractive index) and the velocity distribution of the flow in the LLW—were predicted using CFD. The CFD software, STAR-CD (CD-adapco, USA), which is based on a finite-volume method, was used. To describe the mixing of the core and cladding liquids, a threedimensional Navier–Stokes equation and a convection–diffusion equation based on Fick’s law with laminar flow under steady state were chosen. The physical data used in the calculation were diffusion coefficient of NaCl in water, 1.52 3 109 m2 s1; kinematic viscosity of water, 1.56 3 106 m2 s1; and Schmidt number, 416.5.12 The dimensions of the LLW used for the simulation were the same as those for the experiments, except that the outer capillary was cylindrical (ID 1.2 mm) and not square-shaped. Details of the calculation are shown in the Appendix.
RESULTS AND DISCUSSION Computational Fluid Dynamics Simulation of the Waveguide Structure of the Liquid/Liquid Optical Waveguide. Figure 4 shows the velocity distribution of the sheath flow calculated by the CFD simulation. The flow shown in Fig. 4a developed after the core and cladding flows merged, becoming the Hagen–Poiseuille flow, which is a theoretical solution for a laminar flow. In the downflow region from the tip of the inner capillary, defined as the starting point for Fig. 4b, the core fluid was observed to flow toward the outside and the cladding fluid was observed flow toward the inside; in addition, the x components of velocity gradually decreased to zero at about 2 mm from the starting point, signifying that fluid mixing occurred in the downflow region of the starting point. However, the shape of the tapered inner capillary suppressed the mixing to stabilize the waveguide. Figure 5 shows the NaCl concentration profiles at several cross sections in the LLW calculated by the CFD simulation.
FIG. 4. Velocity distribution in the LLW calculated by the CFD simulation. a) The y-component of velocity vector. b) The x-component of velocity vector.
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FIG. 6. Concentration profiles for NaCl calculated based on Fick’s law. The same physical constants and dimensions of the LLW in Fig. 5 were postulated. FIG. 5. Concentration profiles for NaCl calculated by the CFD simulation.
The distance from the starting point (d, in centimeters) was converted into the contact time of the core and the cladding solutions. Because the average linear velocity of the sheath flow was 2.0 cm s1, the contact time is expressed as d/2 s. It was observed that NaCl diffused to the cladding region and the NaCl concentration at the center of the core deceased with an increase in contact time. The simulation results showed that the NaCl concentration profile was dependent on the contact time. That is, the contact time is useful for comparing LLWs that have the same ratio of the average linear velocities of the core solution and the cladding solution at the initial point but have different average linear velocities. This CFD simulation of the NaCl concentration (Fig. 5) was compared with the calculation (Fig. 6), where only Fickian diffusion of NaCl was taken into account and the effect of flow was not. As shown in these figures, the apparent diffusion of NaCl is faster and the distribution profiles of NaCl concentration are broader for the Fickian diffusion than for the CFD simulation. Careful observation of these figures reveals that the difference in the NaCl profiles occurred at an earlier stage of the LLW and was maintained throughout the LLW, implying that the tapered shape of the inner capillary possibly affects the flow, after which diffusion is the dominant process that determines the NaCl profile. This result suggests the necessity
of using CFD calculations to describe the LLW because the effect of flow is taken into account. Characterization of the Liquid/Liquid Optical Waveguide Using Experiments. Figure 7b shows the changes in the RhB fluorescence profile along with the outer capillary of the LLW. To make comparison easier, the results of the calculation of the NaCl distribution profiles are also shown in Fig. 7a. In Fig. 7b, the intensity of the fluorescence was corrected with consideration of the attenuation of the guided light due to RhB absorption. As shown in the figure, almost no attenuation of the guided light was observed despite the change in the NaCl profile (see Fig. 7a). On the other hand, the region of fluorescence became broader with an increase in contact time (Fig. 7b). This result is in good agreement with that of the calculation (compare Figs. 7a and 7b). Because the light energy can be distributed in the region that has a higher refractive index (RI) than that of the cladding (water, n = 1.333), the fluorescence profile should reflect the RI profile of the LLW (i.e., the NaCl concentration profile). To evaluate the change in the NaCl concentration experimentally, the far-field pattern of the out-coupled guided light was analyzed.13 The experimental setup is shown in Fig. 8a. The critical angle (hc) in the LLW was determined by measuring the radius of the far-field pattern and expressed by hc ¼
p tan1 ar 2 ncore
ð1Þ
FIG. 7. (a) A CFD simulation of the NaCl concentration. (b) Fluorescence intensity profile of RhB. Rhodamine B (1 lmol dm3) was added to both core and cladding solutions. The fluorescence intensity was corrected using the calculation data in Fig. 2.
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FIG. 8. (a) Experimental setup for measurements of far-field pattern of the guided light. The far-field pattern of the guided light was monitored to measure the radius (r) of the pattern. To calculate the radius, the effect of RI changes due to the experimental setup (e.g., the dish and the solution at the outlet) was carefully corrected for. (b) Dependence of critical angle of the LLW on the contact time. The square marks show the experimental results, and the solid line shows the calculation result. The average flow rate was varied from 1.0 to 10 cm s1.
where a denotes the distance between the screen and the outlet of the LLW, r denotes the radius of the far-field pattern in Fig. 8a, and ncore is the maximum RI value of the core at the outlet of the LLW. On the other hand, the critical angle hc should be hc ¼ sin1
nclad ncore
problem. Tentatively, we estimate that a large portion of the guided light had an incident angle much larger than hc; therefore, leakage of the guided light was minimal.
CONCLUSION ð2Þ
where nclad is the RI value of the cladding, water (1.333). Thus, we can calculate hc from the results of the simulation because the RI values of the NaCl solutions can be determined from the NaCl concentrations. Figure 8b demonstrates the relationship between hc and contact time. In this experiment, the average linear velocity (i.e., the contact time) was changed instead of the length of the LLW. The square marks show the experimental result, and the solid line shows the calculation result. As shown in the figure, they were in good agreement with each other, although the experiment gave slightly greater hc values than the calculation. This may be caused by the vagueness of the outlines of the farfield patterns in the experiment. As discussed, the CFD simulation is in good agreement with the actual LLW in terms of NaCl concentration distribution. However, it is unclear why there was no observable leakage of the guided light, as shown in Figs. 2 and 7b, despite the considerable decrease in NaCl concentration in the core of the LLW. In the farfield experiment, the light intensity was also monitored (Fig. 3), and the results confirmed that there was almost no significant change in the light intensity when the contact time was increased. Based on the results of the CFD simulation, we believe that it may be necessary to calculate the light energy distribution in the LLW using electromagnetic field theory to further understand this
A stable LLW was formed using sheath flow where 15% NaCl solution functioned as the core solution and water functioned as the cladding solution (15% NaCl/water LLW). The LLW was at least 200 mm long and yielded no substantial leakage of the guided light. This study demonstrates the usefulness of CFD simulations of LLWs via its ability to characterize and aid in the future designs of LLWs; however, further studies, especially on the distribution of light energy in the LLW, are necessary. This LLW has unique features that are discussed thoroughly in this paper, and it may be a new tool for analytical chemistry, for example, in liquid/liquid interface studies. ACKNOWLEDGMENTS This work was supported in part by a grant-in-aid for exploratory research (No. 16655026) and a grant-in-aid for scientific research (B) (No. 20350033) from Japan Society for the Promotion of Science. The authors thank Takuro Yoshii for his help with the experiments. 1. H. Takiguchi, T. Odake, T. Umemura, K. Tsunoda. ‘‘Development of Liquid/ Liquid Optical Waveguide Using a Two Phase Sheath Flow and its Application to Fluorescent Determination of Rhodamine B’’. In: Y. Baba, S. Shoji, A. van den Berg, editors. Micro Total Analysis Systems 2002. Proceedings of the lTAS 2002 Symposium, held in Nara, Japan, 3-7 November 2002. Dordrecht, Netherlands: Kluwer Academic. Vol. 1. Pp. 278-280. 2. H. Takiguchi, T. Odake, M. Ozaki, T. Umemura, K. Tsunoda. ‘‘A Liquid/ Liquid Optical Waveguide Using Sheath Flow as a New Tool for Liquid/ Liquid Interfacial Measurement’’. Appl. Spectrosc. 2003. 57(8): 1039-1041. 3. H. Takiguchi, T. Odake, T. Umemura, H. Hotta, K. Tsunoda. ‘‘Characteristics of Liquid/Liquid Optical Waveguide Using Sheath Flow
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and Its Application to Detect Molecules at Liquid/Liquid Interface’’. Anal. Sci. 2005. 21(11): 1269-1274. H. Takiguchi, S. Asanuma, H. Hotta, T. Odake, K. Tsunoda. ‘‘Development of Liquid/Liquid Optical Waveguide with Miscible Solvents and its Application to the Observation of 1-Anilino-8-Naphtalene Sulfonate at the Tetrahydrofuran/Water Interface’’. In: T. Kitamori, H. Fujita, S. Hasebe, editors. Micro Total Analysis Systems 2006. Proceedings of the Tenth International Conference on Miniaturized Systems for Chemistry and Life Sciences (lTAS 2006). Tokyo: Chemical and Biological Microsystems Society, 2006. Vol. 2. Pp. 1318-1320. H. Murata, J. Kamiyama, S. Asanuma, K. Sato, K. Tsunoda, H. Hotta, Y. Sugii. ‘‘A Liquid/Liquid Optical Waveguide with Miscible Solvents to Observe Complexation Reaction’’. In: T. Fujii, A. Hibara, S. Takeuchi, T. Fukuba, editors. Proceedings of the 16th International Conference on Miniaturized Systems for Chemistry and Life Sciences (lTAS 2012). Okinawa, Japan: October 28-November 1, 2012. Pp. 1783-1785. D.B. Wolfe, R.S. Conroy, P. Garstecki, M.A. Fischbach, K.E. Paul, G.M. Whitesides. ‘‘Dynamic Control of Liquid-Core/Liquid-Cladding Optical Waveguides’’. Proc. Natl. Acad. Sci. U.S.A. 2004. 101(34): 12434-12438. B.T. Mayers, D.V. Vezenov, V.I. Vullev, G.M. Whitesides. ‘‘Arrays and Cascades of Fluorescent Liquid-liquid Waveguides: Broadband Light Sources for Spectroscopy in Microchannels’’. Anal. Chem. 2005. 77(5): 1310-1316. X.C. Li, J. Wu, A.Q. Liu, Z.G. Li, Y.C. Soew, H.J. Huang, K. Xu, J.T. Lin. ‘‘A Liquid Waveguide Based Evanescent Wave Sensor Integrated onto a Microfluidic Chip’’. Appl. Phys. Lett. 2008. 93(19): 193901. doi:10.1063/ 1.2988648.
9. K.S. Lee, S.B. Kim, K.H. Lee, H.J. Sung, S.S. Kim. ‘‘Three-Dimensional Microfluidic Liquid-Core/Liquid-Cladding Waveguide’’. Appl. Phys. Lett. 2010. 97(2): 021109. doi:10.1063/1.3460279. 10. J.M. Lim, J.P. Urbanski, J.H. Choi, T. Thorsen, S.M. Yang. ‘‘Liquid Waveguide-Based Evanescent Wave Sensor That Uses Two Light Sources with Different Wavelengths’’. Anal. Chem. 2011. 83(2): 585-590. 11. X.-D. Fan, I.M. White. ‘‘Optofluidic Microsystems for Chemical and Biological Analysis’’. Nat. Photonics. 2011. 5(10): 591-597. 12. I. Okada. ‘‘Transport Phenomena’’. In: Chemical Society of Japan, editor. Kagaku Binran, Kiso-Hen [Chemistry Handbook, Fundamentals]. Tokyo: Maruzen, 1984. 3rd ed. Vol. 2, pp. 38-70. 13. S. Kawakami. Hikari Doharo [Optical Waveguides]. Tokyo: Asakura, 1980. Pp. 269-272.
APPENDIX Figure A1 shows the model used for the CFD calculation. The mesh consisted of three different widths of grid in the x direction, as shown in the figure. In addition, the length of the grid in the y direction was varied as described in the figure caption. The core and the area near the core portion were divided into smaller grids. The shape of tapered inner capillary tubing was used in the model, as shown in the figure. Calculations were performed using an algebraic multi-grid method. The maximum calculation number was 105, and the convergence condition was 5.0 3 106.
FIG. A1. The mesh for the CFD simulation. The lengths of the grid (y-direction) are as follows. Upstream of the tip of inner capillary: 0–2.5 mm, 500 lm; 2.5–3.5 mm, 167 lm; 3.5–4.0 mm, 100 lm. Downstream of the tip of inner capillary: 0–0.5 mm, 25 lm; 0.5–1.0 mm, 50 lm; 1.0–2.0 mm, 100 lm; 2.0–3.0 mm, 167 lm; 3.0–60 mm, 500 lm; 60–160 mm, 1000 lm.
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