Laser Doppler velocity profile sensor with time division multiplexing for microscale investigations. Jörg König, Lars Büttner, Jürgen Czarske

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1 Laser Doppler velocity profile sensor with time division multiplexing for microscale investigations Jörg König, Lars Büttner, Jürgen Czarske Laboratory for Measurement and Testing Techniques, Faculty of Electrical Engineering and Information Technology, Technische Universität Dresden, Germany, Abstract In this contribution we present a novel laser Doppler technique for microfluidic diagnostics. Instead of parallel fringe systems, two superposed fan-like interference fringe systems with opposite gradients are employed to determine the velocity distribution inside the measurement volume directly. The sensor utilizes the time division multiplexing technique to distinguish both interference fringe systems. A velocity uncertainty of.18 % and a spatial resolution of 96 nm are demonstrated inside a microchannel. The applicability of the sensor is demonstrated by selecting two applications. Flow rate measurements, in the range of 3 µl min -1 with a statistical uncertainty of are presented. In comparison to a reference, by precise weighing, the mean deviation between both measurement principles amounts to 1 %. Furthermore, a first study of a Lorentz-force-driven flow in the immediate vicinity of an electrode during copper electrolysis is presented. For this application the time division multiplexing technique is combined with fluorescence in order to suppress unwanted reflections of the electrode. The expected linear behavior of the Lorentz-force driven flow is confirmed. However, it is restricted to a few tenths of seconds after starting the electrolysis. Finally, with the advantage of high spatial resolution with simultaneous low velocity uncertainty, the sensor offers a new tool to study flow phenomena at the microscale. In conjunction with fluorescence the new sensor is particularly suitable for near wall measurements. 1. Introduction In recent years, numerous applications emerged in microfluidics, e.g. in medical, chemical or biological analytics. Lindken et al. [1] have given an extensive overview of applications that range from electrokinetic flows to biological flows or mixing processes etc. With the significant advancement in microfluidics, measurement technologies for detailed flow investigations are required. In order to keep up with the small structures in microfluidic devices, several optical measurement techniques were invented []. The probably most well-known representative is Micro Particle Image Velocimetry (µpiv). It was introduced in 1998 [3] and is a modification of the conventional Particle Image Velocimetry (PIV) by using a microscope objective and fluorescent tracer particles, since illumination and observation occur from the same direction through the microscope objective. It offers highly resolved dc measurements and evolved as an often applied and well-established technique for small-scale flow investigations [1]. However, it is a camera based technique and the lateral spatial resolution is limited by diffraction and pixel discretization. As in conventional Particle Image Velocimetry (PIV), the velocity data are determined by correlation methods. Therefore, the velocity uncertainty is usually limited to some percent, e.g. Meinhart demonstrated high resolution measurements with a velocity accuracy of % [4]. Although further optimizations are possible, this value is typical for µpiv measurements [5]. In many applications, this is not sufficient, e.g. for determination of wall shear stress or precise flow rate measurements for drugdelivery. Furthermore, due to the volume illumination the depth of correlation (DOC) affects the axial spatial resolution, since out-of-focus particles can also contribute to the correlation [6]. The DOC depends on the numerical aperture (NA). Thus, high resolution can only be achieved with a sufficiently high NA, which yields a very small working distance and restricts the experimental setups

2 In contrast to camera-based techniques, Laser Doppler Velocimetry (LDV) provides a higher precision, i.e. relative uncertainty in the range of.1 % 1 % typically. Its measurement principle based on interference fringe systems with nearly parallel spacing d, which is formed by two intersecting coherent laser beams. When a small particle passes the measurement volume, the scattered light signal shows an amplitude modulation with the Doppler frequency f = v/d corresponding to the particle velocity v orthogonal to the fringe spacing. Since LDV is a quasipointwise technique, the spatial resolution is determined by the size of the measurement volume, typically 1 μm x 1μm x 1mm. For common microfluidic applications, this is not sufficient. In principle, the spatial resolution can be increased by stronger focusing but due to the wavefront curvature of the Gaussian beams this leads to a higher variation of fringe spacing d. Therefore, a higher uncertainty of the velocity has to be expected. The laser Doppler velocity profile sensor eliminates the fringe spacing variation, since this sensor scheme leverages the wavefront curvature to determine the axial tracer particle position inside the measurement volume [7]. Hence, spatial resolution and velocity uncertainty are significantly improved compared to conventional laser Doppler velocimetry. [8]. The laser Doppler velocity profile sensor.1 Principle of the sensor The laser Doppler velocity profile sensor employs two superposed fan-like fringe systems, one being converging and the other one being diverging along the optical z-axis. Hence, the two fringe spacings have opposite gradients, as illustrated in figure 1. Fig.1 Fan-like interference fringe systems with opposite gradients. Both fringe systems are superposed and form the measurement volume of the laser Doppler velocity profile sensor With a calibration prior to the measurement the fringe spacing functions d 1, ( can be determined. By division a unique calibration function q( = f 1 (v,/f (v, is obtained. When a small particle passes the measurement volume it scatters light from both fringe systems and the Doppler frequencies f 1, of the two coincident burst signals can be estimated. The quotient of the Doppler frequencies [7] q( f1( v, f ( v, v / d v / d 1 ( ( d ( d ( 1 corresponds to the calibration function. Hence, the axial tracer particle position is determined by measuring both Doppler frequencies. Knowing the z-position and therefore the actual fringe spacing the particle velocity v x ( can be derived with the following equation: v x ( f1( v, d1( f ( v, d ( - -

3 The two interference fringes systems have to be physically distinguishable. Due to the interfaces between air, glass capillary and fluid as well as due to the expected small velocities in microfluidic devices time division multiplex technique (TDM) represents the best choice to distinguish both interference fringe systems [8]. The TDM technique offers two major advantages. Dispersion effects are avoided, since only one wavelength has to be used. This technique can be further combined with fluorescence techniques, leading to an improved signal quality by suppressing unwanted reflections of the wall. Moreover, the latter satisfies the often formulated requirement of only on optical access. As accustomed by µpiv, the scattered fluorescent light can be detected in backward direction, while the excitation light is suppressed.. Setup of the sensor utilizing time-division-multiplexing Figure illustrates the setup of the laser Doppler velocity profile sensor utilizing time division multiplexing. The focus here is dedicated to the TDM realization. The optical arrangement of the velocity profile sensor itself has been already discussed in some publications before, e.g. [7]. AOM 1 1. Laser (@ 53 nm) Clk Ch1 Ch. AOM 1.. Dichroic beam splitter Excitation light + fluorescence light Excitation light Measurement volume Filter Fluorescence light x Detector z y Signals to PC Fig. Setup of the laser Doppler velocity profile sensor utilizing time division multiplexing and fluorescence detection in backward direction The TDM sensor uses a frequency-doubled diode-pumped Nd:YVO4 laser at a 53 nm wavelength. The laser light is split into two separate beams by two beam splitter cubes. Each of the beams passes an acoustic-optical modulator (AOM). With alternating operation of the AOMs time division multiplexing is realized. For this purpose, the first diffraction orders are guided to the sensor head by a singlemode fiber and either the converging or the diverging fringe system will be shaped depending on the currently active AOM. To synchronize the data sampling and the pulsing of the AOM the AOM driver signals were locked to the clock signal of the data acquisition card as follows. An external circuit divided the sampling frequency by, in order to distinguish two fringe systems

4 This frequency-divided signal is assigned to the AOMs, alternately. Additionally, one AOM signal has to lead back to a second input channel of the data acquisition card. It ensures a correct assignment, i.e. it indicates which fringe system is currently shaped in the measurement volume. The demultiplexing is accomplished in a reverse manner, i.e. every even-numbered sample of the detected burst signal belongs to the first and every odd sample belongs to the second fringe system. A measured example of two coincident detected burst signals and their reliable distinction is depicted in figure 3. Figure 3(a) represents the acquired raw signal, which contains both burst signals. With the time-demultiplexing technique both coincident burst signals are reliably separated, see figures 3(b), 3(c). Additionally, the spectral behavior of all three signals is depicted in figure 3(d). Due to the similar frequencies of both superposed burst signals, only one broadened Gaussian peak appears in the spectrum of the raw signal. This evidences that a distinction in the frequency domain is not possible, whenever a particle passes the measurement volume, in particular close to the center. However, in the frequency spectrum of the time-demultiplexed signals, two distinguishable Doppler frequencies occur and velocity as well as the position of the tracer particle can be reliably estimated Amplitude [V] Amplitude [V] Time [ms] (a) Time [ms] (b) Amplitude [V] Amplitude [mv] Raw signal Fringe System 1 Fringe System Time [ms] Time [ms] (c) (d) Fig. 3 (a) acquired raw signal of both coincident burst signals, (b) burst signal of fringe system 1 (c) burst signal of fringe system (d) spectrum of all three signals In order to satisfy the requirement of only one optical access, the flow can be seeded with fluorescent particles, which are excited by the illumination light of both interference fringe systems. For this purpose, the illumination light passes a dichroic mirror inside the sensor head (inside the front Keplerian telescope). According to the TDM scheme, the fluorescent particles emit light of both interference fringe systems alternately, that is reflected at the dichroic mirror and passes an additional optical filter

5 3. Current Results 3.1 Evaluation of spatial resolution and velocity uncertainty in a microchannel The axial spatial resolution as well as the uncertainty of the velocity of the sensor was examined first. For this purpose the sensor was applied to measure the centerline velocity profile inside a microchannel with rectangular cross section. Its measured dimensions are 16 µm x 17 µm. Due to the high aspect ratio of 15:1 and the low Reynolds number of Re 3.5, a laminar Poiseuille velocity profile between parallel plates along the short axis can be assumed, approximately [8]. In order to avoid a pulsating behavior of the flow, the flow was driven by hydrostatic pressure. For this purpose, two basins with large cross-sectional surfaces were utilized. The employed fluid was distilled water, seeded with monodisperse polystyrene particles of 1.5 g/cm 3 density and of 7 nm diameter. The measured velocity profile along the short axis of the microchannel is depicted in figure 4. More than 8 data points were collected, where each of them represents the velocity v and the axialposition of a single detected tracer particle (gray dots). To evaluate the uncertainties, the velocity values were averaged with a spatial slot width of 1.5 µm. The averaged velocities were used for a parabolic fit, according to the theoretically expected Poiseuille profile. With the deviation of each slot, the uncertainties of velocity and spatial resolution can be derived as follows. The limited spatial resolution causes an additional deviation of the parabola, depending on the velocity gradient at each point. Within this deviation (±1σ) the parabola can be shifted along the z-axis. In figure 4 it is represented by two additional parabolas (black and red colored). Their distance indicates the spatial resolution. Thus, the spatial resolution amounts to σ 96 nm and can be considered as a mean value over the whole parabola. Due to the velocity gradient, the velocity uncertainty should only be derived at the apex of the parabola. At this point the velocity gradient is zero and the velocity uncertainty should not be affected by the limited spatial resolution, approximately. A relative velocity uncertainty of about.18 % was derived within the central slot width of 1.5 µm around the apex. This value also contains fluctuations of the flow velocity, caused e.g. by temperature and pressure effects. That cannot completely be excluded. Therefore, a lower relative velocity uncertainty of the sensor can be assumed Velocity [mm/s] Position z [µm] Fig. 4 Measured centerline velocity profile. The gray dots are the raw data - 5 -

6 3. Selected Applications 3..1 Precise Flow rate measurements The sensor was applied to measure the micro flow rate inside the microchannel [8]. To achieve a reliable statement about the repeatability, the flow rate was measured with precise weighing (balance manufacturer: Sartorius, type LC 6 D) simultaneously. Six different flow rate measurements in the range of 3 µl/min were performed. Since only the centerline velocity profile was measured the volume flow was derived by a numerical solution of White [9]. The deviation between both measurement principles amounted to 1 %, approximately. However, this deviation contains the uncertainties of both measurement principles. The uncertainty of the balance is affected by several parameters, e.g. tolerances of the calibration weight, readability and linearity. Furthermore, the measurements are affected by changes of density, temperature or humidity, which also contribute to the total error in the measurement process. The uncertainty of the flow rate by utilizing the laser Doppler velocity profile sensor is given by its velocity uncertainty and spatial resolution. In comparison to the deviation between both principles, the statistical uncertainty of the flow rate by utilizing the laser Doppler velocity profile sensor can be neglected. Its relative statistical uncertainty in the order of -4 (confidence interval of 95 %) is more than 1 times lower. The deviation is determined by the systematic uncertainty of the calibration process and the dependence of the applied approach and its related assumptions. However, with an extension to an imaging sensor the flow rate measurement can be significantly improved by measuring the entire cross section of the microchannel. 3.. Electrochemistry For the first time, the sensor has been applied to measure the Lorentz-force-driven flow in the immediate vicinity of an electrode during copper electrolysis. Figure 5 illustrates the measurement setup schematically. The electro-chemical cell consisted of a cuboid glass cuvette with an inner size of mm x mm x mm. The electrolyte was a solution of.5 M CuSO 4 with distilled water. The copper electrodes with a cross-sectional area of mm x mm were vertically fixed to two opposite sides of the cell. A permanent neodymium-iron-boron (NdFeB) magnet ( mm in diameter) was attached to the working electrode at the right hand side. In order to ensure the optical access, the counter electrode was equipped with a small slit of 1 mm width. Permanent magnet Measurement volume Sensor head Slit y x z Cu electrode 5 mm mm Fig. 5 Setup of the electrochemistry experiment - 6 -

7 Due to the long working distance (WD) of the laser Doppler velocity profile sensor, presently 5 mm, the velocity profile at the working electrode was observed within the first approximately µm by measuring through the entire cell of mm width. In order to suppress unwanted reflections of the wall fluorescent monodisperse polysterene particles of 1.5 g/cm 3 and of µm diameter were used for this application. First, the position of the electrode was determined. For this purpose, the cell was moved up and down in x-direction (distance travelled 1.4 mm around the measurement point at the electrode). Due to the slight roughness of the electrode surface, the scattered light signals of both interference fringe systems are modulated with the Doppler frequencies [1]. Thus, the position of the electrode is provided by the laser Doppler velocity profile sensor, as mentioned above. The electrode position was determined to 84 µm inside the coordinate system of the sensor. Second, a 1c1d velocity measurement was performed directly at the electrode during the electrolysis. The current density amounted to -5 ma/cm approximately and was constant over the whole duration of 38 seconds of the electrolysis. It was already known that the expected flow is unsteady, since the Lorentz-force-driven flow decaying in the course of time and is canceled out after a certain time due to natural convection [11]. Therefore, the potential curve was simultaneously acquired with an additional input channel of the data acquisition card, leading to a well-known starting time of the electrolysis. Moreover, the position of the electrode was previously determined. Hence, when a particle passed the measurement volume, it could be addressed to a certain time and to a certain position relative to the electrode. After switching on the electrolysis the expected linear velocity distribution at the electrode is formed immediately. The velocity gradient v / z increases rapidly and stays nearly constant for the time of 5 seconds until 15 seconds after starting the electrolysis. All collected burst signals during this time were summarized and are depicted in figure 6(a). The linear behavior can be clearly confirmed. However, after 15 seconds the Lorentz-force driven flow is decelerated rapidly and converges to a minimum during 11 seconds until 15 seconds after starting the electrolysis. For this duration, all collected data points were summarized again and are depicted in figure 6(b). Obviously, there is a nearly constant velocity distribution over the measurement volume. After this time, the velocity slightly increases again for the remaining duration of the electrolysis. Obviously, this behavior hints to an increasing natural convection. Further results, particularly the transient behavior will be presented for discussion at the conference. 1.8 Electrode 1.8 Raw data Electrode Velocity [mm/s].6.4. Raw data Linear fit function Velocity [mm/s] Position z [µm] (a) Position z [µm] Fig. 6 Measured velocity profiles at different time periods (a) 5 s < t > 15 s (b) 11 s < t > 15 s (b) - 7 -

8 5. Conclusions A novel laser Doppler velocity profile sensor has been developed, in particular for microfluidic applications. The laser Doppler velocity profile sensor employs two superposed fan-like fringe systems to obtain the velocity as well as the position of tracer particles inside the measurement volume. To avoid dispersion effects a time division multiplexing technique (TDM) is utilized. As evidenced by experiment, the velocity uncertainty of the laser Doppler velocity profile sensor amounts to.18 % under real flow conditions. Its spatial resolution can be determined to 96 nm. The sensor has been applied to two selected applications. First, flow rate measurements in the range of 3 µl min 1 were performed. The flow rate was derived from the measured velocity profile of the novel sensor. To achieve a reliable statement about the repeatability, the flow rate was measured with precise weighing, simultaneously. The deviation between both measurements amounted to 1 % approximately. It demonstrates a good agreement. The contribution of the statistical uncertainty of the laser Doppler velocity profile sensor can be neglected. Its relative statistical uncertainty in the range of -4 (confidence interval of 95 %) is more than one order of magnitude lower. Second, the sensor features a long working distance of 5 mm. Hence, it is able to measure microscale phenomena in comparable large environments. For the first time, the sensor has been applied to measure the Lorentz-force-driven flow in the immediate vicinity of an electrode during copper electrolysis. In order to suppress reflections of the electrode the TDM technique has been combined with fluorescence. The velocity distribution at the electrode has been observed within the first approximately µm by measuring through the entire cell of mm width. The expected linear behavior of the Lorentz-force driven flow has been confirmed, after a starting time of 5 seconds. However, despite the presence of the Lorentz-force, the expected linear velocity gradient cannot be sustained and decreases rapidly. 5. Acknowledgments The authors would like to thank Sascha Mühlenhoff for providing the electro-chemical cell for the first measurement and for his many discussions. Furthermore, we thank Dr. Eckert, Dr. Yang and Dr. Shirai for fruitful discussions. The authors are grateful to Mr. Linde for his assistance in the laboratory. References [1] Lindken R, Rossi M, Große S and Westerweel J: Microparticle image velocimetry (µpiv): recentdevelopments, applications, and guidelines Lab Chip 9 (9) [] Sinton D: Microscale flow visualization Micro Nanofluid 1 (4) -1 [3] Santiago J G, Wereley S T, Meinhart C D, Beebe D J and Adrian R J: A particle image velocitmetry system for microfluidics, Exp. Fluids 5 (1998), [4] Meinhart C D, Wereley S T and Santiago J G: PIV measurements of a microchannel flow, Exp. Fluids 7 (1999) [5] Wereley S T and Meinhart C D: Recent advances in micro-particle image velocimetry Annu. Rev. Fluid. Mech. 4 (1)

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