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An Open-Chip for Three-Dimensional Rotation and Translation of Particle Based on Dielectrophoresis

  • Po-Jen ShihEmail author
  • Shih-Wei Wang
  • Shun-Chiu Lin
Original Research
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Abstract

This study developed a three-dimensional device which can manipulate a small specimen in translation and rotation in a three-dimensional space. The device is based on an open-chip device without packaging; thus, the tip of a scanning microscope. This translational, rotational, and overturning device enables optical or scanning probe microscopy to realize the three-dimensional observation of the specimen’s surface. Especially for the atomic force microscope, it helps scan the back side of the specimen, because the back side is always chemically bonded onto the substrate. This device is based on the three-dimensional dielectrophoretic theory, which applies exact solutions on the force and torque terms. Subsequently, these solutions are applied to dielectrophoretic simulation by using a finite element method (FEM) and to simulate the trapping and rotation of this particle and facilitate three-dimensional device design. Furthermore, microelectromechanical fabrication and laser processing were applied to manufacture electrodes in three-dimensional space. The trapping, rotation, shifting, and overturning of an Aspergillus niger particle were tested to demonstrate the manipulation of this device. The results reveal the rotation at 15–35 Hz had nearly constant period, and the angular velocity was proportional to the triggering frequency. Finally, according to the dielectrophoretic theory, the rotational velocities at frequency ranges of 15–35 Hz were recorded to modify the Clausius–Mossotti factor of A. niger; the results of that procedure can serve to adjust parameters for the advanced manipulation of other particles.

Keywords

Tapping mode Atomic force microscope Pressure Vorticity Semianalytical method 

Introduction

Single-cell traps have been successfully used in many biological applications, and numerous methods exist, such as ultrasonic techniques [1], optical tools [2], hydrodynamics [3], and dielectrophoretic forces [4, 5]. Moreover, single-cell rotation is a fundamental technique in modern bioscience, and it enables observation through stereoscopic imaging. Cell rotation is necessary for microscope operations; and cell translation is necessary to orient the target in a focal plane or relative to a focal tip. This is particularly necessary for cells that are not uniform in the buffer liquid. Therefore, cell translation and rotation techniques play crucial roles in stereoscopic imaging, and they involve essential motions in the focal plane and in the plane perpendicular to the focal plane (vertical plane). However, there are no such device which can rotate specimen on the vertical plane, i.e. overturning. Especially for the atomic force microscope, the overturning helps scan and get the contour of the specimen back side, because the back side is always chemically bonded onto the substrate. Furthermore, an open-chip device can present a cell in an open environment with an appropriate buffer; this enables the cell to be observed not only with an optical microscope but also with a scanning probe microscope, where the open environment helps the scanning probe merge in the buffer or liquid environment.

To trap, rotate, and translate a single cell, the trapping forces can be obtained using many methods: ultrasonic, optical, hydrodynamic, or dielectrophoretic forces. The major difference depends on the size of the particle to be trapped. For example, an optical beam is suitable to trap or move nanoparticles, and the dielectrophoresis method or hydrodynamic whirling flow [3] is suitable for microscale particles. An ultrasonic transducer can trap particles that are approximately tens of micrometers wide [1]. In this study, the dielectrophoresis method [6, 7] was applied to produce the trapping forces, and the controlling cell size was between 0.1 and 20 µm [8, 9]. Furthermore, there are three limitations when an atomic force microscope (AFM) is applied for scanning. The chamber must be opened at the top so that the tip can approach; the cell must be trapped or fixed strongly after its motion; and the device must be small and have a plane surface to be clamped. Therefore, the dielectrophoresis method is the most suitable candidate for manipulating a particle, particularly for controlling biological particles. In this method, dielectrophoresis can operate a particle in a fluidic environment, and the particle is in an ideal liquid medium, which enables the particle to float without friction. The major feature is that the particle is suspended when the AFM tip scans. The particle doesn’t need the chemical bonding to stuck on the substrate; on the other hand, its bonding side could be observed. Moreover, the dielectrophoresis method can be applied in fields of separate particles [9], can separate DNA, and can trap particles at a specific location. However, according to these literatures, these applications of dielectrophoresis have been limited to two-dimensional motion in a horizontal plane until now. Thus, we developed a device that can operate a particle moving in three-dimensional space with stereoscopic observation.

The dielectrophoresis method was first invented by Kaler and Pohl [10]; they calculated a range of frequencies and characterized a single living cell. The effective polarizabilities of the yeast cell and a Netrium digitus cell were considered in terms of frequency. Further calculations were completed by Wang et al. [11], and they proposed a time-averaged dielectrophoresis force in an alternating current electric field of angular frequency. They reported a quantitative analysis of the dielectrophoretic forces acting on particles in some practical electrode configurations, including the translational force experienced by particles in practical rotating electric fields. Jones and Washizu [7, 12, 13] followed their concepts to complete a dyadic tensor representation for multipolar moments for dielectrophoretic force and electrorotational torque. In 1998, Hughes and Morgan [8, 9, 14] studied a two-dimensional and time-dependent electric field, and they mentioned two pivotal results. First, a device capable of both translation and rotation could be designed through an ideal configuration of the electrodes. Second, ten distributions of the electrodes were suggested to control the particles. Reichle et al. [15] designed a three-dimensional octupole cage which had two layers and eight electrodes, they was driven by rotating electric fields in the MHz range. The feature of this device is that it could trap a particle as suspension; however, they didn’t discuss the overturning function. Moreover, the total dielectrophoretic force, including conventional dielectrophoretic force and traveling-wave dielectrophoretic force, were introduced [16]. Because both forces and torques were applied on the target subject without the device directly contacting the subject, the method was widely used for biological particles and cells. In the total dielectrophoretic mode, when a dielectric particle experiences a nonuniform electric field, the dielectrophoretic force is greater than the initial inertial force.

In this paper, we developed a device that can trap, rotate, translate, and overturn a single particle to realize stereoscopic observation in optical imaging or scanning probe microscopy. In this study, the finite element method (FEM) simulation demonstrated the possibility of an open-chip device through the application of dielectrophoresis equations, including force and torque terms. Conventional forces can trap a single cell at the center of the device, and traveling-wave dielectrophoretic force can rotate and translate the cell in various directions within the three-dimensional space. The device can trap, rotate, shift, and overturn a single particle, and Aspergillus niger was considered the target in a physical experiment. The results revealed the rotation, translation, and overturning at triggering frequencies ranging from 15 to 35 Hz.

Materials and Methods

Total Dielectrophoretic Forces

Dielectrophoresis is introduced in terms of conventional and traveling-wave dielectrophoresis. Dielectrophoresis is a force induced by the effective dipole of a particle, and an electric dipole can be expressed by the electric potential. Thus, the dielectrophoretic force can be written as a function of these electric potentials. The particle must be suspended in some liquid to enable manipulation; therefore, the fluidic force is an essential consideration for particle suspension.

Traditional dielectrophoresis, a general type of dielectrophoresis, involves a particle experiencing a nonuniform electric field. Regardless of whether the particle is charged, the particle will be affected by dielectrophoresis. Once the particle is exposed under the field, the particle will be immediately polarized. After the polarization, the particle starts to move and starts to follow the distribution of the electric paths. For the quasi-static condition, the electric field can be expressed by the following equation:
$$\varvec{E}\left( {x,y,z;t} \right) = \mathop \sum \limits_{n = 1}^{3} E_{n} \left( {x,y,z} \right){ \cos }(\omega t + \varphi )\varvec{x}_{n} ,$$
(1)
where (x, y, z) denote the coordinate system (E1, E2, E3) are the amplitudes of the electric field, \(\varphi\) is the phase, t is time, \(\omega\) is the angular frequency, and xn are the unit vectors. Wang et al. [11] reported the time-averaged general solution of dielectrophoresis by an effective moment method,
$$\varvec{F}\left( {\varvec{x},\varvec{y},\varvec{z};\varvec{t}} \right) = \left( {\varvec{m} \cdot \nabla } \right)\varvec{E,}$$
(2)
where the effective dipole moment, m, of a spherical particle with radius, r is known.
$$\varvec{m}\left( {x,y,z;t} \right) = 4\pi \in_{m} r^{3} \mathop \sum \limits_{n = 1}^{3} E_{n} \left\{ {\text{Re} \left[ {K^{*} \left( \omega \right)} \right]\cos \left( {\omega t + \varphi } \right) -\, \text{Im} [K^{*} \left( \omega \right)]\sin (\omega t + \varphi )} \right\}x_{n} .$$
(3)
Thus, the force can be written as
$$\varvec{F}\left( {x,y,z;t} \right) = 2\pi \in_{m} r^{3} \left\{ \text{Re} \left[ {K^{*} \left( \omega \right)} \right]\nabla \left(\frac{1}{2}\mathop \sum \limits_{n = 1}^{3} E_{n}^{2} \right) +\, \text{Im} \left[ {K^{*} \left( \omega \right)} \right]\mathop \sum \limits_{n = 1}^{3} E_{n}^{2} \nabla \varphi_{n} \right\} x_{n} ,$$
(4)
where \({\text{Re}}\left[ {K^{*} \left( \omega \right)} \right]\) and \({\text{Im}}\left[ {K^{*} \left( \omega \right)} \right]\) are the real and imaginary parts of a complex Clausius–Mossotti factor. It is defined by \(K^{*} \left( \omega \right) = \frac{{\varepsilon_{p}^{*} - \varepsilon_{m}^{*} }}{{\varepsilon_{p}^{*} + 2\varepsilon_{m}^{*} }}\), such that \(\varepsilon_{p}^{*} = \varepsilon_{p} + \frac{{\sigma_{p} }}{i\omega }\) and \(\varepsilon_{m}^{*} = \varepsilon_{m} + \frac{{\sigma_{m} }}{i\omega }\). \(\varepsilon_{p}\) and \(\varepsilon_{m}\) are the permittivity values of the particle and surrounding medium, respectively. And \(\sigma_{p}\) and \(\sigma_{m}\) are the conductivity values of the particle and surrounding medium, respectively. All parameters can be obtained from Gimsa [17], and \(\in_{p} = \left[ {50 + \frac{0.162}{{1 + \left( {\frac{f}{{f_{c} }}} \right)^{2} }}} \right] \in_{0}\) and \(\sigma_{p} = 0.4 + \frac{{0.135\left( {\frac{f}{{f_{c} }}} \right)^{2} }}{{1 + \left( {\frac{f}{{f_{c} }}} \right)^{2} }}\), where f is the frequency, fc = 15 MHz, \(\in_{m}\) = 78.5 \(\in_{0}\), and \(\sigma_{m} = 1.327 s/m\). Torque T can be calculated using the effective moment approach [12]
$$\varvec{T}\left( {x,y,z;t} \right) = \varvec{m} \times \varvec{E},$$
(5)
where the torque acts on the center axis of the particle. Furthermore, the force and torque can be formalized as
$$T\left( {x,y,z;t} \right) = 4\pi \in_{m} r^{3} \text{Im} \left[ {K^{*} \left( \omega \right)} \right]\left\{ {\begin{array}{*{20}c} {E_{2} E_{3} \sin \left( {\varphi_{2} - \varphi_{3} } \right)} \\ {E_{1} E_{3} \sin \left( {\varphi_{3} - \varphi_{1} } \right)} \\ {E_{1} E_{2} \sin \left( {\varphi_{3} - \varphi_{1} } \right)} \\ \end{array} } \right\}.$$
(6)
When the electric potential is explained by
$$V\left( {x,y,z;t} \right) = \text{Re} [\varPhi \left( {x,y,z} \right)e^{i\omega t} ],$$
(7)
in which \({{\varPhi }}\left( {x,y,z} \right) = [{{\varPhi }}_{{r\left( {x,y,z} \right)}} + i{{\varPhi }}_{i} (x,y,z)]\), the force becomes
$$\begin{aligned} F\left( {x,y,z;t} \right) =\, & 2\pi \in _{m} r^{3} \sum\limits_{{l = 1}}^{3} {\{ \text{Re} [K^{*} (\omega )\frac{1}{2}\frac{\partial }{{\partial x_{l} }}\sum\limits_{{n = 1}}^{3} {\left[ {\left( {\frac{{\partial \Phi _{r} }}{{\partial x_{n} }}} \right)^{2} + \left( {\frac{{\partial \Phi _{i} }}{{\partial x_{n} }}} \right)^{2} } \right]} } \\ & + \text{Im} \left[ {K^{*} \left( \omega \right)} \right]\frac{\partial }{{\partial x_{l} }}\sum\limits_{{n = 1}}^{3} {\left[ {\frac{{\partial ^{2} \Phi _{i} }}{{\partial x_{l} \partial x_{n} }}\frac{{\partial \Phi _{r} }}{{\partial x_{n} }} - \frac{{\partial ^{2} \Phi _{r} }}{{\partial x_{l} \partial x_{n} }}\frac{{\partial \Phi _{i} }}{{\partial x_{n} }}} \right]} \} x_{l} , \\ \end{aligned}$$
(8)
and the torque is reduced to
$$\begin{aligned} T\left( {x,y,z;t} \right) =\, & 4\pi \in_{m} r^{3} \text{Im} \left[ {K^{*} \left( \omega \right)} \right] \left\{ {\left[ {\frac{{\partial \varPhi_{i} \partial \varPhi_{r} }}{{\partial x_{2} \partial x_{3} }} - \frac{{\partial \varPhi_{i} \partial \varPhi_{r} }}{{\partial x_{3} \partial x_{1} }}} \right]} \right.x_{1} \\ & + \left\{ {\left[ {\frac{{\partial \varPhi_{i} \partial \varPhi_{r} }}{{\partial x_{3} \partial x_{1} }} - \frac{{\partial \varPhi_{i} \partial \varPhi_{r} }}{{\partial x_{1} \partial x_{3} }}} \right]x_{2} } \right. + \left\{ {\left[ {\frac{{\partial \varPhi_{i} \partial \varPhi_{r} }}{{\partial x_{1} \partial x_{2} }} - \frac{{\partial \varPhi_{i} \partial \varPhi_{r} }}{{\partial x_{2} \partial x_{1} }}} \right]} \right.x_{3} . \\ \end{aligned}$$
(9)

Equations (8) and (9) are the exact solutions of the force and torque and are inputted into the FEM.

Finite Element Method Analysis

The horizontal plane of the model had a square observation area and four rectangular electrodes. The length of the observation area is normalized to 1 × 1 × 1.5 (Fig. 1), and the four cuboid electrodes are 0.5 long, 0.35 wide, and 0.05 high. The top and bottom of the chamber also has electrodes. The finite element analysis was executed with COMSOL (COMSOL Inc. USA), and the mesh of the observation area contained more than 106 elements. Notably, Eqs. (8) and (9) were applied to the definitions in the software calculations as the governing equations. The particle was considered a spherical specimen, and the parameters of the particle and medium are presented in Table 1. We calculated the imaginary part of the Clausius–Mossotti factor and then solved the conductivity of the A. niger. Its conductivity is assumed to be 52 mS/m, less than the surrounding medium 55 mS/m but higher than normal. The reason for high conductivity may due to the A. niger is immersed in medium after 24 h to avoid the particle floating on the medium surface. The horizontal dielectrophoretic field was considered first; the four electrodes in the horizontal plane were 5, 5i, −5, and −5i. Precisely, they were the 90° phase changes in nearby electrodes. Furthermore, the time interval was set from 0 to 180, and the solution was as illustrated in Fig. 2. Accordingly, the traveling-wave force gathered the particle rapidly to the center of the observation area at the beginning. Otherwise, this force would have pushed the particle out of the observation area at the two-diagonal direction areas, and the particles that were very close to the electrodes would stick on the electrodes’ surfaces. When the measuring time exceeded 180, the particles moved slowly.
Fig. 1

a Three-dimensional electrodes and b the liquid material of the dielectrophoretic device

Table 1

Parameters of the fluidic medium

Parameters of Aspergillus niger and fluidic medium

 Frequency of the electric field

55 (Hz)

 Conductivity of the medium

55 (mS/m)

 Relative permittivity of the medium

80

 Density of the medium

1000 (kg/m3)

 Viscosity of the medium

0.001 (Pa-s)

 Density of the Aspergillus niger

1050 (kg/m3)

 Diameter of the Aspergillus niger

4.0 (um)

 Conductivity of the Aspergillus niger

52 (mS/m)

 Relative permittivity of the Aspergillus niger

1

Parameters of the silicon

 Relative permittivity

11.7

 Conductivity

10−12 (S/m)

 Density

2329 (kg/m3)

Fig. 2

Solution of the particle tracing on the horizontal plane at time a 0, b 60, c 120, and d 180. The colors represent the voltage distribution

Moreover, the four electrodes in the horizontal plane were set to 5, 5i, −5, and −5i, and the bottom electrode was set to 1. The dielectrophoretic force was obtained numerically, and the particle tracing was calculated on the x–y and y–z planes. The force pattern revealed that the center of the space was the minimum force area, and the particle can be trapped at the center. The tracking results of this model are presented in Fig. 3 to demonstrate that the particles were moved to the center at a certain time in the given dielectrophoretic field. Notably, the moving velocity of the particle was controlled by the electric potential field. These results revealed the feasibility of the design and that of manipulating the dielectrophoretic device in the three-dimensional space. In our design, the four horizontal electrodes control the rotation with periodical voltages; two of the horizontal electrodes combined with the bottom electrode can provide the trapping field in the vertical plane and can provide the overturning torque. In Fig. 3, the vectors indicate the direction of motion. The simulation revealed that the particles can move and be trapped near the center of the observation space at a point slightly above the absolute center. According to the limitations of the software, the particles are moved to a minimum distance, but they will not be shown as overlapped particles in the simulation. Furthermore, the trapping height can be adjusted by tuning the amplitude of the voltage at the bottom electrode to control the suspension position.
Fig. 3

Total dielectrophoretic force direction on a 3-D simulation, b x–y planes, and c y–z planes of the three-dimensional model

This simulation has four limitations: (1) the viscous force and torque on the particle caused by the liquid are not considered; therefore, the moving velocity is not accreted in the simulation; (2) the Clausius–Mossotti factor of A. niger was approximately obtained from a previous study [17] and that results in an approximation of the gathering time; (3) the shape of the electrodes in the simulation is rectangular, which results in tip discharges at the corners and affects the dielectrophoretic field; thus, the mesh density of the electrodes must be adjusted to avoid this phenomenon; (4) for the vertical plane, only three electrodes exist without the top electrode, resulting in an asymmetric field along the horizontal axis. The fourth electrode could be set up as an AFM probe in the future.

Experimental Setup

We applied a microelectrical mechanical system process to manufacture a three-dimensional device, which included four electrodes coated on a glass wafer surface and one bottom electrode. The bottom electrode was fabricated by drilling a hole and then inserting a steel needle. Figure 4 shows the process flow of the fabrication of the device on a glass substrate. Most of these steps were performed in a standard clean room environment. To pattern the bottom electrode, a lift-off method was used. First, a cleaning step was applied. The cleaning solution was a typical mixture, namely a 3:1 concentrated sulfuric acid (H2SO4) to hydrogen peroxide (H2O2) solution. It was used to clean mineral residues from the surface of the glass wafer substrate. Subsequently, acetone and isopropanol were used to remove organic residues, such as lubricating oil, from the glass. Finally, the glass wafer was rinsed with deionized water and dried with nitrogen. After this cleaning process, a positive photoresist (JSR Micro Inc.), with AZP-4620 as the sacrificial layer, was spun on the glass wafer substrate and an exposure machine patterned the shapes of the bottom electrodes. Subsequently, the positive photoresist was developed with 3% TMAH liquid. After that lithography process, the bottom electrode was deposited with a 30 nm Ti and a 220 nm Pt thin-film layer on the top side of the glass wafer by using an E-gun evaporator. The AZP-4620 sacrificial layer was then removed with acetone. Finally, the device was cleaned with deionized water and dried with nitrogen. Thereafter, the device assembly was complete.
Fig. 4

Processing procedure flowchart for the device

For microelectromechanical fabrication, the horizontal electrodes were transferred from a mask, as shown in Fig. 5. The width of each electrode was 120 μm; the glass substrate had a 12-cm diameter. The gap between opposite electrodes was 100 μm, and two types of electrode materials were considered: (1) for the electrodes composed of copper, a layer of chrome was deposited between the substrate glass and electrodes and (2) for the platinum electrodes, titanium was deposited between the substrate and electrodes. A layer of positive photoresist was spin-coated on each metal film. After a process of soft baking, the film with photoresist was exposed to an aligner with a mask and was developed using a developer. Finally, we etched away the parts of the metal coating that were not protected by photoresist, and the electrodes were obtained when the photoresist was removed.
Fig. 5

a Device design of the two-dimensional electrodes, b the observation area and the A. niger cells, and c the system setup

For the bottom electrode, a hole (inner diameter, 150 μm and outer diameter, 200 μm) was drilled at the center of the observation through laser processing (Fig. 6a–c). Because the laser-drilling process destroyed the electrode pattern, the electrodes were recovered again through the same microelectromechanical processing. After opening the hole and recovering the electrodes, a needle (diameter, 160 μm) was inserted into the hole (from the outer hole) to serve as the fifth electrode in the bottom of the device (Fig. 6c). The needle was fixed in a plastic base, and the top of the needle was approximately 50 μm below the surface of the substrate. Excluding the microelectromechanical device, the external apparatus included a dynamic isolation platform, vertical movement controller, three-dimensional movement controller, 2000 × microscope with a tilting control, National Instruments signal generator, and light source. Some A. niger spores served as the target in this experiment, and they were cultured from some moldy bread in our laboratory. Each spore is a spheroid particle, with a diameter of 4 μm.
Fig. 6

a The laser-drilled hole (the laser exit hole), b the bottom electrode shown at center of the observation area, c the bottom electrode, a needle embedded in the plastic plate, d the whole system setup

The four electrodes were controlled using a functional program written by LabVIEW; the power was generated by an NI USB-6343 signal generator (National Instrument Company), with a maximum sampling rate of 900,000 simple-rate/s. The apparatus had four analog output channels, and the sampling frequency at each electrode was limited from 10 to 30 kHz, which was confirmed by comparison with the amplitudes of the signals measured using an oscilloscope. An optical microscope (1100–1500 ×) with a charge-coupled device camera was used to observe and record particle movement. The rotational sequence was a program for single traveling waves, in which the desired frequency and amplitude were inputted through a panel controller in LabVIEW. In the test mode, the voltage amplitude and rotation frequency were set to 5 V and 20 kHz, respectively, for the four electrodes.

Results

Two-Dimensional Rotation

The rotation tests of A. niger spores based on the R02 device with the Pt electrodes are shown in Fig. 7, and the images were captured at 0–3.5 s. In the tests, the two particles started to get together and to move immediately when the signal was applied, and the particles rotated initially after the particles translated to the observation center. According to the experiment, the period of one rotation is nearly uniform within one period. However, precisely, the angular velocity of the motion is variable within one period because the particle experiences interference in a specific angle range in the electric field. Thus, the frequency was tuned to 25, 30, and 35 kHz, and the same phenomenon was found. We tested the Pt electrodes for long time observation as shown in Fig. 8. In this figure, the A. niger spores moving toward the center was obvious, and the paths represented the dielectrophoretic isoclinics. Moreover, we tested the Pt and Cu electrodes, and the angular velocity–frequency curves are shown in Fig. 9.
Fig. 7

Rotation test of double spores on Cu-electrode device, with a frequency of 20 kHz at a 0 s, b 0.5 s, c 1 s, d 1.5 s, e 2 s, f 2.5 s, g 3 s, and h 3.5 s

Fig. 8

Rotation and movement of A. niger spores on a Pt-electrode device, with a frequency of 35 kHz at a 17 s, b 24 s, c 39 s, d 48 s, e 58 s, f 64 s, g 70 s, and h 73 s

Fig. 9

Relationship between angular velocity and frequency of A. niger spores based on two types of electrodes

Two-Dimensional Translation

For the translation test, a LabVIEW program controlled a particle to travel in a square path. The program code consisted of eight steps: (1) 0–20 s, (2) 21–30 s, (3) 31–40 s, (4) 41–60 s, (5) 61–80 s, (6) 81–100 s, (7) 101–110 s, and (8) 111–120 s. The first step prepared to trap a particle stably in the dielectrophoresis field with (5, 5, 5, 5) V in amplitude at the electrodes (left, top, right, bottom). Then in the second step, the amplitude of the left electrode was reduced to 1 V producing a configuration of (1, 5, 5, 5) at the four electrodes, and the particle started to move from the center to the left. In the third step, the amplitudes at left and top electrodes were set 1 V, producing (1, 1, 5, 5) at the electrodes, and the particle moved to the left-top. Then the configurations (5, 1, 1, 5), (5, 5, 1, 5), (5, 5, 1, 1), (1, 5, 5, 1), (1, 5, 5, 5), and (5, 5, 5, 5) were produced. Following these processes, the controlling paths formed a rectangular frame, and the particle in the observation area during the 120-s interval was recorded as illustrated in Fig. 10. The particle did not move perfectly along the designed path. Three possible causes were (1) the particle traveled over an excessively long distance where the dielectrophoretic distribution was not perfect; (2) the density of the particle was higher than that of water, thus the particle settled down and stopped at the bottom; and (3) the fluid hydrodynamic force also caused the particle to move slowly.
Fig. 10

Translation test of the A. niger spores on a Cu-electrode device, at a frequency of 20 kHz during a 10-s interval in al, and the overall path showing in blue curve in (a)

Three-Dimensional Overturning

For the three-dimensional overturning test, the program code controlled a particle to be trapped at the center and then to be rotated in a vertical plane. The overturned particle was observed at the center of the observation space, where the four Pt electrodes were positioned on the horizontal plane and one needle electrode was at the bottom. The images were captured at 0, 1, 2, 3, 5, and 6 s. The particles started to move immediately when the signal was applied and overturned initially after they were translated to the center of the observation space. Because the density of the A. niger spores was higher than water, to prevent the spores from settling on the bottom of the device, the amplitude of the bottom electrode was set to be larger than that of the horizontally positioned electrodes. Here, we set the voltage amplitude at 5.5 V, and the paths are shown in Fig. 11.
Fig. 11

Overturning test of A. niger spores based on a Cu-electrode device, at a frequency of 20 kHz during a 0.5-s interval. The spores rotated vertically and were therefore not on the focal plane

Clausius–Mossotti Factor

According to the dielectrophoretic theory, electrodes composed of different materials may result in similar phenomena. For example, dissimilar electrodes may have similar rotational velocities. However, as shown in Fig. 6, the differences between the Cu and Pt electrodes, and the ratio of the angular velocities (\(\omega_{cu} /\omega_{pt}\)), increased when the triggering frequencies were changed from 0.78 at 15 kHz to 0.89 at 35 kHz. Thus, it may be deduced that the viscous torque effect was present. Here, the viscous torque could be quantified as
$$\varvec{T}_{visc} = - 8\pi \mu r^{3} {{\varOmega }} \,\dot{\varvec{x}}_{3} .$$
(10)
The torque induced by dielectrophoresis was as follows
$$\varvec{T}_{dep} = 4\pi \varepsilon_{m} r^{3} Im[K^{*} \left( \omega \right)]\left( {\frac{{\partial {{\varPhi }}_{i} \partial {{\varPhi }}_{r} }}{{\partial x_{1} \partial x_{2} }} - \frac{{\partial {{\varPhi }}_{i} \partial {{\varPhi }}_{r} }}{{\partial x_{2} \partial x_{1} }}} \right)\varvec{x}_{3} .$$
(11)
Subsequently, the rotational equation of a particle could be written as
$$m\ddot{\theta } + \varvec{T}_{visc} = \varvec{T}_{dep} .$$
(12)
We have the motion equation,
$$m\varvec{\ddot{x}}_{3} - 8\pi \mu r^{3} {{\varOmega }}\dot{\varvec{x}}_{3} = 4\pi \varepsilon_{m} r^{3} {\text{Im}}[K^{*} \left( \omega \right)]\left( {\frac{{\partial {{\varPhi }}_{i} \partial {{\varPhi }}_{r} }}{{\partial x_{1} \partial x_{2} }} - \frac{{\partial {{\varPhi }}_{i} \partial {{\varPhi }}_{r} }}{{\partial x_{2} \partial x_{1} }}} \right)\varvec{x}_{3} .$$
(13)
Here, we assumed the velocity of the motion is a constant, and it reduces to
$$- 8\pi \mu r^{3} \varOmega \dot{x}_{3} = 4\pi \varepsilon_{m} r^{3} \text{Im} [K^{*} \left( \omega \right)]\left( {\frac{{\partial \varPhi_{i} \partial \varPhi_{r} }}{{\partial x_{1} \partial x_{2} }} - \frac{{\partial \varPhi_{i} \partial \varPhi_{r} }}{{\partial x_{2} \partial x_{1} }}} \right)x_{3} .$$
(14)
The relationship between the angular velocity and imaginary part of the Clausius–Mossotti coefficient, Im[K*(ω)] can be obtained. A comparison of the experimental results with the calculation results yielded the values of Im[K*(ω)] for low concentrations of A. niger at 20 kHz (Fig. 12).
Fig. 12

Clausius–Mossotti coefficient, Im[K*(ω)], of the A. niger spores

Conclusion

The rotation, translation, and overturning of the A. niger spores were performed successfully at a specific frequency by using a dielectrophoresis traveling wave. The dielectrophoresis field was expanded into an exact solutions and quantified with finite element analysis. A simulation supported the design of the device and demonstrated the electric field and particle tracing. Subsequently, a three-dimensional device, including four electrodes on the horizontal plane and one electrode on the bottom, demonstrated the A. niger spores in rotation with single, double, and multiple spores, demonstrated translation on a rectangular path, and demonstrated overturning in a vertical plane. According to the rotation test, the Clausius–Mossotti factor was modifiable. In our experience, the positions of the fifth electrode and power supply for the uniform dielectrophoresis were key points for trapping a particle precisely at the center (or any position) of the device and for controlling movement. Furthermore, the translation and rotation velocities were not constant because of the viscosity of the liquid. This device successfully realizes the vertical overturning technique, and that helps observe the back side of the specimen, while the specimen is chemically bonded on the substrate.

Notes

Acknowledgements

The authors thank the Ministry of Science and Technologies of Taiwan, ROC, for the support under contract NSC-104-2628-E-390-001. This manuscript was edited by Wallace Academic Editing.

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Copyright information

© Korean Multi-Scale Mechanics (KMSM) 2019

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringNational University of KaohsiungKaohsiungTaiwan
  2. 2.NEMS Research CenterNational Taiwan UniversityTaipeiTaiwan

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