Near-surface velocimetry using evanescent wave illumination

Total internal reflection velocimetry (TIRV) is used to measure particle motion in the near-wall region of a microfluidic system. TIRV images are illuminated with the evanescent field of an incident laser pulse and contain only particles that are very close to the channel surface. Sub-micron-sized fluorescent particles suspended in water are used as seed particles and their images are analyzed with a particle tracking velocimetry (PTV) algorithm to extract information about apparent slip velocity. At relatively low shear rates (less than 2,500 s^-1), a velocity proportional to the shear rate was observed. The statistical difference between velocities measured over hydrophilic and hydrophobic surfaces was found to be minimal. The results suggest that the slip length, if present, is less than 10 nm, but uncertainty regarding the exact character of the illumination field prevents a more accurate measurement at this time. Numerical simulations are presented to help understand the results and to provide insight into the mechanisms that result in the experimentally observed distributions. Issues associated with the accuracy of the experimental technique and the interpretations of the experimental results are also discussed.A version of this paper was presented at the 5th international symposium on particle image velocimetry (PIV 2003), Busan, Korea, 22–24 September 2003.     

Micro particle-image velocimetry of bead suspensions and blood flows

We present and discuss velocity profiles of microflows obtained by micro particle-image velocimetry in a transmission setup. We have measured suspensions of beads in water and on human blood, using the red blood cells as a natural particle seeding. The limitations imposed by our optical system on the spatial resolution normal to the focal plane, the so-called focal depth, have also been analyzed. The first direct observations of the influence of the focal depth on the observed velocity profiles are presented. Good agreement is obtained between observations and calculated profiles modified by the finite focal depth through a weight function.     

A study with particle-image velocimetry of the influence of drag-reducing polymers on the structure of turbulence

Particle-image velocimetry has been used to study the effect of drag-reducing polymers on the structure of turbulence in a channel flow, under conditions of 41% and 55% drag reduction. The fluctuating velocity fields in the x-y plane and in one x-z plane were measured. The striking features of these results are the damping of small scales and the repression of fluctuations of the velocity component normal to the wall. The role of the wall in creating turbulence diminishes greatly at large drag reductions; Warholic et al. (1999) have shown that a turbulent flow with zero Reynolds stress exists at maximum drag reduction. Velocity fields presented for conditions approaching this critical behavior are of particular interest. Received: 23 April 1999/Accepted: 12 February 2001     

High-speed quantum dot tracking and velocimetry using evanescent wave illumination

Total internal reflection velocimetry (TIRV) is applied to measure the dynamics of 17 nm diameter, colloidal quantum dot (QD) tracer particles within 200 nm of a microchannel wall at shear rates in excess of 20,000 s⁻¹. QDs are quickly developing into viable tracer particles for measuring microscale fluid dynamics. However, the low emission intensities of QDs usually require long exposure and inter-frame times, which limit velocity resolution and compromise accuracy (due to their fast diffusion as a consequence of a small diameter). In this study, a two-stage, high-speed image intensifier and camera were integrated into an evanescent wave microscopy imaging system. This provided the necessary temporal resolution to image the fast diffusion dynamics of QDs in real-time (up to 10,000 fps), which allowed individual particles to be tracked continuously for extended periods of time. In addition to examining the trajectories of individual particles, ensemble-averaged tracking measurements reveal near-wall velocity distributions in high-speed microchannel flows (Re ∼ 10), where velocities on the order of 5 mm/s are measured within 200 nm of the microchannel wall. This data provides a robust confirmation of recent results demonstrating diffusion-induced bias error for near-wall velocimetry.     

Flow characterization of diffusion flame oscillations using particle image velocimetry

Particle image velocimetry (PIV) was used to measure velocity fields inside and around oscillating methane-air diffusion flames with a slot fuel orifice. PIV provided velocity and directional information of the flow field comprised of both the flame and air. From this, information on flow paths of entrained air into the flame were obtained and visualized. These show that at low fuel flow rates for which the oscillations were strongest, the responsible mechanism for the oscillating flow appeared to be the repetitive occurrence of flame quenching. PIV findings indicated that quenching appears to be associated primarily with air entrainment. Velocity was found to be considerably larger in regions where quenching occurred. The shedding of vortices in the shear layer occurs immediately outside the boundary of the flame envelope and was speculated to be the primary driving force for air entrainment.     

Near-wall hindered Brownian diffusion of nanoparticles examined by three-dimensional ratiometric total internal reflection fluorescence microscopy (3-D R-TIRFM)

A three-dimensional nanoparticle tracking technique using ratiometric total internal reflection fluorescence microscopy (R-TIRFM) is presented to experimentally examine the classic theory on the near-wall hindered Brownian diffusive motion. An evanescent wave field from the total internal reflection of a 488-nm bandwidth argon-ion laser is used to provide a thin illumination field on the order of a few hundred nanometers from the wall. Fluorescence-coated polystyrene spheres of 200±20 nm diameter (specific gravity=1.05) are used as tracers and a novel ratiometric analysis of their images allows the determination of fully three-dimensional particle locations and velocities. The experimental results show good agreement with the lateral hindrance theory, but show discrepancies from the normal hindrance theory. It is conjectured that the discrepancies can be attributed to the additional hindering effects, including electrostatic and electro-osmotic interactions between the negatively charged tracer particles and the glass surface.

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Flow characterization of flickering methane/air diffusion flames using particle image velocimetry

Phase-resolved measurements of the velocity field in acoustically forced, flickering laminar co-flowing methane/air diffusion flames were made. Identical flames have been studied extensively in the past in order to characterize the effects of the vortical structures responsible for the flicker on the flame structure, but the initial velocity perturbation and the velocity fields have not been reported previously. Phase-locked measurements of the instantaneous two-dimensional velocity field at ten phases within a full excitation cycle were made using particle image velocimetry. The velocity measurements were complemented by phase-resolved shadowgraphs recorded in the vicinity of the flame base. Measurements are reported for the two forcing conditions that have most often been studied for this burner. When integrated with the results of previous studies, these measurements provide a clearer picture of the interactions between the buoyancy-induced vortical structures and the flame sheets, as well as providing the initial conditions required for realistic modeling of these flames.     

Investigations of the measurement accuracy of stereo particle image velocimetry

With a stereo PIV system, in order to perform reliable measurements of the three velocity components in liquid flow, it is mandatory to minimise the errors made in determining the 2D displacement vectors and the viewing direction of each of the two cameras. We present a method for determining the viewing direction in the angular displacement stereo system by means of a digital imaging procedure such that the direct measurement of geometrical parameters of the set-up is avoided. This makes the method particularly useful for measurements through the transparent walls confining the liquid flow. A third order polynomial used for calibrating the stereo system is shown to provide more accurate results than imaging functions of lower order. Further improvement of the evaluation accuracy is obtained with the application of an artificial neuronal network, but at the expense of considerably increasing the computation time. A comparison of the evaluation results obtained with the operational procedures presented in this paper with those generated with another method that is applicable to liquid flow (Soloff et al. 1997) shows, that the present procedures can be considered as a viable alternative to existing methods.     

Effect of resolution on the speed and accuracy of particle image velocimetry interrogation

Particle image velocimetry incorporates a process by which an image of a flow field, bearing double images of seeding particles, is analyzed in small regions called “interrogation spots.” Each spot is imaged onto a photodetector array whose digitized output is evaluated computationally using the auto-correlation technique. This paper examines the effects of resolving the spot using arrays of various resolutions, motivated primarily by a gain in speed. For this purpose, two specially created test photographs representing (i) uniform flow and (ii) solid body rotation, were interrogated using array sizes ranging from 32 × 32 to 256 × 256. Each reduction in resolution by a factor of two gains a factor of four in interrogation speed, but this benefit is counteracted by a loss in accuracy. The particle image diameter strongly influences accuracy through two distinct error mechanisms. When the particle image is small compared to the pixel size, mean bias error becomes significant due to finite numerical resolution of the correlation function. Conversely, when the particle image is large, random error due to irregularities in the electronic images predominates. The optimum image size, therefore, lies not at either extreme but at an intermediate value such that the particle image is small in an absolute sense, and yet large relative to the pixel size. A version of this paper was presented at the 12th Symposium on Turbulence, University of Missouri-Rolla, 24–26 September 1990     

Theoretical and experimental analysis of the accuracy and reproducibility of cell tracking velocimetry

A theoretical and experimental analysis has been conducted to determine the accuracy of cell tracking velocimetry (CTV). CTV is an analytical technique for quantifying magnetically induced velocity of immunomagnetically labeled cells (or particles), in which the computer algorithm, particle tracking velocimetry (PTV), has been modified and combined with a well-defined magnetic energy gradient. In addition, this technique can calculate the size of a cell (or particle) through the use of experimentally measured settling velocities. A model was developed which determines the minimum and maximum cell velocities that can be determined based on a number of intrinsic constants and variables associated with this technique. This model was experimentally tested using a number of calibration particles and very good agreement between model and experimental data was obtained. The combination of model and experimental validation establishes the proper operating parameters for CTV. Received: 14 January 2000/Accepted: 10 July 2000     

Spatially averaged time-resolved particle-tracking velocimetry in microspace considering Brownian motion of submicron fluorescent particles

A time-series measurement method is proposed to detect velocity fields in a microchannel taking into account Brownian motion of submicron tracer particles. The present study proposes spatially averaged time-resolved particle-tracking velocimetry (SAT–PTV), which can detect temporal variations of fluid flow and eliminate errors associated with Brownian motion without losing temporal resolution. Velocity vectors of tracer particles obtained by PTV are spatially averaged in each interrogation window of particle-image velocimetry, yielding full velocity field information with temporal resolution. Synthetic particle images, which include Brownian motion of submicron fluorescent particles in flow fields with linear velocity gradients, are generated to validate the ability of SAT–PTV to track particles. SAT–PTV correctly captures the velocity gradient profiles. The spatial resolution based on the size of the first interrogation window and the measurement depth of the microscope system is 6.7 m×6.7 m×1.9 m, within which several vectors are averaged. SAT–PTV is shown to measure the velocity field of a pulsating flow generated by an electrokinetic pump.An earlier version of this paper appeared in the Fourth International Symposium on Particle Image Velocimetry at Göttingen, Germany, 17–19 September 2001.     

A non-Fickian,particle-tracking diffusion model based on fractional Brownian motion

The work is motivated by the recent discovery that ocean surface drifter trajectories contain fractal properties. This suggests that the dispersion of pollutants in coastal waters may also be described using fractal statistics. The paper describes the development of a fractional Brownian motion model for simulating pollutant dispersion using particle tracking. Numerical test cases are used to compare this new model with the results obtained from a traditional Gaussian particle-tracking model. The results seems to be significantly different, which may have implications for pollution modelling in the coastal zone. © 1997 John Wiley & Sons, Ltd.     

Study of the phenomena affecting the accuracy of a video- based particle tracking velocimetry technique

 The development of a video-based Particle Tracking Velocimetry (PTV) technique has focused on the problem of the accuracy of this method. The PTV-method can be decomposed into three parts: the recording of the experiment, the image processing and the evaluation of the velocities. The accuracy of each stage has been studied. Inaccuracies due to resolution, length scale, light intensity and distortion of the x and y direction are analysed. One of the main factors influencing the accuracy is the selection of the time difference between frames. During the evaluation of velocities, incorrect identifications of particles may occur. The relation between the time-step of the frames and the percentage of incorrect identifications has been shown. The percentage of false identifications increases with the size of the time-step. The resolution accuracy is however improved when the time-step is increased. An adequate selection of the time-step has to be made to obtain a high resolution accuracy and a limited number of incorrect identifications. Received: 22 April 1996 / Accepted: 17 November 1996     

On the accuracy of a nonlinear finite volume method for the solution of diffusion problems using different interpolations strategies

In this paper, we consider a nonlinear finite volume method to solve the steady‐state diffusion equation in nonhomogeneous and non‐isotropic media. The method is nonlinear even if the original problem is linear. In its original form, the scheme is monotone, because the coefficient matrix is monotone under certain assumptions and, as a consequence, whenever the analytic operator demands, it preserves the positivity of numerical solutions. On the other hand, the scheme is unable to reproduce piecewise linear solutions exactly. In order to recover this interesting feature, we use two different interpolation strategies. In this case, even though we are unable to prove monotonicity, we show some numerical evidences that the combined method has an improved behavior, producing second order accurate solutions, even for nonhomogeneous and strongly anisotropic media. Copyright © 2013 John Wiley & Sons, Ltd.     

Rheology of pulp suspensions using ultrasonic Doppler velocimetry

Conventional rheometry coupled with local velocity measurements (ultrasonic Doppler velocimetry) are used to study the flow behaviour of various commercial pulp fibre suspensions at fibre mass concentrations ranging from 1 to 5 wt.%. Experimental data obtained using a stress-controlled rheometer by implementing a vane in large cup geometry exhibits apparent yield stress values which are lower than those predicted before mainly due to existence of apparent slip. Pulp suspensions exhibit shear-thinning behaviour up to a high shear rate value after which Newtonian behaviour prevails. Local velocity measurements prove the existence of significant wall slippage at the vane surface. The velocimetry technique is also used to study the influence of pH and lignin content on the flow behaviour of pulp suspensions. The Herschel–Bulkley constitutive equation is used to fit the local steady-state velocity profiles and to predict the steady-state flow curves obtained by conventional rheometry. Consistency between the various sets of data is found for all suspensions studied, including apparent yield stress, apparent wall slip and complete flow curves.     

The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer

To investigate the accuracy of tomographic particle image velocimetry (Tomo-PIV) for turbulent boundary layer measurements, a series of synthetic image-based simulations and practical experiments are performed on a high Reynolds number turbulent boundary layer at Re_θ = 7,800. Two different approaches to Tomo-PIV are examined using a full-volume slab measurement and a thin-volume “fat” light sheet approach. Tomographic reconstruction is performed using both the standard MART technique and the more efficient MLOS-SMART approach, showing a 10-time increase in processing speed. Random and bias errors are quantified under the influence of the near-wall velocity gradient, reconstruction method, ghost particles, seeding density and volume thickness, using synthetic images. Experimental Tomo-PIV results are compared with hot-wire measurements and errors are examined in terms of the measured mean and fluctuating profiles, probability density functions of the fluctuations, distributions of fluctuating divergence through the volume and velocity power spectra. Velocity gradients have a large effect on errors near the wall and also increase the errors associated with ghost particles, which convect at mean velocities through the volume thickness. Tomo-PIV provides accurate experimental measurements at low wave numbers; however, reconstruction introduces high noise levels that reduces the effective spatial resolution. A thinner volume is shown to provide a higher measurement accuracy at the expense of the measurement domain, albeit still at a lower effective spatial resolution than planar and Stereo-PIV.     

二维对流扩散方程的高精度全隐式多重网格方法

提出了数值求解二维非定常变系数对流扩散方程的一种时间二阶、空间四阶精度的三层全隐紧致差分格式。为了加快迭代求解隐格式时在每一个时间步上的收敛速度,采用多重网格加速技术,建立了适用于本文高精度金隐紧致格式的多重网格算法。数值实验结果验证了本文方法的精确性、稳定性和对高网格雷诺数问题的强适应性。     

Examination of the flow around a hot-wire probe using particle image velocimetry

Previous work has shown that the k ² term in the effective cooling velocity equation for inclined hot-wires can become negative under certain probe configurations and wire length-to-diameter ratios. It was hypothesised that this was due to a downwash component of velocity along the wire when prong interference effects were expected to be minimal. Direct measurements of the flow around a typical hot-wire probe using digital particle image velocimetry have shown that this downwash velocity component does exist, leading to negative values of k ² as calculated from the angle of deviation from the free stream.List of symbols d diameter of hot-wire mm - k factor in equation for effective dimensionless velocity for inclined hot-wire - l length of hot-wire mm - Q effective velocity mm/s - U free stream velocity mm/s - angle between free stream and degrees wire normal - angle through which flow is degrees deflected at working section of wire     

Investigation of thermal convection in water columns using particle image velocimetry

Particle image velocity measurements were applied on thermally driven convection at low Rayleigh numbers. In a model experiment using a water column heated from bottom and cooled from above, the velocity field was studied at different vertical temperature gradients. In the testing facility with high aspect ratio (about 19) representing a 1-m-long column with 5?cm diameter, occurrence of free convection was verified for destabilizing temperature gradients of 0.1–2?K/m. The PIV results revealed that significant flow exists already at low vertical temperature gradients. The velocity of the stable large-scale circulations increased linearly with temperature gradient (<1?K/m) from 8?×?10^?5 to 1?×?10^?3?m/s. At higher temperature gradients (1–2?K/m), a transition from quasi-stationary into time-dependent flow was observed, where convection cells changed position, number, and form temporarily. The motivation of this research was to gain more insight into density-driven convection in boreholes and groundwater monitoring wells.