Journal of Visualization

, Volume 21, Issue 4, pp 569–583 | Cite as

Three-dimensional particle behavior using defocusing method in micro-toroidal vortex generated by optoelectrokinetic flow

  • Dong Kim
  • Yining Ma
  • Kyung Chun Kim
Regular Paper


This paper demonstrates a technique to realize multiphysics simulation and experimental validation of micro-toroidal vortex and utilizing the defocusing method to obtain the three-dimensional particles trajectory using a single camera. Fluorescent polystyrene particles were suspended at a concentration of 3.7 × 108 count mL−1 solution diluted with DI water. These were carried by the toroidal vortex fluid motion and showed an optoelectrokinetic phenomenon. We used a defocusing method to trace the three-dimensional trajectory of the particles. The size of the ring pattern increased as particles moved far away from the focusing plane and close to the objective lens. By recording the ring pattern size of one particle in every continuous frame, we successfully implemented the described techniques to obtain the three-dimensional trajectory of particles in an optoelectrokinetic experiment. Simulation results in COMSOL® Multiphysics (v4.3a) were compared to the trajectory and particle velocity variation in the experiment.

Graphical abstract


Optoelectrokinetic Multiphysics simulation Defocusing method Three-dimensional trajectory Micro-toroidal vortex 

1 Introduction

Recently, the development of optoelectrokinetic technology for non-invasive manipulation in systems has been demonstrated to yield high throughput and controllable particle aggregation in microfluidic systems (Wang et al. 2014). The technology typically utilizes a parallel plate electrode system and a highly focused laser beam to create a localized “hot spot” on the electrode. The hot spot leads to electrothermal flows, which allow for rapid collection of analytes at a desired location on the electrode. The concept of this technique is called rapid electrokinetic patterning (REP), which was first introduced by Williams et al. (2008). REP technology has recently received much attention for the promising prospect for controlling and concentrating target objects at the micro scale (Kwon and Wereley 2015). Colloidal particle accumulation could be characterized by varying the applied voltage, frequency, and illumination intensity (Williams et al. 2009, 2010). Wang et al. (2014) summarized the force analysis in an empirical model for various frequency situations.

Kumar et al. (2010) measured the temperature profiles at the center of laser illumination as a function of the laser power. This is vital for REP exploration due to laser irradiation and Joule heating, which produce a temperature gradient distribution and determine the electrothermal drag force in the microvortex flow. Optoelectrokinetics techniques can rapidly manipulate or transport fluids and suspended species such as particles, cells, and molecules in flows. These species can be programmably manipulated according to the shape of the laser or sorted based on their properties in a biological assay system (Wood et al. 2013; Hoettges et al. 2003).

The biocompatibility of REP was demonstrated for the first time by Kwon et al. (2012). Mishra et al. (2014) summarized the application of REP in biology like cell trapping, call sorting, electroporation, and concentration of molecules. Recently, Kwon et al. (2010) successfully applied the technology for separating, sorting, and manipulating live bacteria in a bio-particle system. These techniques offer new opportunities through their dynamic nature, and their ability for parallel operation has created novel applications and devices (Kumar et al. 2011a, b).

Mizuno et al. (1995) firstly observed the generation of microvortex flow formation in liquid films using an IR laser to focus on a point and cause electrothermal flows. They did an experiment and obtained the two-dimensional microvortex flow field. The electrode was set up vertically, but recently, the electrode has been set up horizontally. Because of the different location of the electrode, the direction of the particle flow is inversed.

Kumar et al. (2009) did an experiment to observe the generated microfluidic vortices in three dimensions. They implemented a defocusing method to demonstrate a micro-toroidal vortex. They used inter-digitized electrodes without laser irradiation to prove that particles experienced negative dielectrophoresis (DEP) and aggregate above the electrode digits. After applying laser irradiation, the particles showed opto-electrostatic microvortex behavior in the middle of an electrode strip. Kumar et al. (2011a, b) later used wave-front deformation particle-tracking velocimetry to demonstrate a three-dimensional and three-component electrothermal microvortex with a single camera. However, there were some limitations to the velocity measurement, such as lower accuracy for the location of micro-particles and optical access.

Three-dimensional flow measurement technologies suffer from the difficult operational approaches and complicated experimental devices. In order to overcome these drawbacks, defocusing methods and signal-camera measurements have been implemented. Willert and Gharib (1992) used defocusing in conjunction with a mask (with three pin holes) embedded in the camera lens to decode three-dimensional point sources of light. Yoon and Kim (2006) successfully detected three-dimensional particle positions and conducted microflow diagnostics via a three-pinhole defocusing concept. However, there are also some restrictions in using the three-pinhole defocusing method. Measurements and experiments are operated at the micro scale, and if a mask is embedded in the camera lens, the light intensity would be weakened, which is a disadvantage for observations. Wu et al. (2005) reported a new approach to track the three-dimensional trajectory of particles that can avoid the weak light drawback; they used a quantitative defocusing method. The ring radius increases as the particles move away from the reference plane and closer to the lens.

Although many attempts have made to visualize 3D micro-toroidal vortex motion by numerical and experimental methods, the coincidence of the particle trajectory and streamlines still remains in question. In this study, mathematical equations were developed to illuminate the relationships among the effect of several fields in optoelectrokinetic technology, and a mathematical model was developed for a simulation using COMSOL Multiphysics software. The most important purpose of this study is to realize multiphysics simulation and experimental validation of micro-toroidal vortex and utilizing the defocusing method to obtain the three-dimensional florescent particles trajectory using a single camera. Since a common defocusing technique uses a device such as a three-pinhole aperture, there is a problem that the amount of light intensity is small. This method can solve the problem of the amount of light. Then we compared the results of the simulation and a micro-toroidal vortex experiment for validation in both two-dimensional velocity fields and three-dimensional trajectories of particles.

2 Theoretical background

In general, an optoelectrically generated microfluidic vortex is a coupling of three main fields: the electric field, the temperature field, and the velocity field (Green et al. 2001).

The electric field combines with laser illumination and induces an AC electrothermal body force, and the time-averaged expression for this force is
$$\left\langle {f_{\text{e}} } \right\rangle = \frac{1}{2}\text{Re} \left[ {\frac{{\sigma_{\text{m}} \varepsilon_{\text{m}} (\alpha - \beta )}}{{\sigma_{\text{m}} + i\omega \varepsilon_{\text{m}} }}(\nabla T \cdot E)E^{ * } } \right.\left. { - \frac{1}{2}\varepsilon_{\text{m}} \alpha |E|^{2} \nabla T} \right],$$
where * indicates a complex conjugate and Re(…) indicates the real part of the expression. For an AC signal of frequency ω, E is the electric field; σm and εm are the conductivity and permittivity of the fluid, and β and α are (1/σm)(∂σm/∂T) and (1/εm)(∂εm/∂T), respectively. The first term of this equation is the Coulomb force, and the second term represents the dielectric force. This equation indicates that the temperature gradient is more important than the absolute temperature in the electrothermal flow (Wang et al. 2014).
There is also a DEP force in the microfluidic vortex motion. Kumar et al. (2009) did not introduce a DEP force to the tracer particles, but they proved that latex particles experience negative DEP force in the absence of laser heating at interdigitated electrodes. Kim et al. (2015) presented a compressing DEP force under an AC electric field. The DEP force can be expressed using the following function:
$$F_{\text{DEP}} = 2\pi \varepsilon_{\text{m}} r^{3} \text{Re} \left[ {f_{\text{CM}} } \right]\nabla \left| {\overrightarrow {{E_{0} }} } \right|^{2} ,$$
where r is the radius of the particle. Re[fCM] is the real part of the Clausius-Mossoti (CM) factor (Ivory and Srivastava 2011). The details about the relationship between the ACET effect and DEP effects are well presented by Kim et al. (2015).

The temperature gradient field results from Joule heating and the laser beam. Green et al. (2000) used a broad-wavelength illumination source and set up a 25-μm electrode gap in an experiment. They revealed the effect of illumination, which generated a temperature gradient. The liquid permittivity and conductivity also changed due to the temperature gradient, and the electric field was responsible for the motive force. They also explained that the light used seems to have a stronger influence than Joule heating (Green et al. 2001).

The generation of heat is governed by the following energy equation:
$$\rho_{\text{m}} c_{\text{p}} \frac{\partial T}{\partial t} + \rho_{\text{m}} c_{\text{p}} \cdot \nabla T = k\nabla^{2} T + \sigma E^{2} ,$$
where cp is the specific heat at constant pressure; k is the thermal conductivity, and σE2 is the Joule heating term. We have neglected the viscous term (Batchelor 2000; Backstrom 1999). For sufficiently high frequencies, we can simplify this equation to the steady state (Ramos et al. 1998). The movement of particles in a micro-system also showed that the velocity of particles is too slow to change the temperature field. Therefore, the heat convection is smaller than the heat conduction, and the Peclet number is approximated by the following expression (Castellanos et al. 2003):
$$\left| {\frac{{\rho_{\text{m}} c_{\text{p}} \overrightarrow {u} \cdot \nabla T}}{{k\nabla^{2} T}}} \right| \ll 1.$$
Consequently, the temperature field by Joule-heating was calculated using the following:
$$k\nabla^{2} T + \left\langle {\sigma E^{2} } \right\rangle = 0.$$
Non-uniform temperature distribution, which is due to a laser irradiation, is applied to the surface of the electrode. Kumar et al. (2010) derived the temperature distribution experimentally as a Lorenz peak function.
$$T = T_{0} + a\left( {\frac{b}{{4r^{2} + b^{2} }}} \right),$$
where a and b are the fitting parameters having values of 0.0015 and 0.00015, respectively. These parameters were obtained by fitting the experimentally measured temperature value using a microscopic IR camera.

The Joule-heating source by the electric field and the local temperature condition according to the Lorenz peak function produce a temperature distribution inside the micro-channel.

Electrothermal fluid flow arises from the non-uniform action of the electric field in the medium induced by the temperature field. For the velocity field of the fluid flow, Green et al. (2001) used the Navier–Stokes equation to demonstrate the velocity of the fluid \(\overrightarrow {u}\) in the low Reynolds number approximation:
$$0 = - \nabla p + \eta \mathop \nabla \nolimits^{2} \overrightarrow {u} + f_{\text{e}} + \Updelta \rho_{\text{m}} g,$$
where p is the pressure; η is the viscosity of the fluid; fe is the electric force density, and ∆ρmg is the buoyancy force density. Compared to the electrical force, the buoyancy force is very small, so we neglected the force (Ramos et al. 1998). Finally, for the velocity and pressure, we compute the electrical force and solve the Navier–Stokes’ equation:
$$- \nabla p + \eta \mathop \nabla \nolimits^{2} \overrightarrow {u} + \left\langle {f_{\text{e}} } \right\rangle = 0.$$

3 Experiment setup and numerical method

3.1 Fabrication of parallel electrode microchip and setup of experimental devices

As shown in Fig. 1, the microchip was composed of an upper electrode made of ITO glass (~ 200 μm, Sigma-Aldrich) and a bottom electrode glass with a gold film. The gold bottom side of the electrode was fabricated by coating a ~ 150-nm layer of gold and a ~ 25-nm Cr adhesive layer on a glass slide using an E-beam evaporator. The height of the gap between the two electrodes was almost ~ 100 μm, and the two layers were attached with Scotch Tape (one layer: ~ 50 μm; 3M). The microchip was assembled by clamping the ITO and gold electrode with paper clips. Every time after use, the ITO glass and gold film electrode were rinsed by ethanol and deionized water and then sonicated in acetone for several minutes.
Fig. 1

a Illustration of the micro-channel used for the micro-toroidal vortex fluid motion in an optoelectrokinetic trapping system. On the bottom gold film electrode, there are two rectangular regions attached to two layers of conductive tape in order to create a spacer (~ 100 μm) between the two electrodes. The height of one layer of conductive tape is ~ 50 μm. b Diagram of the rapid electrokinetic patterning experiment setup

The medium was 4 mL of DI water and a 15-μL mixture of fluorescent polystyrene particles (Thermo Fisher Scientific, GO500, Dukr, USA). Particles with diameters of 5 μm were suspended in DI water, and the concentration was 3.7 × 108 count mL−1. The conductivity of the suspension was adjusted to 0.3 mS m−1. The density of particles is 1.05 g mL−1, which is a little denser than DI water. A 532-nm wavelength power-adjustable laser (LPC-1500, Suwtech) was focused on a motorized mirror (T-MM2, Zaber Technologies), and the light path was transformed from the horizontal direction to the vertical direction. The laser beam was passed through a 35-mm focusing lens (LA1027, Thorlabs) and then the bottom side of the gold electrode. The microchip was connected to a function generator (AFG3251, Tektronix) and a power amplifier (Pa-151, Labworks, Inc.) by wires. The particle motion was observed by a microscope (BX51, Olympus) and captured by a CCD camera (PCO1200hs, PCO, Germany) using a ×10/0.30 objective lens (UplanFI, Olympus, Japan).

3.2 Three-dimensional particle tracking using a defocusing method

Wu et al. (2005) reported a novel imaging technique to track the coordinates (x, y, z, t) of multiple fluorescent particles at the micro scale (< 10 μm) simultaneously using a quantitative defocusing method. The ring pattern grows as the particles move far away from the reference plane and near the objective lens. When the particle ring radius is the smallest, the plane is the reference plane and the image is in the focal plane. This method can be implemented successfully and simply for obtaining three-dimensional particle trajectories.

Figure 2 shows four planes (I, O, R, L, planes): the image plane is the location of the image sensors, the objective plane is the position of the particles, the reference plane is the position of the particles that will be in focus at the image plane, and the lens center plane is in the middle of the two lenses. If a particle is in the reference plane, it is in focus on the image plane, and the image will be a sharp and bright dot as in Fig. 2a. If the objective is moved a distance z away from the reference plan, there will be a ring pattern in the image plane because of spherical lens aberration, as shown in Fig. 2b. The ring diameter depends on the distance from the objective plane to the reference plane. Therefore, if we know the relationship between the ring pattern diameter and the height z, we can find the three-dimensional location (x, y, z) of the particle.
Fig. 2

Schematic of the defocusing method imaging system (Wu et al. 2005). a The point light source is at the reference plane. b The point light source is away from the reference plane

The advantages of the technique are as follows: (1) A single camera is used, which simplifies the experimental operation and is suitable for complicated microvortex fluid motion with a limited space for observation. (2) Without a mask pinhole, the incoming and outgoing light will not be blocked, so the light intensity of the imaging system is increased. (3) By using a calibration step, this technique could be used in various kinds of experiments. Each experiment condition would correspond to a group of calibration targets, which would improve the applicability of this method.

3.3 Calibration

In a study on a calibration-based defocusing method (Yoon and Kim 2006; Min and Kim 2011), the calibration and main experiment should be conducted in the same experimental conditions using the same materials. Figure 3 shows the calibration images that were captured before the REP experiment when the particles were in a static state. Many particles were captured at each height of image defocusing, but clear and obvious ring patterns could only be selected and processed by Matlab code. After obtaining diameters of clear ring patterns, we used the average value of diameters for calibration data. Every 10-μm height of image defocusing was considered one group corresponding to a special diameter of the circle ring pattern of this group of images. The relationship (Eq. 7) between the particle defocusing ring size and the height of particles in the z coordinate could be obtained as shown in Fig. 4. According to this method, the three-dimensional (x, y, z) trajectory of particles was obtained. The calibration equation is
$$z = 1.23 \times d + 5.82,$$
where d is the diameter of the defocusing ring, and z is the height of particles. The fitting correlation coefficient was R2 = 0.969.
Fig. 3

Defocused images of 5-μm-diameter particles. Experimental calibration images using 20 × objective microscope lens. The size of the capture area is 1.096 × 1.096 mm in the image plane. Each image is 1024 × 1024 pixels

Fig. 4

Ring diameter d versus z

3.4 Numerical simulation

After generating a non-uniform electric field induced by an electric field within the micro-channel, the motion of a three-dimensional toroidal vortex resulting from the REP effect was simulated numerically using COMSOL® Multiphysics software. To simulate the effect of REP on the particle-suspended fluid motion, the three governing equations need to be analyzed, which are the energy equation (Eq. 3), current conservation equation (Eq. 8), and momentum conservation equation (Eq. 9). In an electric field, an electric potential was produced, and as a result, the charge conservation in the field should be as follows:
$$\nabla \cdot (\sigma \vec{E} + i\omega \varepsilon \vec{E}) = 0,$$
where σm is the conductivity of the fluid; ɛ is the permittivity of fluid, and ω = 2πf as the frequency of an external AC field. The electric field \(\overrightarrow {E}\) can be obtained from the charge conservation coupled with the temperature generation in a micro-channel, which results from the generation of heat due to the Joule heating effect governed by the energy equation (Eq. 3).
Figure 5 depicts the calculated temperature field profile. An isothermal boundary condition was set on the top of the channel with ambient temperature (293.15 K). Near the position with a high concentration of particles, a temperature gradient was generated by the changes in the dielectric constant, as well as an electric conductivity gradient due to the non-uniform electric potential made by the laser irradiation source. The maximum change in temperature at the center of the laser spot was approximately 10 K higher than in other places. In the simulation, the temperature distribution showed a gradient that decreased from the laser illumination center to the ambient environment of the microchip. When the laser irradiation was combined with the electric field, there was little difference in the electric potential between the center point and edge of the micro-channel. As already mentioned, the difference of the electric potential resulted from the temperature gradient changing the electric properties, such as the electric permittivity and conductivity.
Fig. 5

Simulation result of electrothermal effect distribution under Joule heating and laser illumination heating

Figure 6 shows the electrothermal fluid flow motion from the REP effect. The surface color code means the velocity magnitude of the fluid inside the channel. Arrows are shown to clarify the flow direction during the concentration process. For a general fluid, the electrothermal force per unit volume on a fluid is governed by
$$\rho_{\text{m}} \left( {\frac{{\partial \overrightarrow {u} }}{\partial t} + \overrightarrow {u} \cdot \nabla \overrightarrow {u} } \right) = \nabla \cdot (\eta \nabla \overrightarrow {u} ) + \left\langle {f_{\text{e}} } \right\rangle ,$$
where ρm is the density of the fluid medium. The simulation should be carried out in three steps for the electric field, thermal field, and induced fluid flow velocity. The fluid flow velocity comes from the Navier–Stokes equation (for which Eq. 5 was transformed into Eq. 9). The parameters and values in this simulation are listed in Table 1.
Fig. 6

The combination result of an electric field and laser irradiation shows the velocity distribution under the electrothermal flow effect. Voltage = 15 Vpp; F = 5 kHz. a Bottom view of the velocity distribution of fluid flow. b Velocity distribution of fluid flow in an internal section

Table 1

Values of different computational parameters



Electric potential (Vpp)

Case study

Frequency (kHz)


Dynamic viscosity (Pa s)

1.002 × 10−3

Density of medium (kg m−3)

1 × 103

Electrical conductivity of medium (S m−1)

0.3 × 10−3

Electrical conductivity of particle (S m−1)

0.038 × 10−3

Relative permittivity of medium


Relative permittivity of particle


Thermal conductivity of medium (W m−1 K−1)


Heat capacity of medium (J kg−1 K−1)


Temperature peak increase (∆K)

Case study

Simulation time (s)


Particle size (µm)

Case study

Diffusion coefficient (m2 s−1)


4 Results and discussion

4.1 The height of the activated plane where the particle concentration occurred

By comparing the simulation and experimental results of particle velocity distribution in a two-dimensional plane, we can find the location of the activated plane of the particle concentration when the electrode polarization occurs. Polarized particles produce negative DEP near the electrode. This effect also provides a non-uniform electric field that produces DEP force. The REP experiment should be conducted within a short time because the electric field and Joule heating will continuously exhaust the electrodes and make them less sensitive to the electric potential, leading to inaccurate results. The frame rate was 20 frames per second (ΔT = 0.05 s), and the CCD camera can capture 1250 images at most in each experiment. Shutter speed of the CCD camera was 0.05 s (= 1/fps).

At the beginning of the experiment, the micro-channel had no electric or temperature fields, and 5-μm particles were randomly distributed, as shown in Fig. 7a. At this time, particles are on the focal plane, and the size of the ring pattern of particles is the smallest. For Fig. 7b, an electric field was applied. Particles were polarized and instantly began to shake and float to a height h from the initial position from the focal plane to an activated plane. The patterning of particles became brighter, and the ring became larger compared with Fig. 7a. In this activated plane, when the laser beam was applied, the electrothermal flow produced a drag force, and the non-uniform electric field generated a DEP force. Therefore, particles were driven toward the laser irradiation center by the electrothermal flow (Kwon and Wereley 2015), as shown in Fig. 7c. Figure 7d shows the particle path that formed toroidal vortex motion due to the height of particles changing. This resulted in defocusing of the ring pattern. The related simulation results are described in detail in our previous paper (Kim et al. 2015).
Fig. 7

Top view of active motion of a 5-μm-diameter particle in experiment images. For this experiment setup, the AC frequency was 5 kHz, and the electric potential was 15 Vpp (peak to peak), while the laser power was 200 mW. The laser focus point is approximately at the center of the red cross. a Particles were in the focal plane without the optoelectrokinetic effect. b While applying an electric field, particles were polarized; they floated to a height, and they started shaking continuously. c When the laser beam was focused on the bottom gold film electrode, particles began to move towards the focus center of the laser illumination. d When particles experienced toroidal vortex motion due to the height of particles changing, the defocusing ring pattern was became obvious

Using the results of the simulation, we can analyze the height h to which the particles moved due to the electric polarization. We next used a defocusing method in an experiment to prove the accuracy of the simulation results. Figure 8a shows the velocity distribution field of the flow in the zr plane (where r can be x or y). The simulated volume is axisymmetric, and the optical axis serves as the axis of symmetry. As shown in the simulation result, the velocity distribution is also axisymmetric, and the axis is the middle line of the height of the micro-channel. Therefore, we divided the overall height into five parts: 10, 20, 30, 40, and 50 μm. The streamline is shown to clarify the flow velocity magnitude during the concentration process. Figure 8b shows the experimental results of the velocity distribution, which consists of 60 overlapped images. The experimental images were captured by a CCD camera, and a two-frame cross correlation method was used to obtain the velocity vector. Six contours of velocity magnitude (20, 50, 100, 150, 200, and 250 μm) were set up from the laser focal center to the ambient environment.
Fig. 8

Parameters in simulation and experiment were 15 Vpp and 5 kHz. a Simulation result of flow velocity distribution in an internal section on the zr plane. b 60 overlapped images of tracer particles creating path lines showing the inward fluid and the velocity magnitude in the plane (top view). c Comparison of the velocity magnitude distribution between five divided heights calculated from the simulation (solid lines) and measured from the experimental result (dashed line) along the r-direction

In Fig. 8c, the results of the velocity distribution of each height along the r direction are shown as solid lines. The experimental results are also shown as a dashed line. By comparing the results, the height h of the plane where particles were polarized and moved to the center point of the laser beam could be obtained, which was approximately ~ 20 μm (red line) and ~ 30 μm (blue line), as shown in Fig. 8c.

4.2 Three-dimensional trajectory of particles

When applying laser illumination and an electric field together, particles moved towards to the center part of the temperature gradient. The ring pattern size did not change much because the particles were approximately at the same plane height (Fig. 9a, b). However, as the particles moved near the center point, the size of the defocusing ring pattern became larger (Fig. 9c). At this time, particles moved to the center point and the upward direction simultaneously. When particles moved to the nearest point of the center region, they stopped moving ahead and just moved to the upward direction. The height increased, and the defocusing ring pattern became larger and larger (Fig. 9d).
Fig. 9

Experiment using defocusing method to trace the trajectory of 5-μm particles in electrothermal flow. All measurements were performed at V = 15 Vpp, laser power was 200 mW, and AC frequency was fixed at 5 kHz. ag 150 Continuous images were calculated from the CCD camera capturing 20 images per second. h Three-dimensional trajectory of the particle in ag

Next, the size of the ring pattern became the largest, which means the particles were at the highest location in their trajectories. Then, the particles moved to the outer direction of the micro-channel and finally came back to almost the original location. During this process, the size of the defocusing ring pattern became smaller and smaller (Fig. 9e–g). Figure 9h shows the three-dimensional trajectory of this particle from Fig. 9a–g during 7.5 s in the experiment. Therefore, the whole trajectory was a toroidal vortex shape. Because the velocity of particles varied with the movement, we selected different time periods (∆t) among Fig. 9a–g to show the change of the image size of the particle diameter.

Figure 10 shows the whole three-dimensional trajectory of this particle during 26 s. The trajectory was a toroidal vortex motion, and it is clear that the distance between two adjacent points where one particle was recorded in two continuous frames is different with respect to the location of the vortex region. The distance near the laser focus center is greater than that of adjacent points far away from the center point. This means that near the laser focus center, the velocity of a particle is faster. This result corresponds to the simulation results in that when particles moved to the upward direction, the velocity was highest.
Fig. 10

The whole path line of a particle for 26 s, which was composed of 520 frames with ∆t = 0.05 s. Start point was (− 27, − 135.9, 31.5)

The first step of the Matlab procedure to track the particle trajectory is confirming the start and end images from one group of images of the REP experiment, then selecting a particle to track. During the calculation procedure, the Matlab code records the (x, y) location and the ring pattern size change of the particle in every image. Finally, using the relationship between d and z (Eq. 7), the three-dimensional location (x, y, z) of a particle is obtained. From the results of tracking the trajectory of one example particle, we found the height where particles began to concentrate at the center of the laser beam to be around 20–30 μm. This result is identical to the result shown in Fig. 8c.

Based on the theoretical analysis, we obtained the steady flow streamlines in the simulation results. The comparison between streamlines in the simulation and the trajectory of particles in the experiment is shown in Fig. 11a. The trajectory was the same as in Fig. 10, but the x and y coordinates were converted onto the r coordinate. For the simulation, we simply defaulted our case as steady flow (∂V/∂t = 0). As shown in Fig. 11a, the coordinates of the starting point were (138.5, 31.4) at the beginning of the first red dotted loop. The particle moved to the laser beam focal area and almost stayed at the same height. Then, the particle moved to the upward direction and higher than the streamline because of the particle inertia, and the trajectory could not follow the streamline.
Fig. 11

a Comparison between streamline of flow simulation and trajectory of experiment particle. Experimental conditions are the same as in figure. b Top view of the particle trajectory at xy plane

When the velocity of the particle was very high, the inertia was more pronounced. As the flow velocity became lower, the inertia of the particle was also smaller, and then the particle turned to the downward direction. Due to gravity, the trajectory of the particle was much lower than the streamline. When the velocity of the particle decreased, the inertia was negligible, and the trajectory was nearly coincident with the streamline. Then, the particle moved to the region near the beginning point and started the second part of the trajectory shown by a blue triangle loop, which was similar to the first loop. As for the third loop (pink rectangles) and fourth loop (green stars), the size of the circular pattern of the particle trajectory became smaller. Particles in micro-toroidal vortex motion tend to move to the center of the vortex. The main reason for this phenomenon is due to the inertia of the particle. Another possible reason is the changing medium properties due to continuous heating of the gold film by the laser beam. However, we could not quantify the unsteady effect during our experiment. Figure 11b shows the particle trajectory at the xy plane (top view). Theoretically, the particle trajectory should be in a straight line at the xy plane. However, the particle in the micro-toroidal vortex moved along axisymmetric paths with a certain circumferential margin. Statistically averaged path could be axisymmetric with about two times of particle diameter variance. This nature can be expected by slight change of particle location in perpendicular direction of axisymmetric plane due to Brownian motion.

5 Conclusion

We showed that non-uniform AC electric fields with a strong laser beam can generate a three-dimensional toroidal vortex structure in the flow motion. By using a defocusing method, we successfully obtained the trajectory of particles in three-dimensional coordinates (x, y, z). Before every REP experiment, a calibration procedure for the relationship between the actual height of particles in a micro-channel and the ring pattern size of the particles in images should be recorded first. Then, by combining the functions of z and d, particles in any time period can be traced.

Through comparison of the simulation results and experimental results of the velocity field, we proved that the height of the activated plane where particles were concentrated at the laser irradiation center was approximately 20–30 μm away from the focus plane. We also compared the streamline in the simulation with the trajectory of a particle in an experiment, and they were not completely coincident because of inertia and gravity.



This study was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIT) through GCRC-SOP (No. 2011-0030013).


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Copyright information

© The Visualization Society of Japan 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringPusan National UniversityPusanRepublic of Korea

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