Article pubs.acs.org/ac
Evanescent Wave-Based Particle Tracking Velocimetry for Nanochannel Flows Yutaka Kazoe, Keizo Iseki, Kazuma Mawatari, and Takehiko Kitamori* Department of Applied Chemistry, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan ABSTRACT: Understanding fluid flows in 10−1000 nm space, which we call extended nanospace, is important for novel nanofluidic devices in analytical chemistry. This study therefore developed a particle tracking velocimetry for measuring velocity distribution in nanochannel flows, by using the evanescent wave illumination. 64 nm fluorescent nanoparticles were used as flow tracer. The particle position was determined from fluorescent intensity by the evanescent wave field, with a spatial resolution smaller than light wavelengths. The time resolution of 260 μs was achieved to make error by the Brownian diffusion of the tracer small to be neglected. An image processing by multitime particle tracking was established to detect the tracer nanoparticles of weak fluorescent intensity. Though the measurement region was affected by nonuniform particle distribution with the electrostatic interactions, pressure-driven flows of water in a nanochannel of 50 μm width and 410 nm depth were successfully measured. The results of the velocity distribution in the depth-wise direction approximately showed agreement with the fluid dynamics with the bulk liquid properties from the macroscopic view, however, suggested slip velocities even in the hydrophilic channel. We suggest a possibility of appearance of molecular behavior in the fluid near the wall within 10 nm-order scale. he field of microchemistry has been rapidly expanded, and various chemical operations have been integrated on a microchip by manipulating a small volume of sample in microscale fluidic channels. Microchemistry has achieved highefficiency and high-throughput chemical processing for biomedical and chemical analysis and chemical synthesis, and is now moving toward practical applications.1−4 As top-down nanofabrication methods developed, the integration chemistry is shifting from microscale to 10−1000 nm scale, which we term extended-nanoscale. Our group has created fluidic devices with size-regulated 10−100 nm channels (extended nanochannel) fabricated on a microchip as a platform of this new engineering field.5 An ultrasmall volume of aL−fL provides a potential of single molecule analysis in single cell for proteomics and regenerative medicine. Unique transport phenomena by dominant surface effects enable novel devices for separation, ion transport and energy harvesting. Understanding fluid flows in extended nanospace, where the liquid is in a transitional regime from single molecules to condensed phase, is fundamental issue in extended nanochemistry. Assuming the fluid dynamics with the bulk liquid properties, many researchers have considered fluid behavior in extended nanospace affected by the electric double layer, that is, an ion screening layer to cancel the surface charge. The double layer effects become dominant in extended nanospace because of increased surface-to-volume ratio, and can induce flows under double layer overlap,6−8 enhanced/suppressed ion transport,9,10 and electroviscosity.11,12 However, previous studies suggested that the conventional model of double layer in the far-field liquid cannot explain the experimental results
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© 2013 American Chemical Society
sufficiently. The liquid in nanochannels is more conductive than expected.13,14 Tendency of the electroviscosity does not agree with that of the experimental results.15,16 Most recent study suggested that the hydrogen ion distribution at dilute solution in a 400 nm nanochannel cannot be explained by the conventional model.17 On the other hand, our group has revealed unique liquid properties in extended nanospace, such as higher viscosity and lower permittivity.5,18 Especially, NMR studies of water confined in fused-silica extended nanospace revealed that the translational motion of water molecules is inhibited, and the proton exchange rate in water molecules increases with decreasing the space size. From these findings, we hypothesized a proton transfer phase of loosely coupled water molecules by hydrogen bond within the surface of 50 nm, which exists between the well-known adsorbed water phase on the surface and the bulk water phase.19,20 This hypothesis was supported by recent studies showing higher proton diffusion coefficients and enhanced proton dissociation.21,22 Currently, we consider an extended-nanoscale liquid model with the heterogeneous liquid structure.23−25 On the basis of these unique properties in extended nanospace, unique fluid flows with the heterogeneous liquid structure in 100 nm-order channels can be predicted. In addition, many researchers in fluid dynamics reported the fluid slip at the boundary, which can be induced by molecular Received: June 30, 2013 Accepted: October 21, 2013 Published: October 21, 2013 10780
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interactions at interfaces. The fluid near the surface has been investigated by various methods mainly in open/microspaces such as atomic force microscopy, capillary, surface force apparatus and particle image velocimetry.26,27 However, results are inconsistent, changing by the method and the scale of the fluidic system. Therefore, a direct measurement method with a spatial resolution smaller than the light wavelength for flow velocity distribution in nanochannels, which is most basic information for fluid dynamics, is strongly required. Recently, stimulated emission depletion (STED) microscopy, which is one of super resolution microscopy with far-field optics, was applied to the velocity measurements in a 100 nmorder capillary.28 STED microscopy can make illumination spot narrower than 100 nm to achieve a spatial resolution smaller than the light wavelength. Although the method requires a calibration process based on an assumption that the bulk theory of fluid dynamics is valid even in the extended nanospace, a flow profile in the extended naocapillary was obtained by using photobleaching of fluorescent molecules. However, revealing the fluid flow in extended nanospace is difficult owing to the measurement principle. In addition, effect of significant diffusion of molecular tracer in the nanocapillary on the flow measurement is not revealed. On the other hand, using near-field optics, evanescent wavebased particle tracking velocimetry has been developed to measure near-wall fluid flows within 100 nm-order scale.29,30 The evanescent wave generated by total internal reflection of light, which penetrates into the liquid within 100 nm from the surface, is used to illuminate near-wall particles flowing through the channel. Recent studies could measure the near-wall velocity distribution in microchannels, by using the exponentially decaying intensity of evanescent wave.31−33 The position of fluorescent tracer particles was determined from the fluorescent intensity with the evanescent wave field. In most cases, particles of 100 nm-order diameter have been used to ensure the signal intensity. This method is applicable to measurement of the fluid flow with heterogeneous liquid structure. In addition, by combining with nanochannels to confine the fluid, only the near-wall fluid can be focused. However, applying the method to nanochannel flows is still difficult because of the size of tracer particles in similar order to the channel. For the measurements of velocity distribution in 100 nmorder channels by the evanescent wave-based particle velocimetry, using 10 nm-order tracer particles is required. However, when the 10 nm-order tracer particles are used, the Brownian fluctuation of tracers by a typical time resolution of 10−3−10−2 s becomes similar order to the extended nanospace, and this will result in significant errors of velocity distribution. Also, the smaller tracer particles decrease signal intensity, making particle detection much difficult, especially in the exponentially decaying evanescent wave field. In addition, owing to dominant electrostatic surface effects, measurement results will be affected by nonuniform particle distribution in the nanochannels. In this study, we developed the evanescent wave-based particle tracking velocimetry to achieve spatially resolved measurements of extended nanochannel flows by using 64 nm tracer particles. A measurement system of 10−4 s time resolution was developed to make errors by the Brownian diffusion of tracers small to be neglected. In order to detect the flowing nanoparticles of weak fluorescent signal, a multitime particle tracking algorithm, which can remove error tracking,
was developed. Then errors of the particle detection and measurement region with the nonuniform particle distribution were evaluated. The developed method was demonstrated for measurements of velocity distribution of pressure-driven flows in a fused-silica channel of 410 nm depth. The fluid behavior in the nanochannel was discussed from the results.
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EXPERIMENTAL SECTION Materials and Chemicals. Carboxylate-modified fluorescent polystyrene particles of 64 ± 6 nm diameter, which was evaluated by dynamic light scattering, were used as the flow tracer. The tracer particles were seeded into water at a volume fraction of 0.002% to avoid the flow perturbation by the particles. The zeta-potential of the particle was evaluated to be −54 ± 8 mV by a Malvern Instruments Zetasizer. As a reference for the zeta-potential in a fused-silica nanochannel, the zeta-potential of 500 nm silica particles was evaluated to be −64 ± 6 mV. Extended Nanofluidic Device. The fabrication of microchip of nanochannels has been described previously.34,35 Nanochannels of 50 μm width, 410 nm depth and 2 mm length were fabricated on a fused-silica plate of a 0.17 mm thickness by electron beam lithography and plasma etching. The width and depth of the channels were measured by scanning electron microscopy and atomic force microscopy, respectively. Noted that error of the depth of the nanochannel is less than 2%, as shown in previous work.36 Then microchannels for the sample injection were fabricated on another fused-silica plate. Holes for inlets and outlets were made, and the channels were sealed by thermal fusion bonding. Figure 1 shows a schematic of pressure-driven flow control system, developed previously.34 The sample solution was driven
Figure 1. Schematic of (a) an fluidic device with fused-silica nanochannels, combined with a pressure-driven flow control system. (b) Cross-sectional view of the nanochannel.
and injected into the nanochannels by an air pressure of 100− 300 kPa. Since the microchannels were optimally designed to make a ratio of pressure loss in the nanochannel to that in the microchannel more than 99.9%, the applied pressure to the microchip can be regarded as that applied to the nanochannel. Prior to the experiments, the channels were cleaned by flashing acetone, ethanol, deionized water, 10−1 mol/L potassium hydroxide (KOH), and then rinsed by deionized water. Measurement System. Figure 2a illustrates a schematic of a measurement system, which consists of an inverted microscope, a CW Nd:YAG laser of 532 nm wavelength, and 10781
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Figure 3. Instantaneous fluorescence images of nanoparticles flowing through the nanochannel (t1 = t0 + Δt, t2 = t0 + 2Δt, t3 = t0 + 3Δt).
scale to the tracer particles. Noted that the displacement of the Brownian diffusion becomes much smaller in the near-wall region due to hydrodynamic hindrance effects by the channel wall.37,38 Image Processing. Using the fluorescence images, position, and velocity of nanoparticles flowing through the nanochannel were determined. The tracer nanoparticles in the fluorescence image were detected by an algorithm using binarization with dynamic thresholds. In this step, a diameter of particle image of 1.9 pixel, which was estimated from the point spread function, was also used for the particle detection from binarized image. However, owing to the exponentially decaying evanescent wave field, the nanoparticles far from the wall of total internal reflection have weak fluorescent intensity. When the fluorescent intensities of nanoparticles are weak, it is difficult to distinguish flowing nanoparticles from particle-like random noise and particles stuck on the wall of weak intensities by photobleaching. To remove the error tracking by the random noise and particles stuck on the wall, multitime particle tracking using sequential images was developed, as depicted in Figure 4a. This method is based on a principle that the tracer particle moves with the fluid flow, while the noise is generated randomly and the particles stuck on the wall have zero displacement. In the first step, the particle tracking during two frames was conducted by determining most neighboring particle images with highest cross correlation value between two images. Noted that the particle tracking in this study has a 37 nm uncertainty. Then the individual particles were tracked over four frames as shown in Figure 3. Since only the displacements by the tracer nanoparticle have components of the fluid flow, the tracer nanoparticles in the fluorescence image can be detected. The position of particles in the nanochannel was determined using the fluorescent particle images after correcting a nonlinearity of EMCCD sensitivity. The particle edge-wall distance h was estimated based on the exponentially decaying fluorescent intensity with the evanescent wave given by Ip ∝ exp(−h/zp), where Ip is the fluorescent intensity of particles and zp is the penetration depth. To ensure the exponential decay of the fluorescent intensity, the laser beam was adjusted to be p-polarized light to avoid interference of the light by multiple reflections in the tracer particles.30,32 Since whole region of the nanochannel in the depth-wise direction was illuminated, the particle edge-wall distance can be determined
Figure 2. Schematic of (a) a measurement system and (b) the evanescent wave illumination in the nanochannel.
an EMCCD camera (512 × 512 pixels, 16 μm/pixel, vertical shift rate of electron: 0.6 μs/row). The laser beam was converted to laser pulses by an acoustic optics modulator, and introduced into a prism located on a microchip. Then, the evanescent wave was generated by total internal reflection at an interface between the fused-silica wall and water in the nanochannel to illuminate the flowing nanoparticles (figure 2b). The power of laser beam was minimized to avoid fluorescence bleaching. Furthermore, considering the Gaussian intensity profile of the laser beam, only the center region of the evanescent wave illumination area was used for the measurements to achieve uniform illumination with error of the excitation intensity less than 7%. The fluorescence emitted from the tracer nanoparticles was collected by a 60 × oil immersion objective lens (NA = 1.42), and detected by the EMCCD camera through an optical filter passing wavelengths of 580−680 nm. Timings of image acquisition and laser pulse were synchronized by a pulse generator to control the time resolution Δt and avoid smear during frame transfer process of the EMCCD. The time resolution was controlled to be Δt = 10−4 s for suppressing errors by the Brownian fluctuation of tracer nanoparticles. The time resolution of particle tracking is the summation of the frame interval of EMCCD camera and the exposure time of the fluorescence imaging. In order to decrease the frame interval with transferring the electrons on the EMCCD, a region of 100 × 512 pixels (27 μm × 137 μm of the image), which was determined by limiting the exposure area by a slit, was used for the imaging. Hence the frame interval was 60 μs with the vertical shift of electrons through 100 rows. The time resolution was 260 μs by setting the exposure time to be 200 μs to obtain sufficient fluorescent intensities of nanoparticlesas shown in figure 3, with signal-to-noise ratio more than 5. The displacement of the Brownian fluctuation represented by (2DΔt)1/2, where D is the diffusion coefficient by the Stokes−Einstein relation, was 62 nm, which is similar 10782
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nanoparticles flowing through the extended nanochannel were successfully detected. This suggests an importance of the multitime particle tracking method for detecting nanoparticles of weak light intensities in measurements of nanochannel flows. The method to determine the particle position using the fluorescent intensity by the evanescent wave was verified. Figure 5a shows the number density of particles as function of
Figure 4. (a) Schematic of multitime particle tracking to detect the tracer nanoparticles by distinguishing these from the particle-like noises and particles stuck on the wall. (b) Number of detected particles as function of the particle displacement in comparison between the multitime particle tracking using four images and normal particle tracking using two images.
by using two reference particle intensities at the channel walls: maximum intensity I1 at h = 0 and minimum intensity I2 at h = H − 2a, where H is the channel depth and a is the particle radius h = (H − 2a)
Figure 5. (a) Number density of tracer nanoparticles as function of the depth-wise position z at different applied pressures. (b) The number density of tracer nanoparticles in the nanochannel as function of the applied pressure.
ln Ip − ln I1 ln I2 − ln I1
(1)
Here, the fluorescent intensity of particle Ip was calculated from summation of intensities within the diameter of particle image. Based on the particle position and displacement, the velocity distribution in the nanochannel was estimated.
the depth-wise position z estimated from the fluorescent intensities and the channel depth by eq 1. The fluorescent intensities of nanoparticles stuck on the channel walls (h = 0 and h = H − 2a) were used as references to determine the particle position. Since the penetration depth of the evanescent wave of zp = 127 nm calculated by eq 1 well agrees with that of zp = 132 nm calculated by the geometrical optics, the method using the fluorescent intensities and the channel depth was validated. In principle, the particles should be located at 32 nm ≤ z ≤ 346 nm by the measurement using 64 nm particles in the 410 nm channel. However, 1.2% of the whole particles are at z < 32 nm and z > 346 nm, which mean the particles are located inside the wall. This is considered to be errors due to the polydispersity and the Brownian diffusion of nanoparticles. From the error propagation law considering the particle polydispersity and variation of the fluorescent intensities, error of the particle position was estimated to be 33 nm, which is sufficiently small for determining the position of 64 nm particle. As reported in previous studies in colloid science,39 the nonuniform particle distribution was induced mainly by the electrostatic repulsion between the negatively charged fusedsilica and particle surfaces, as shown in Figure 5a. Since the Debye length40 is in the order of 100 nm in case of the water, depletion of nanoparticles near the wall is observed. This suggests that the quantity of data is less in the near-wall region
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RESULTS AND DISCUSSION Evaluation of Measurement Method for Nanochannel Flows. The method of multitime particle tracking for particle detection in fluorescence images was evaluated. Figure 4b shows the stream-wise displacements in pressure-driven flow at 100 kPa, obtained by the three-time particle tracking using four sequential images (figure 3), compared with those by the normal particle tracking using two images. For both cases, there are two peaks of the number of particles toward the displacement. Since ensemble average of the random noise is zero and the particles stuck on the wall do not move, the particles of the peak around the zero displacement are particlelike noises and the stuck particles. The particles of another peak of a displacement increasing with time are the tracer particles flowing through the nanochannel. However, for the normal tracking method, it is difficult to completely separate the displacements by particle motion from those by the random noise and the stuck particles. On the other hand, the displacements by particle motion were easily distinguished in the three-time particle tracking: 30% of the obtained displacements in Figure 4b are by the particle motion. Hence the tracer 10783
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The velocities have parabolic profile, and increase with increasing the applied pressure. Since the fused-silica surface is hydrophilic with strong interactions with water molecules, the no-slip boundary condition is considered in the bulk theory. On the basis of the Reynolds number of 10−3 in this study, the results were compared with the theory given by the Hagen− Poiseuille equation for the fluid flow between flat plates
than the channel center, and affects the experimental results. In the present study using 1500 image pairs for particle tracking, the measurement region having more than 100 data was 52 nm < z < 352 nm. Furthermore, the results suggest that the number of particles in the nanochannel is increased with increasing the applied pressure. The spatially averaged number density of particles in the nanochannel shows approximately linear relationship with the applied pressure, as shown in Figure 5b. These results suggest that the particle injection into the nanochannel is prevented by resistive interactions at an interface between microchannel and nanochannel. One reason is considered to be the electrostatic repulsive interaction between the negatively charged particles and the nanochannel of negative electrostatic potential with the 100 nm-order Debye length. Entropic effect in the particle behavior can be another reason considering the particle size and the diffusion scale. Since the pressure-driven injection of materials into the nanochannel is an important issue not only in the particle tracking velocimetry but also in nanofluidics such as selective transport, separation and manipulating biomolecules, this will be studied precisely in future work. In conclusions, evanescent wave-based particle tracking velocimetry was developed for the measurements of extended nanochannel flows. The nanoparticles flowing through the channel of weak fluorescent intensities were successfully detected by the multitime particle tracking method. The particle position could be determined by using the fluorescent intensity, and the method can be applied to the measurement of velocity distribution in the extended nanochannel. However, because of the particle diameter of 64 nm and the particle depletion near the wall, it is still difficult to directly investigate the near-wall region within 50 nm. Therefore, the method will be further developed by using smaller tracers, considering possible error factors such as weaker signal intensity, significant particle diffusion and effect of the polydispersity. Velocity Distribution of Pressure-Driven Flow. The developed method was demonstrated for pressure-driven flows in the 410 nm channel. Figure 6 shows velocity distribution as function of the depth-wise position z obtained by the evanescent wave-based particle tracking velocimetry. Since the velocities of 5000 individual tracer particles were shown, the measured velocities have fluctuation by the Brownian diffusion.
u=−
1 dp (Hz − z 2) 2μ dx
(2)
where μ is the viscosity and p is the pressure. Our recent study revealed that the water viscosity is significantly increased in 100 nm-order square channels (nanoscale width and depth), while that is similar to the bulk value in plate channels of microscale width and 100 nm-order depth.36 Hence the viscosity of bulk water at 25 °C of 0.894 × 10−3 Pa s was used for the calculation by eq 2. The results suggest that the magnitude of velocities approximately agrees with the theoretical values. To further investigate the fluid flows in the nanochannel, the flow profile was estimated by the fitting using least-squares method. In contrast to the bulk theory for hydrophilic surface, the flow profiles obtained by the fitting show slip velocities at the walls. The magnitude of slippage was evaluated as the slip length b, given by us = b
∂u ∂z
z=0
(3)
where us is the slip velocitiy and ∂u/∂z|z=0 is the shear rate at the wall. From the results, the slip length was estimated to be b = 189 ± 32 nm. However, in such large slip length, the flow velocity must be much higher than the theoretical value with the bulk viscosity, which is inconsistent with the experimental results. Therefore, the estimated wall velocities cannot be simply regarded as “slip”. Several possibilities are suggested to explain the results. Since the particle size is only 6.4 times smaller than the channel size, the hydrodynamic interaction between the particle and the walls, which has been studied traditionally,41 can be considered. Previous study for the particle motion between two parallel walls suggested that the particle velocity becomes lower than the fluid velocity by the hydrodynamic interaction when 2a/H > 0.2.42 On the other hand, in the present study, the particle is sufficiently small (2a/H = 0.16), and the tendency is opposite to the experimental results indicating higher velocities than the theoretical fluid velocity near the wall. Therefore, the hydrodynamic interaction by the walls is considered to be negligible. Another possibility is that the bulk fluid dynamics does not hold in 10 nm-order scale because of the appearance of molecular behavior. Recent studies by molecular dynamics simulation suggest that the hydrodynamics holds down to approximately 3−6 nm though the fluid viscosity and slip condition affected by the adsorbed layer of liquid molecules within 1 nm must be considered.43,44 However, these results have not been sufficiently proved due to lack of experimental methodology. Recently, evanescent wave-based particle tracking velocimetry using 100 nm-order tracer particles has been applied to examine near-wall flows in microchannels.31,45 These results also suggested velocities at the wall, which were evaluated as slip lengths of less than 50 nm for hydrophilic surfaces, as well as the present study. Furthermore, our group has revealed that molecular behavior affected by the fused-silica
Figure 6. Velocity of tracer nanoparticle u as function of the depthwise position z at different applied pressure. The velocities of 5000 nanoparticles at Δt = 260 μs were shown. Solid line and dotted line indicate the theoretical values calculated from the Hagen−Poiseuille equation and the fitting curve obtained by the least-squares method, respectively. 10784
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ACKNOWLEDGMENTS This work was supported by a Grant-in-Aids for Specially Promoted Research and Young Researchers (A) from the Japan Society for the Promotion of Science (JSPS) and JSPS Core-toCore Program.
surface appeared in the water properties in 10−100 nm spaces.18 To clarify the hydrodynamic boundary effect with molecular picture in this scale, further study is required after solving subjects such as error of the particle position by polydispersity and smaller tracer particles for higher resolution.
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CONCLUSIONS
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AUTHOR INFORMATION
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REFERENCES
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Particle tracking velocimetry using the evanescent wave illumination was developed to measure velocity distribution of fluid flows in extended nanochannels. 64 nm fluorescent particles were used as the flow tracer in order to conduct the measurements in a fused-silica channel of 410 nm depth. The velocity was estimated from the particle displacement, and the particle position was determined from the fluorescent intensity with the exponentially decaying evanescent wave field with a resolution smaller than the light wavelengths. For suppressing error by the Brownian diffusion of tracer particle, a measurement system of a time resolution of 260 μs was developed to achieve a diffusion scale within the particle size. An image processing by multitime particle tracking using sequential particle images was established to detect the tracer particles of weak fluorescent intensities. Effect of nonuniform distribution of tracer particles in the nanochannel by the electrostatic interaction was verified. Then the developed method was demonstrated for pressure-driven flows of water in the nanochannel. The developed method could be applied to the measurements of extended nanochannel flows. By using the multitime particle tracking method, the flowing nanoparticles in the nanochannel were successfully detected by distinguishing the tracer particles from particle-like noises in the images. The particle position in the nanochannel was determined with an error of 33 nm. The measurement region was far from the wall of 50 nm, owing to the particle depletion near the wall by the electrostatic repulsion between negatively charged surfaces. In addition, resistive interaction for the particle injection into the nanochannel was observed, probably due to the electrostatic and entropic effects. The method developed in this study can be applied to study not only fluid flows but also particle behaviors in extended nanospace, which are fundamental issues for designing novel devices in extended nanochemistry. Velocity distribution of pressure-driven flows in the 410 nm channel was successfully obtained. The particle velocities showed parabolic profiles with velocity magnitude in approximate agreement with the bulk theory of fluid dynamics. However, the obtained velocities indicated slip velocities even in the hydrophilic nanochannel. We suggest a possibility of appearance of molecular behavior in the fluid near the wall within 10 nm-order scale, based on our previous study revealing unique water properties in 10−100 nm spaces. We will further investigate the fluid flows in extended nanochannels, by developing the method of greater spatial resolution.
Corresponding Author
*Phone: +81-3-5841-7231. Fax: +81-3-5841-6039. E-mail: [email protected]. Notes
The authors declare no competing financial interest. 10785
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Evanescent Wave-Based Particle Tracking Velocimetry for Nanochannel Flows Yutaka Kazoe, Keizo Iseki, Kazuma Mawatari, and Takehiko Kitamori* Department of Applied Chemistry, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan ABSTRACT: Understanding fluid flows in 10−1000 nm space, which we call extended nanospace, is important for novel nanofluidic devices in analytical chemistry. This study therefore developed a particle tracking velocimetry for measuring velocity distribution in nanochannel flows, by using the evanescent wave illumination. 64 nm fluorescent nanoparticles were used as flow tracer. The particle position was determined from fluorescent intensity by the evanescent wave field, with a spatial resolution smaller than light wavelengths. The time resolution of 260 μs was achieved to make error by the Brownian diffusion of the tracer small to be neglected. An image processing by multitime particle tracking was established to detect the tracer nanoparticles of weak fluorescent intensity. Though the measurement region was affected by nonuniform particle distribution with the electrostatic interactions, pressure-driven flows of water in a nanochannel of 50 μm width and 410 nm depth were successfully measured. The results of the velocity distribution in the depth-wise direction approximately showed agreement with the fluid dynamics with the bulk liquid properties from the macroscopic view, however, suggested slip velocities even in the hydrophilic channel. We suggest a possibility of appearance of molecular behavior in the fluid near the wall within 10 nm-order scale. he field of microchemistry has been rapidly expanded, and various chemical operations have been integrated on a microchip by manipulating a small volume of sample in microscale fluidic channels. Microchemistry has achieved highefficiency and high-throughput chemical processing for biomedical and chemical analysis and chemical synthesis, and is now moving toward practical applications.1−4 As top-down nanofabrication methods developed, the integration chemistry is shifting from microscale to 10−1000 nm scale, which we term extended-nanoscale. Our group has created fluidic devices with size-regulated 10−100 nm channels (extended nanochannel) fabricated on a microchip as a platform of this new engineering field.5 An ultrasmall volume of aL−fL provides a potential of single molecule analysis in single cell for proteomics and regenerative medicine. Unique transport phenomena by dominant surface effects enable novel devices for separation, ion transport and energy harvesting. Understanding fluid flows in extended nanospace, where the liquid is in a transitional regime from single molecules to condensed phase, is fundamental issue in extended nanochemistry. Assuming the fluid dynamics with the bulk liquid properties, many researchers have considered fluid behavior in extended nanospace affected by the electric double layer, that is, an ion screening layer to cancel the surface charge. The double layer effects become dominant in extended nanospace because of increased surface-to-volume ratio, and can induce flows under double layer overlap,6−8 enhanced/suppressed ion transport,9,10 and electroviscosity.11,12 However, previous studies suggested that the conventional model of double layer in the far-field liquid cannot explain the experimental results
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sufficiently. The liquid in nanochannels is more conductive than expected.13,14 Tendency of the electroviscosity does not agree with that of the experimental results.15,16 Most recent study suggested that the hydrogen ion distribution at dilute solution in a 400 nm nanochannel cannot be explained by the conventional model.17 On the other hand, our group has revealed unique liquid properties in extended nanospace, such as higher viscosity and lower permittivity.5,18 Especially, NMR studies of water confined in fused-silica extended nanospace revealed that the translational motion of water molecules is inhibited, and the proton exchange rate in water molecules increases with decreasing the space size. From these findings, we hypothesized a proton transfer phase of loosely coupled water molecules by hydrogen bond within the surface of 50 nm, which exists between the well-known adsorbed water phase on the surface and the bulk water phase.19,20 This hypothesis was supported by recent studies showing higher proton diffusion coefficients and enhanced proton dissociation.21,22 Currently, we consider an extended-nanoscale liquid model with the heterogeneous liquid structure.23−25 On the basis of these unique properties in extended nanospace, unique fluid flows with the heterogeneous liquid structure in 100 nm-order channels can be predicted. In addition, many researchers in fluid dynamics reported the fluid slip at the boundary, which can be induced by molecular Received: June 30, 2013 Accepted: October 21, 2013 Published: October 21, 2013 10780
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interactions at interfaces. The fluid near the surface has been investigated by various methods mainly in open/microspaces such as atomic force microscopy, capillary, surface force apparatus and particle image velocimetry.26,27 However, results are inconsistent, changing by the method and the scale of the fluidic system. Therefore, a direct measurement method with a spatial resolution smaller than the light wavelength for flow velocity distribution in nanochannels, which is most basic information for fluid dynamics, is strongly required. Recently, stimulated emission depletion (STED) microscopy, which is one of super resolution microscopy with far-field optics, was applied to the velocity measurements in a 100 nmorder capillary.28 STED microscopy can make illumination spot narrower than 100 nm to achieve a spatial resolution smaller than the light wavelength. Although the method requires a calibration process based on an assumption that the bulk theory of fluid dynamics is valid even in the extended nanospace, a flow profile in the extended naocapillary was obtained by using photobleaching of fluorescent molecules. However, revealing the fluid flow in extended nanospace is difficult owing to the measurement principle. In addition, effect of significant diffusion of molecular tracer in the nanocapillary on the flow measurement is not revealed. On the other hand, using near-field optics, evanescent wavebased particle tracking velocimetry has been developed to measure near-wall fluid flows within 100 nm-order scale.29,30 The evanescent wave generated by total internal reflection of light, which penetrates into the liquid within 100 nm from the surface, is used to illuminate near-wall particles flowing through the channel. Recent studies could measure the near-wall velocity distribution in microchannels, by using the exponentially decaying intensity of evanescent wave.31−33 The position of fluorescent tracer particles was determined from the fluorescent intensity with the evanescent wave field. In most cases, particles of 100 nm-order diameter have been used to ensure the signal intensity. This method is applicable to measurement of the fluid flow with heterogeneous liquid structure. In addition, by combining with nanochannels to confine the fluid, only the near-wall fluid can be focused. However, applying the method to nanochannel flows is still difficult because of the size of tracer particles in similar order to the channel. For the measurements of velocity distribution in 100 nmorder channels by the evanescent wave-based particle velocimetry, using 10 nm-order tracer particles is required. However, when the 10 nm-order tracer particles are used, the Brownian fluctuation of tracers by a typical time resolution of 10−3−10−2 s becomes similar order to the extended nanospace, and this will result in significant errors of velocity distribution. Also, the smaller tracer particles decrease signal intensity, making particle detection much difficult, especially in the exponentially decaying evanescent wave field. In addition, owing to dominant electrostatic surface effects, measurement results will be affected by nonuniform particle distribution in the nanochannels. In this study, we developed the evanescent wave-based particle tracking velocimetry to achieve spatially resolved measurements of extended nanochannel flows by using 64 nm tracer particles. A measurement system of 10−4 s time resolution was developed to make errors by the Brownian diffusion of tracers small to be neglected. In order to detect the flowing nanoparticles of weak fluorescent signal, a multitime particle tracking algorithm, which can remove error tracking,
was developed. Then errors of the particle detection and measurement region with the nonuniform particle distribution were evaluated. The developed method was demonstrated for measurements of velocity distribution of pressure-driven flows in a fused-silica channel of 410 nm depth. The fluid behavior in the nanochannel was discussed from the results.
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EXPERIMENTAL SECTION Materials and Chemicals. Carboxylate-modified fluorescent polystyrene particles of 64 ± 6 nm diameter, which was evaluated by dynamic light scattering, were used as the flow tracer. The tracer particles were seeded into water at a volume fraction of 0.002% to avoid the flow perturbation by the particles. The zeta-potential of the particle was evaluated to be −54 ± 8 mV by a Malvern Instruments Zetasizer. As a reference for the zeta-potential in a fused-silica nanochannel, the zeta-potential of 500 nm silica particles was evaluated to be −64 ± 6 mV. Extended Nanofluidic Device. The fabrication of microchip of nanochannels has been described previously.34,35 Nanochannels of 50 μm width, 410 nm depth and 2 mm length were fabricated on a fused-silica plate of a 0.17 mm thickness by electron beam lithography and plasma etching. The width and depth of the channels were measured by scanning electron microscopy and atomic force microscopy, respectively. Noted that error of the depth of the nanochannel is less than 2%, as shown in previous work.36 Then microchannels for the sample injection were fabricated on another fused-silica plate. Holes for inlets and outlets were made, and the channels were sealed by thermal fusion bonding. Figure 1 shows a schematic of pressure-driven flow control system, developed previously.34 The sample solution was driven
Figure 1. Schematic of (a) an fluidic device with fused-silica nanochannels, combined with a pressure-driven flow control system. (b) Cross-sectional view of the nanochannel.
and injected into the nanochannels by an air pressure of 100− 300 kPa. Since the microchannels were optimally designed to make a ratio of pressure loss in the nanochannel to that in the microchannel more than 99.9%, the applied pressure to the microchip can be regarded as that applied to the nanochannel. Prior to the experiments, the channels were cleaned by flashing acetone, ethanol, deionized water, 10−1 mol/L potassium hydroxide (KOH), and then rinsed by deionized water. Measurement System. Figure 2a illustrates a schematic of a measurement system, which consists of an inverted microscope, a CW Nd:YAG laser of 532 nm wavelength, and 10781
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Figure 3. Instantaneous fluorescence images of nanoparticles flowing through the nanochannel (t1 = t0 + Δt, t2 = t0 + 2Δt, t3 = t0 + 3Δt).
scale to the tracer particles. Noted that the displacement of the Brownian diffusion becomes much smaller in the near-wall region due to hydrodynamic hindrance effects by the channel wall.37,38 Image Processing. Using the fluorescence images, position, and velocity of nanoparticles flowing through the nanochannel were determined. The tracer nanoparticles in the fluorescence image were detected by an algorithm using binarization with dynamic thresholds. In this step, a diameter of particle image of 1.9 pixel, which was estimated from the point spread function, was also used for the particle detection from binarized image. However, owing to the exponentially decaying evanescent wave field, the nanoparticles far from the wall of total internal reflection have weak fluorescent intensity. When the fluorescent intensities of nanoparticles are weak, it is difficult to distinguish flowing nanoparticles from particle-like random noise and particles stuck on the wall of weak intensities by photobleaching. To remove the error tracking by the random noise and particles stuck on the wall, multitime particle tracking using sequential images was developed, as depicted in Figure 4a. This method is based on a principle that the tracer particle moves with the fluid flow, while the noise is generated randomly and the particles stuck on the wall have zero displacement. In the first step, the particle tracking during two frames was conducted by determining most neighboring particle images with highest cross correlation value between two images. Noted that the particle tracking in this study has a 37 nm uncertainty. Then the individual particles were tracked over four frames as shown in Figure 3. Since only the displacements by the tracer nanoparticle have components of the fluid flow, the tracer nanoparticles in the fluorescence image can be detected. The position of particles in the nanochannel was determined using the fluorescent particle images after correcting a nonlinearity of EMCCD sensitivity. The particle edge-wall distance h was estimated based on the exponentially decaying fluorescent intensity with the evanescent wave given by Ip ∝ exp(−h/zp), where Ip is the fluorescent intensity of particles and zp is the penetration depth. To ensure the exponential decay of the fluorescent intensity, the laser beam was adjusted to be p-polarized light to avoid interference of the light by multiple reflections in the tracer particles.30,32 Since whole region of the nanochannel in the depth-wise direction was illuminated, the particle edge-wall distance can be determined
Figure 2. Schematic of (a) a measurement system and (b) the evanescent wave illumination in the nanochannel.
an EMCCD camera (512 × 512 pixels, 16 μm/pixel, vertical shift rate of electron: 0.6 μs/row). The laser beam was converted to laser pulses by an acoustic optics modulator, and introduced into a prism located on a microchip. Then, the evanescent wave was generated by total internal reflection at an interface between the fused-silica wall and water in the nanochannel to illuminate the flowing nanoparticles (figure 2b). The power of laser beam was minimized to avoid fluorescence bleaching. Furthermore, considering the Gaussian intensity profile of the laser beam, only the center region of the evanescent wave illumination area was used for the measurements to achieve uniform illumination with error of the excitation intensity less than 7%. The fluorescence emitted from the tracer nanoparticles was collected by a 60 × oil immersion objective lens (NA = 1.42), and detected by the EMCCD camera through an optical filter passing wavelengths of 580−680 nm. Timings of image acquisition and laser pulse were synchronized by a pulse generator to control the time resolution Δt and avoid smear during frame transfer process of the EMCCD. The time resolution was controlled to be Δt = 10−4 s for suppressing errors by the Brownian fluctuation of tracer nanoparticles. The time resolution of particle tracking is the summation of the frame interval of EMCCD camera and the exposure time of the fluorescence imaging. In order to decrease the frame interval with transferring the electrons on the EMCCD, a region of 100 × 512 pixels (27 μm × 137 μm of the image), which was determined by limiting the exposure area by a slit, was used for the imaging. Hence the frame interval was 60 μs with the vertical shift of electrons through 100 rows. The time resolution was 260 μs by setting the exposure time to be 200 μs to obtain sufficient fluorescent intensities of nanoparticlesas shown in figure 3, with signal-to-noise ratio more than 5. The displacement of the Brownian fluctuation represented by (2DΔt)1/2, where D is the diffusion coefficient by the Stokes−Einstein relation, was 62 nm, which is similar 10782
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nanoparticles flowing through the extended nanochannel were successfully detected. This suggests an importance of the multitime particle tracking method for detecting nanoparticles of weak light intensities in measurements of nanochannel flows. The method to determine the particle position using the fluorescent intensity by the evanescent wave was verified. Figure 5a shows the number density of particles as function of
Figure 4. (a) Schematic of multitime particle tracking to detect the tracer nanoparticles by distinguishing these from the particle-like noises and particles stuck on the wall. (b) Number of detected particles as function of the particle displacement in comparison between the multitime particle tracking using four images and normal particle tracking using two images.
by using two reference particle intensities at the channel walls: maximum intensity I1 at h = 0 and minimum intensity I2 at h = H − 2a, where H is the channel depth and a is the particle radius h = (H − 2a)
Figure 5. (a) Number density of tracer nanoparticles as function of the depth-wise position z at different applied pressures. (b) The number density of tracer nanoparticles in the nanochannel as function of the applied pressure.
ln Ip − ln I1 ln I2 − ln I1
(1)
Here, the fluorescent intensity of particle Ip was calculated from summation of intensities within the diameter of particle image. Based on the particle position and displacement, the velocity distribution in the nanochannel was estimated.
the depth-wise position z estimated from the fluorescent intensities and the channel depth by eq 1. The fluorescent intensities of nanoparticles stuck on the channel walls (h = 0 and h = H − 2a) were used as references to determine the particle position. Since the penetration depth of the evanescent wave of zp = 127 nm calculated by eq 1 well agrees with that of zp = 132 nm calculated by the geometrical optics, the method using the fluorescent intensities and the channel depth was validated. In principle, the particles should be located at 32 nm ≤ z ≤ 346 nm by the measurement using 64 nm particles in the 410 nm channel. However, 1.2% of the whole particles are at z < 32 nm and z > 346 nm, which mean the particles are located inside the wall. This is considered to be errors due to the polydispersity and the Brownian diffusion of nanoparticles. From the error propagation law considering the particle polydispersity and variation of the fluorescent intensities, error of the particle position was estimated to be 33 nm, which is sufficiently small for determining the position of 64 nm particle. As reported in previous studies in colloid science,39 the nonuniform particle distribution was induced mainly by the electrostatic repulsion between the negatively charged fusedsilica and particle surfaces, as shown in Figure 5a. Since the Debye length40 is in the order of 100 nm in case of the water, depletion of nanoparticles near the wall is observed. This suggests that the quantity of data is less in the near-wall region
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RESULTS AND DISCUSSION Evaluation of Measurement Method for Nanochannel Flows. The method of multitime particle tracking for particle detection in fluorescence images was evaluated. Figure 4b shows the stream-wise displacements in pressure-driven flow at 100 kPa, obtained by the three-time particle tracking using four sequential images (figure 3), compared with those by the normal particle tracking using two images. For both cases, there are two peaks of the number of particles toward the displacement. Since ensemble average of the random noise is zero and the particles stuck on the wall do not move, the particles of the peak around the zero displacement are particlelike noises and the stuck particles. The particles of another peak of a displacement increasing with time are the tracer particles flowing through the nanochannel. However, for the normal tracking method, it is difficult to completely separate the displacements by particle motion from those by the random noise and the stuck particles. On the other hand, the displacements by particle motion were easily distinguished in the three-time particle tracking: 30% of the obtained displacements in Figure 4b are by the particle motion. Hence the tracer 10783
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The velocities have parabolic profile, and increase with increasing the applied pressure. Since the fused-silica surface is hydrophilic with strong interactions with water molecules, the no-slip boundary condition is considered in the bulk theory. On the basis of the Reynolds number of 10−3 in this study, the results were compared with the theory given by the Hagen− Poiseuille equation for the fluid flow between flat plates
than the channel center, and affects the experimental results. In the present study using 1500 image pairs for particle tracking, the measurement region having more than 100 data was 52 nm < z < 352 nm. Furthermore, the results suggest that the number of particles in the nanochannel is increased with increasing the applied pressure. The spatially averaged number density of particles in the nanochannel shows approximately linear relationship with the applied pressure, as shown in Figure 5b. These results suggest that the particle injection into the nanochannel is prevented by resistive interactions at an interface between microchannel and nanochannel. One reason is considered to be the electrostatic repulsive interaction between the negatively charged particles and the nanochannel of negative electrostatic potential with the 100 nm-order Debye length. Entropic effect in the particle behavior can be another reason considering the particle size and the diffusion scale. Since the pressure-driven injection of materials into the nanochannel is an important issue not only in the particle tracking velocimetry but also in nanofluidics such as selective transport, separation and manipulating biomolecules, this will be studied precisely in future work. In conclusions, evanescent wave-based particle tracking velocimetry was developed for the measurements of extended nanochannel flows. The nanoparticles flowing through the channel of weak fluorescent intensities were successfully detected by the multitime particle tracking method. The particle position could be determined by using the fluorescent intensity, and the method can be applied to the measurement of velocity distribution in the extended nanochannel. However, because of the particle diameter of 64 nm and the particle depletion near the wall, it is still difficult to directly investigate the near-wall region within 50 nm. Therefore, the method will be further developed by using smaller tracers, considering possible error factors such as weaker signal intensity, significant particle diffusion and effect of the polydispersity. Velocity Distribution of Pressure-Driven Flow. The developed method was demonstrated for pressure-driven flows in the 410 nm channel. Figure 6 shows velocity distribution as function of the depth-wise position z obtained by the evanescent wave-based particle tracking velocimetry. Since the velocities of 5000 individual tracer particles were shown, the measured velocities have fluctuation by the Brownian diffusion.
u=−
1 dp (Hz − z 2) 2μ dx
(2)
where μ is the viscosity and p is the pressure. Our recent study revealed that the water viscosity is significantly increased in 100 nm-order square channels (nanoscale width and depth), while that is similar to the bulk value in plate channels of microscale width and 100 nm-order depth.36 Hence the viscosity of bulk water at 25 °C of 0.894 × 10−3 Pa s was used for the calculation by eq 2. The results suggest that the magnitude of velocities approximately agrees with the theoretical values. To further investigate the fluid flows in the nanochannel, the flow profile was estimated by the fitting using least-squares method. In contrast to the bulk theory for hydrophilic surface, the flow profiles obtained by the fitting show slip velocities at the walls. The magnitude of slippage was evaluated as the slip length b, given by us = b
∂u ∂z
z=0
(3)
where us is the slip velocitiy and ∂u/∂z|z=0 is the shear rate at the wall. From the results, the slip length was estimated to be b = 189 ± 32 nm. However, in such large slip length, the flow velocity must be much higher than the theoretical value with the bulk viscosity, which is inconsistent with the experimental results. Therefore, the estimated wall velocities cannot be simply regarded as “slip”. Several possibilities are suggested to explain the results. Since the particle size is only 6.4 times smaller than the channel size, the hydrodynamic interaction between the particle and the walls, which has been studied traditionally,41 can be considered. Previous study for the particle motion between two parallel walls suggested that the particle velocity becomes lower than the fluid velocity by the hydrodynamic interaction when 2a/H > 0.2.42 On the other hand, in the present study, the particle is sufficiently small (2a/H = 0.16), and the tendency is opposite to the experimental results indicating higher velocities than the theoretical fluid velocity near the wall. Therefore, the hydrodynamic interaction by the walls is considered to be negligible. Another possibility is that the bulk fluid dynamics does not hold in 10 nm-order scale because of the appearance of molecular behavior. Recent studies by molecular dynamics simulation suggest that the hydrodynamics holds down to approximately 3−6 nm though the fluid viscosity and slip condition affected by the adsorbed layer of liquid molecules within 1 nm must be considered.43,44 However, these results have not been sufficiently proved due to lack of experimental methodology. Recently, evanescent wave-based particle tracking velocimetry using 100 nm-order tracer particles has been applied to examine near-wall flows in microchannels.31,45 These results also suggested velocities at the wall, which were evaluated as slip lengths of less than 50 nm for hydrophilic surfaces, as well as the present study. Furthermore, our group has revealed that molecular behavior affected by the fused-silica
Figure 6. Velocity of tracer nanoparticle u as function of the depthwise position z at different applied pressure. The velocities of 5000 nanoparticles at Δt = 260 μs were shown. Solid line and dotted line indicate the theoretical values calculated from the Hagen−Poiseuille equation and the fitting curve obtained by the least-squares method, respectively. 10784
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ACKNOWLEDGMENTS This work was supported by a Grant-in-Aids for Specially Promoted Research and Young Researchers (A) from the Japan Society for the Promotion of Science (JSPS) and JSPS Core-toCore Program.
surface appeared in the water properties in 10−100 nm spaces.18 To clarify the hydrodynamic boundary effect with molecular picture in this scale, further study is required after solving subjects such as error of the particle position by polydispersity and smaller tracer particles for higher resolution.
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CONCLUSIONS
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AUTHOR INFORMATION
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REFERENCES
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Particle tracking velocimetry using the evanescent wave illumination was developed to measure velocity distribution of fluid flows in extended nanochannels. 64 nm fluorescent particles were used as the flow tracer in order to conduct the measurements in a fused-silica channel of 410 nm depth. The velocity was estimated from the particle displacement, and the particle position was determined from the fluorescent intensity with the exponentially decaying evanescent wave field with a resolution smaller than the light wavelengths. For suppressing error by the Brownian diffusion of tracer particle, a measurement system of a time resolution of 260 μs was developed to achieve a diffusion scale within the particle size. An image processing by multitime particle tracking using sequential particle images was established to detect the tracer particles of weak fluorescent intensities. Effect of nonuniform distribution of tracer particles in the nanochannel by the electrostatic interaction was verified. Then the developed method was demonstrated for pressure-driven flows of water in the nanochannel. The developed method could be applied to the measurements of extended nanochannel flows. By using the multitime particle tracking method, the flowing nanoparticles in the nanochannel were successfully detected by distinguishing the tracer particles from particle-like noises in the images. The particle position in the nanochannel was determined with an error of 33 nm. The measurement region was far from the wall of 50 nm, owing to the particle depletion near the wall by the electrostatic repulsion between negatively charged surfaces. In addition, resistive interaction for the particle injection into the nanochannel was observed, probably due to the electrostatic and entropic effects. The method developed in this study can be applied to study not only fluid flows but also particle behaviors in extended nanospace, which are fundamental issues for designing novel devices in extended nanochemistry. Velocity distribution of pressure-driven flows in the 410 nm channel was successfully obtained. The particle velocities showed parabolic profiles with velocity magnitude in approximate agreement with the bulk theory of fluid dynamics. However, the obtained velocities indicated slip velocities even in the hydrophilic nanochannel. We suggest a possibility of appearance of molecular behavior in the fluid near the wall within 10 nm-order scale, based on our previous study revealing unique water properties in 10−100 nm spaces. We will further investigate the fluid flows in extended nanochannels, by developing the method of greater spatial resolution.
Corresponding Author
*Phone: +81-3-5841-7231. Fax: +81-3-5841-6039. E-mail: [email protected]. Notes
The authors declare no competing financial interest. 10785
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