MICRO/NANO SURFACE TENSION MEASUREMENT BY 2D-CAPILLARY WAVE RESONANCE 1,2 3 2* Myungwha Chung , Christian Pigot and Akihide Hibara 1University of Tokyo, Tokyo, Japan 2Tokyo Institute of Technology, Tokyo, Japan 3LIMMS/CNRS-IIS UMI 2820, Institute of Industrial Science, Tokyo, Japan
ABSTRACT The analysis of capillary waves in confined microspace by quasi-elastic laser scattering (QELS) method enables surface tension measurements. In contrast to previous works, a simple single-beam-focusing method based on spontaneous capillary wave resonance with its confined size is proposed. The capillary wave resonance has been successfully demonstrated in confined two-dimensional micro surface at circular apertures. Moreover, the surface tension dependence on surfactant concentration has been successfully measured at 44-µm-sized circular liquid surface. This method is expected to be a powerful tool for bio and chemical sensing at micro- / nano-scale liquid interfaces.
KEYWORDS: Surface tension measurement, Capillary wave resonance, Quasi-elastic laser scattering method, microscale liquid interface.
INTRODUCTION QELS method is a tool for measuring the frequency of capillary waves on liquid interfaces, which depends on species and amount of surface-active compounds. The surface tension can be obtained from hydrodynamic relationship between its frequency and wave number. Previously, with a dual beam setup, the tension measurement in 300-µm-wide microfluidic channel was reported [1]. In our recent work [2], we found spontaneous resonance of capillary waves under one-dimensional (1D) spatial restriction, which enables to measure surface tension with a simple single-beam focusing setup. Two-dimensional (2D) confinement condition should be considered in order to apply the method to spot or array measurements. In this paper, spontaneous resonance of capillary waves on 2D-confined liquid interfaces has been investigated. For the first step of the investigation, circular-confined liquid surface was prepared and the QELS spectra were analyzed based on the wave equation, considering the dispersion relationship of the capillary wave. In addition, the tension dependence on surfactant adsorption has been demonstrated.
Table 1: Vibration on infinite liquid surface and confined micro liquid surfaces (1D and 2D).
~ µm
∞ ~ µm ~ µm
Infinite surface Confined micro Confined micro surface (1D) surface(2D) Random wave Resonance wave Resonance wave
THEORY Interfaces between two immiscible fluids are perturbed by random thermal fluctuations of a few angstroms amplitude. As a consequence, a flat fluidic interface is agitated by an ever changing roughness. One way to restore equilibrium is to propagate these perturbations through capillary waves. Thus on an interface, propagating waves are excited by thermal fluctuations. Due to the viscosity of the fluids, the waves are attenuated, ensuring that the surface remains flat. The capillary wave dispersion relation is given by Lamb’s equation as [3]
f = 1/2π [(γ / ρ) k 3]1/2, (1) where f, γ, ρ, and k, are the frequency, surface tension, and the wavenumber of the capillary wave, respectively. The surface tension can be obtained from the relationship between f and k in Eq. 1. The spectrum of resonated capillary waves on a confined circular surface is estimated by a vibration model for circular membrane [4].
978-0-9798064-6-9/µTAS 2013/$20©13CBMS-0001 922 17th International Conference on Miniaturized Systems for Chemistry and Life Sciences 27-31 October 2013, Freiburg, Germany EXPERIMENTAL Capillary waves were observed with QELS method, which is an angular-resolved light-scattering method. Briefly, as a laser beam passses the interfaces, the propagating capillary waves scatter a part of the incident photons. Along with the change in direction, the photons experience a frequency change that is equal to the frequency of the scattering wave (Eq. 1). In our previous report [2], we proposed a simple quasi-elastic laser scattering method (QELS) to microscale liquid interface. This method uses the single beam not dual beam for optical setup because the strict regulation of angles between scattered light and local light is unnecessary in principle. Figure 1 illustrates optical setup for the single-beam QELS method and measurement cell with the air/liquid interface at the aperture. The measurement cell is composed of a 60-μm-thick film of polydimethylsiloxane (PDMS), slide glass, and acryl plate spacer. A circular aperture (diameter; 44-μm) was fabricated in PDMS film by a soft-lithography. For surfactant adsorption measurement, 1 mM, 10 mM, and 50 mM aqueous solutions of sodium dodecylsalfate (SDS) were measured.
Pinhole
Photodiode Slide glass
Sample Acryl cell
Spectrum analyzer PDMS film Objective
Laser (532nm) Mirror
Figure 1: Schematic diagram of single beam QELS method.
RESULTS AND DISCUSSION When the incident light to the interface/surface, the light is scattered with Doppler shift because the scattered point is fluctuated by capillary waves. Figure 2 shows Doppler spectra of water surface (a) without confinement (10-mm-sized drop), and (b) with 44-µm circular confinement. In the confined case (Figure. 2b), several resonant modes are observed. The assignment of the peak frequencies is summarized in Table 2. Significant difference between the theoretical and experimental values was observed in (1,0) mode while most experimental values agree well with the theoretical ones. The reason has not been clarified yet, but non-elastic characteristic of PDMS might affect the mode. By analyzing their size- dependence and shape-dependence (data not shown), we concluded that the 2D spontaneous resonance has been demonstrated for the first time. Figure 3 shows the results of the mode frequency dependence on SDS concentration at 44- µm circular surface. When concentration increased, the frequency shifted downwards, which corresponds to surface tension decreased.
(a) (b) -54 -56
-58 -60 -62 (dB) (dB) -66 -64
-70 Intensity Intensity -68 -74
-78 -72 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (kHz) Frequency (kHz)
Figure 2: Doppler spectra of water surface (a) without confinement (10-mm-sized drop), and (b) with 44- µm circular confinement. In the confined case, clear peaks corresponding to the spontaneous 2D resonance are observed.
923 Table 2: Assignments of the resonant peaks. The theoretical values are calculated based on the circular membrane vibration and the dispersion of capillary wave.
Resonant mode (1, 0) (1, 1) (1, 2) (2, 0) (2, 1) (3, 0) Theoretical 49.6 99.7 154.8 172.4 247.0 338.4 Frequency / kHz Experimental 63.8 100.1 - 171.0 253.8 341.5 Frequency / kHz
-40
1 mM -45
10 mM
Intensity Intensity (dB) -50 50 mM
-55 0 100 200 300 Frequency (kHz)
Figure 3: Frequency shift corresponding to the SDS concentration. The arrows indicate (2,0) resonant mode at each 44-µm circular surface.
CONCLUSION Here, we demonstrated measurement of microscale liquid surface with the simple optical setup with the spontaneous resonant phenomena, for the first time. The most important feature of this method is that there is no limitation in scale of the liquid interface even when it’s down to a few tens of micrometer. In future work, nanometer-sized liquid interfaces will be analyzed.
ACKNOWLEDGEMENTS The authors thank Prof. Sebastian Volz of Ecole Centrale Paris for the fruitful discussion. A part of this work was supported by KAKENHI (Kiban B 24350038), and the JSPS Core-to-Core Program, the JSPS the International Training Program. MJ acknowledges the JCIA Program and TEIJIN Scholarship Foundation .
REFERENCES [1] Akihide Hibara et al., “Spectroscopic analysis of liquid/liquid interfaces in multiphase microflows”, J. Am. Chem. Soc., 125, 14954-14955 (2003). [2] Christian Pigot, Akihide Hibara, “Surface tension measurement at the microscale by passive resonance of capillary waves”, Anal. Chem., 84, 2557-2561 (2012). [3] Lamb, H., “Hydrodynamics”, 6th ed., Cambridge University Press, Cambridge (1932). [4] S. Mitani, K. Sakai, “Resonance of liquid surface wave induced by laser”, The institute of electronics, information and communication engineers (2007-10).
CONTACT *Akihide Hibara, tel: +81-3-5734-2233; [email protected]
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