Title of Paper
Velocity measurement of whole flow field in a microchannel
Zhan-Hua Silber-Li1, Hongwei Gai2 and Bingcheng Lin2
1. LNM, Institute of Mechanics, Chinese Academic of Sciences, Beijing 100080,China
2. Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023,China
Corresponding author Zhan-Hua Silber-Li
E-mail: , Telephone: 86-10-6252 4839
Correspond address: 15, Bei Si Huan Xi Lu, Beijing 100080
Abstract
With the system combining with the wide field and the evanescent wave excitation modes, we can measure the flow velocities in the middle and at bottom of a microchannel simultaneously. Fluorescent microbeads with a diameter of 175 nm and lDNA molecules were used as flowing tracers. The measured velocities of particles or single molecules in microchannel with two modes were compared qualitatively with the calculated values based on Hagen-Poiseuille theory when the diameter of microbead was considered. The experiment demonstrates that, with the evanescent wave mode, the observation of flow field in micro scale will be more completed.
Keyword: TIR, Micro/Nano-PIV, lDNA, microchannel
1. Introduction
This PIV is a major and well-established technique for measuring velocity fields in macroscopic fluid systems 1. With the development of Microfluidic system, the visualization in microchannels has been required. Santiago et al. (1998) 2 and Meinhart et al (1999) 3 developed the Micro-PIV, which has been successfully used in measuring flow field in microchannels 4. But limited by the depth of field of the imaging optics, the spatial resolution of PIV system is approximately a few microns. In order to observer flow field with sub-micron or nanometer length scales, Zetter and Yoda (2003) 5 have developed recently a Nano-PIV system using evanescent wave from the TIR. The penetration depth of illumination light by evanescent wave can reach to ~0(10-100nm), therefore this new generation PIV permitted us to observer the flow field in the order of nanometer from the bottom. Breuer et al (2004) 6 have introduced this kind system in their studies about wall slip etc.
In this paper, we will present the preliminary experimental results obtained in a Micro/NanoPIV system, which is developed by Gai et al 7, ICP, CAS, China. This system includes a laser-induced fluorescence imaging system that can be easily switched between evanescent wave excitation mode and wide field excitation mode, therefore we can choose Micro- or Nano-PIV simultaneously. The 175 nm fluorescence microbeads and lDNA molecules were used to measure velocities respectively. The experimental results, in the middle and at the bottom of the channel, were compared qualitatively with the theoretic values.
2. Experimental methods
2.1 Experimental equipment
The experimental setup is shown in Figure 1A. A Zeiss Microscope was used to collect the fluorescence from the microchannel with a 20×/0.75 NA plan Apochromat objective or a 40×/0.75 NA plan Neofluar objective. The light source was a water-cooled argon ion laser (488 nm; Spectra Physics, Mountain View, CA, USA). Extraneous light and plasma lines from the laser were eliminated prior to its entry into the observation region with the aid of an equilateral dispersing prism and an optical pinhole. The laser beam passed through a mechanical shutter with programmable control (LS2Z2, Vincent Associates, Rochester, NY, USA) and was focused with a 20-cm focal length lens (Melles Griot, Irvine, CA, USA). A beamsplitter (Factory Affiliated of Shanghai University of Technology, Shanghai, China) was used to split the laser beam into two orthogonal beams. The horizontal beam was directed to the right angle fused-silica prism at an angle of about 40 o -45o with respect to the normal on to one of the legs of the surfaces of the prism. This beam was refracted through the prism and undergoes total internal reflection (TIR) with an angle of incidence q≈74 o at the bottom of the fused silica channel-sample interface. It formed the Nano-PIV optical path. The vertical laser beam reflected through two mirrors, passed through the prism and reflected at the top of the microchannel. It formed the Micro-PIV optical path. These two laser beams could be selectively obstructed by the gobos placed in the light paths. One 488-nm holographic notch filters (Kaiser Optical, Ann Arbor, MI; HNFP) with optical density over than 6 and a 514-nm bandpass filter (Melles Griot, Irvine, CA) were placed between the objective and the CCD. An electron multiplier CCD camera (EMCCD, iXon87, Andor Technology, North Ireland) was mounted on top of the microscope. The digitization rate of the camera was 5 MHz (12 bits) with the software controller gain set at 255 and the camera was maintained at –60oC. The camera was operated in the internal synchronization mode and in the frame-transfer mode for molecular tracking.
An evanescent wave is generated by the total internal reflection (TIR). When a parallel beam of light propagates to an interface from the higher dense medium to the less one and the incident angle q exceeds the critical angle qc, its penetration distance zp away from the interface is calculated by the formula 5.In our experiments, the laser at l0 = 488 nm was focused at an angle of incidence of 40 o ~ 45 o onto the fused silica prism (n2=1.46). The laser beam was refracted through the prism at an angle of incidence q =71 o ~74 o at the fused silica-water interface in the microchannel (n1 = 1.33, qc = 66 o). The penetration distance zp was 107~89nm.
Fig.1A Fig.1B
Fig. 1 A) Sketch of the evanescent wave illumination and wide field lighting: 1.laser; 2.shutter; 3.mirrors; 4.lens; 5.beam splitter; 6.gobos; 7.prism; 8.Microchip; 9.objective; 10. 514nm bandpass filter; 11. 488nm notch filter; 12. EMCCD. B) Coordinate of the channel: X-axis is the flow direction; Y-axis is the channel height; Z-axis is the channel wide; O locates in the plane of H/2 and W/2.
2.2 Microchannel
A fused-silica microchip, custom manufactured by Alberta Microelectronics Corp. (Alberta, Canada), was used in all experiments. The chip channel was 10 mm in depth, 300 mm in width and 3.5 cm in length (Figure 1B). The chip was placed on the hypotenuse face of a right-angle fused-silica prism (Melles Griot, Irvine, CA; Prism UVGSFS, A＝B＝C＝2.54 cm). The chip and the prism were index-matched with a drop of type FF immersion oil (R. P. Cargille Laboratories, Inc., Cedar Grove, NJ). The prism and the microchannel were fixed to a sturdy holder to minimize position shift from sample loadings. Before each experiment, the channel was washed successively with 10 mL sodium hydroxide (1.0 M), 10 mL water, 10 mL hydrochloric acid (1.0M) and 10 mL water.
2.3 Tracing particles
The diameter of fluorescence micro spheres purchased from Molecular Probes (PS- speck Microscope Point Source Kit, Eugene, OR, USA) was 175nm. The fluorescence microbeads were diluted with D.I. water ten folds. The concentration of microbeads was about 3×10-8 beads/mℓ; lDNA samples (48,502bp, Takara Biotechnology, Dalian, China) were labeled with YOYO-1 (Molecular Probes, Eugene, OR, USA) at a ratio of one dye molecule per five base pair. The concentration of DNA stock solution was 109 pM. Samples were further diluted to 1.09pM, 0.109pM and 0.0109pM (pH2.0) in the experiments. Water used was doubly distilled.
2.4 Procedures
One micro-liter microbead solution or lDNA sample were added into one of the reservoirs at the end of the channel and another one was empty. The difference of liquid levels at two reservoirs drove the flow passing through the microchannel. When the flow was steady, the images were first recorded with evanescent wave mode, then with wide field excitation mode.
3. Results and discussions
3.1 Flow velocities observed with microbeads
Figure 2A shows the images of fluorescence microbeads flowing in a microchannel driven by hydrostatic pressure when the evanescent wave was used for excitation. Single arrowhead and double arrowhead represent different microbeads in a series of images, respectively. With the cross-correlation method based on two frames successively, the velocity of microbead was calculated by migration distance divided by interval time. Figure 2B demonstrated the motion of microbeads in wide field excitation mode. More fluorescence microbeads were illuminated in this case. At a suitable exposure time, the fluorescence particle formed a trace in the movement. With the particle tracking velocimetry method, the track length divided by exposure time would be the migration velocity of microbeads. We followed 30 microbeads and calculated their velocities. The coordinates of the channel are X-axis the flow direction, Y-axis the channel height and Z-axis the channel wide. The point O locates in the plane of H/2 and W/2. The velocity distribution in a horizontal plate (xoz) is shown in Figure 3. The velocity date in the middle of channel are calculated from images of Fig. 2B and the date near wall are calculated from images of Fig. 2A. The velocities values at the bottom of the channel are really approach each other along z-axis and the average velocity is above 38.7 mm/s. However, the velocities in the middle of the channel scatter from 120.5mm/s to 260.2mm/s, because the light illuminated several microns in the depth of the channel with wide field mode. From Fig.3, it shows that the wide field mode is difficult to catch the velocity near the wall, but the evanescent wave mode can capture the minimum velocity near the bottom.
The microbeads could not completely be immersed into the evanescent field, because the diameter of microbeads is larger than the evanescent field depth. The centres of microbeads located in the range of 87.5nm to 187.5nm from the bottom surface of the channel could be observed. One microbead seen in the evanescent field were located in various flow-velocity regions from 0 to 275nm at the bottom of the channel. To simplify the calculation, we only considered the translation movement of a microbead and neglected the trundle movement in this paper. The particle motion measured reflects an average velocity in that range.
Fig. 2A Fig. 2B
Fig. 2. Motion of fluorescence microbeads under hydrostatic pressure in a microchannel at 7.513 frames/s illumination with different excitation modes: 20×objective (NA=0.75); sample, 3×10-8 beads/mℓ in water; microchannel, 300mm in width and 10mm in depth; 111ms exposure time and 22.1ms delay time. (A) in evanescent field excitation mode, imaging area is 57.6 mm×86.4 mm; (B) in wide field excitation mode, imaging area is 208mm×214.4mm (from Ref.7).
Fig. 3 Fig. 4
Fig. 3. The distribution of velocities measured by microbeads with wide field and evanescent field (TIR) (from Ref.7).
Fig. 4. The distribution of velocity measured by lDNA molecules with wide field and evanescent field (TIR) (from Ref.7).
3.2 Brownian error
Brownian diffusion is an important factor for measurement uncertainty when sub-micron particles were used to probe flow fields 2,8,9. The mean square distance of diffusion is , where is the time interval and D is the diffusion coefficient. The diffusion coefficient D is given as （Einstein 1905）. Here, dp is the particle diameter, k is Boltzman’s constant, T is the absolute temperature of the fluid, and is the dynamic viscosity of the fluid. Therefore, the velocity due to Brownian motion over interval time can be estimated by . The diffusion coefficient of 175nm particles in unconfined flow is 2.5×10－8cm2/s. During the 133.1ms interval time, the velocity of Brownian diffusion of a particle is 6.13mm/s. For N number of particle detected, Brownian diffusion error decreases to . Comparing with the velocity in the middle of the channel, the Brownian error is small to be negligible. The impact of hindered Brownian diffusion on the accuracy of particle-image velocimetry using evanescent-wave illumination was studied by Sadr et al10, and they concluded that “the errors due to Brownian diffusion-induced particle mismatch are negligible compared with various experimental errors such uncertainties in estimating magnification and the discretization of the image by the CCD array”.
3.3 Flow velocities observed with lDNA molecules
With the technique system presented, lDNA molecules are also used as tracers in the measurement. The form of a lDNA molecule is like an ellipse. The diameter of its cross section is smaller than that of a microbead, but we haven’t measure accurately in current experiment. A 20×/0.75 NA objective was used in wide field mode and a 40×/0.75 NA objective was used in the evanescent wave mode. The velocities are calculated with the particle-image correlation method and the particle-tracking method respectively. Both standard deviations are less than 3%. The results are shown in Fig.4. The data obtained by wide field mode demonstrated the velocities range from 110.2mm/s to 250.1mm/s. We haven’t controlled exactly the same pressure in this experiment as the experiments with microbeads, so the velocity values are not same as that in §3.1. With the wide field mode, the velocity can be caught at rather far from the wall. But with the evanescent wave mode, we can catch the average minimum velocity of 27.1 mm/s, which is very close to the wall.
3.4 Comparing with Hagen-Poiseuille flow theory
The velocity profile of Hagen-Poiseuille flow is presented as11:
(1)
In the experiments, we have no method to adjust the vertical position along y-axis with a precision of more than 1 micron. From the velocity distribution (Fig.3 and Fig.4), we can calculate the average velocity of the depth at each horizontal position z. The non-dimensional formula by maximum velocity Vmax and width W/2 is expressed as:
(2)
Here, V* and z* are the normal velocity and width respectively. Fig.5 shows the velocity profile based on Eq.2 and the experimental data. The experimental data obtained by wide field are the average values at each z position and that obtained by evanescent wave are considered at ~200nm from bottom. With the evanescent wave mode, the velocity distribution seems to be more completed, because of the experimental date obtained more approach to the wall of the channel.