A three dimensional model - THE FINITE ELEMENT METHOD

CHAPTER 3 NUMERICAL SIMULATION AND DEVICE DESIGN

3.2 THE FINITE ELEMENT METHOD

3.2.2 A three dimensional model

According to the previous study, a three-dimensional model was built for the analysis of three-dimensional movement. In three-dimensional analysis,

the effect of the AFM tip and the arrangement of the electrodes are the topic we concerned. The three-dimensional rotation and translation behaviors were also studied. A successful three-dimensional device should exert enough force on the particle, and also the forces should be symmetric. By applying such device, the particle would be trapped at the center of the device. From the improvement of the two-dimensional model, the three-dimensional model was set as shown in Figure 3.7. The outer cube is the chamber, in which the length of this cube is 2, the inner cube is the observation area with a length 1, the cuboid electrodes with 0.5 in long, 0.35 in wide, and 0.05 in high. The bottom surface. A device with four electrodes at the four sides of the device could fulfill the condition and the dielectrophoretic force was strong enough shown on the x-y plane. The electrodes at the top and the bottom had to be the same geometry, because the distribution of the electric field would be symmetry under this configuration. As the results shown in Figure 3.10, both of the force direction and the magnitude of the force show that the device is

able to manipulate the particle in the observation area. To avoid the particle escaping along the diagonal direction in any cut plane, we extend the electrodes at the four sidea one unit length high. Moreover, we added a tip into the three-dimensional simulation of the particle tracing, and we extended the whole model into a real size. So that the length is 100 times longer than the previous simulation. The tracking results of longer electrodes model are shown in Figure 3.11 and in Figure 3.12. In the figures, the particles were successfully gathered by dielectrophoretic device in every cut plane. The velocity of the translation motion was controlled by the electric potential.

These results proved the feasibility of manipulating the micro-particles by the three dimensional dielectrophoretic device.

After the simulations of different arrangement of the electrodes were done, we added a tip into the model (see Figure 3.13). The radius of the top and the bottom of the tip were 10 μm and 5 μm, and the height was 100 μm.

This simulation was expected to demonstrate how a tip affect the particles in a dielectrophoretic device. Here the tip was assumed to be made of silicon.

The parameters are showed on Table 3.2. The results of longer electrodes and with an AFM tip model show in Figure 3.14 and Figure 3.15. On x-y plane, the device was obviously viable; but, on y-z plane, the particle would start to approach and stick on the tip after 21 seconds. The reason is that, in this simulation, the tip was polarized in the electric field, and the particles ware

attracted by the tip. Even if the silicon has such low relative permittivity, the motion of the particle was affect by the tip.

3.2.3 Simulation of the practical parameters

In three-dimensional test, a phenomenon that the particles rotated at arbitrary position around the electrodes was happened. Thus, we calculated the imaginary part of the Clausiuss-Mossotti factor, and the conductivity of the Aspergillus Niger could be obtained as 52 mS/m. Here we built models to simulate this condition, and we designed a three steps sequence to discuss the practical problem. First step, we applied parameters which are shown on Table 3.3 into a two-dimensional model, and this simulation proved the feasibility of the parameters. The results of two-dimensional model were shown in the Figure 3.16. Here the observation area was extended to a 200 three-dimensional model based on the real design is that being shown in the Figure 3.17. The particles were not gathering to the center of the device in this simulation, and most of the particles stayed at the original position. Third,

we analyzed the force direction of five electrodes design. It turns out that the ideal trapped position was located at the upper area of the liquid medium instead of the center of the device (see Figure 3.18). We proposed a solution for this problem after the analysis. The problem can be solved by enhancing the voltage of the bottom electrode. This improvement can make the particles suspend in higher position. In higher position the particles can be trapped at the center.

Figure 3.1 Boundary conditions for the numerical calculation.  is the electric potential.

Figure 3.2 Distributions of (a) the conventional dielectrophoresis and (b) the traveling-waved dielectrophoresis. These results were calculated by the numerical method.

Figure 3.3 (a) The conventional dielectrophoretic force and (b) the traveling waved dielectrophoretic force calculated by the FEM.

Figure 3.4 The modified configuration for the FEM.

Figure 3.5 (a) The conventional dielectrophoretic force and, (b) the traveling-waved dielectrophoretic force calculated by the FEM.

Figure 3.6 Solution of the particle tracing at (a) 0 (b) 60 (c) 120 (d) 180 second. Blue and red mean -5 Volt and 5 Volt

Figure 3.7 Three-dimensional distribution of the dielectrophoretic device.

Figure 3.8 Simulation result of the three dimensional device.

Figure 3.9 modified configuration of the dielectrophoretic device.

Figure 3.10 Simulation result of the three dimensional device.

Figure 3.11 The three-dimensional simulation at x-y plane of the particle tracing (a) 0 s (b) 21 s (c) 61 s (d) 100 s

Figure 3.12 The three-dimensional simulation at y-z plane of the particle tracing (a) 0 s (b) 21 s (c) 61 s (d) 100 s

Figure 3.13 A three-dimensional model with a tip. The bottom of the tip locates at the center of the device.

Figure 3.14 The result at (a) 0 s, (b) 21 s, (c) 61 s, and (d) 100 s of the simulation with the tip in the x-y plane.

Figure 3.15 The result at (a) 0 s, (b) 21 s, (c) 61 s, and(d) 100 s of the simulation with the tip in the y-z plane.

Figure 3.16 The result at (a) 0 s, (b) 5 s, (c) 10 s, (d) 15 s, and (e) 20 s.

Figure 3.17 The result at (a) 0 s, (b) 5 s, (c) 10 s, and (d) 15 s.

Figure 3.18 The total dielectrophoretic force direction at (a) x-y plane, and (b) y-z plane of the three dimensional model based on the real device.

Table 3.1 The parameters of the RBC and of the fluidic medium.

Frequency of the electric field 1 [Hz]

Conductivity of the medium 55 [mS/m]

Relative permittivity of the medium 80 Density of the medium 1000 [kg m/ ³]

Viscosity of the medium 0.001 [Pa-s]

Density of the RBC 1050 [kg m/ ³]

Diameter of the RBC 1.8 [um]

Conductivity of the RBC 0.25 [S/m]

Relative permittivity of the RBC 50

Table 3.2 The parameters of the silicon

Relative permittivity 11.7

Conductivity 10^¹² [S/m]

Density 2329 [kg m/ ³]

Table 3.3 The modified parameters of Aspergillus Niger and fluidic medium.

Frequency of the electric field 20 [kHz]

Conductivity of the medium 55 [mS/m]

Relative permittivity of the medium 80 Density of the medium 1000 [kg m/ ³]

Viscosity of the medium 0.001 [Pa-s]

Density of the Aspergillus Niger 1050 [kg m/ ³] Diameter of the Aspergillus Niger 4 [um]

Conductivity of the Aspergillus Niger 52 [mS/m]

Relative permittivity of the Aspergillus Niger 1

Chapter 4 Dielectrophoresis Experimental Test

In this chapter, the modified device from the previous simulations (as shown in Ch. 3) will be developed; and, accordingly, the electric effects of potential and frequency will be measured by applying the electrorotation test.

The two-dimensional experiment was executed by the dielectrophoretic device in which the configuration of four electrodes are with polynomial and rectangular electrodes (as shown in Figure 4.1). The electrodes were applied with AC current with the amplitude Volts and a frequency ω. Electrodes made of different materials (such as: copper, and platinum) were applied in the experiments of the rotating test and the shifting test. The rotating test could provide a result that helps us to estimate the imaginary part of the Clausius-Mossotti factor. The shifting test aimed that the particles traveled through the paths which we designed, and that provided the data to calculate the real part of the Clausius-Mossotti factor. A three-dimensional device needed to provide an electrode at the bottom of the device, and so we used a soft substrate to build a 3D device. In the experiments, spores of Aspergillus Niger were used as the specimen. The spore of Aspergillus Niger is a spheroid particle with the diameter is about 4 μm (as shown in Figure 4.2). The spore image which was scanned by an AFM is shown in the Figure 4.3

4.1 A two-dimensional electrode development

There are three different methods to manufacture the two-dimensional dielectrophoresis device, and there are: the photolithography based process, the eraser based process, and the acupuncture needles electrode based process.

Using a process of manufacturing the MEMS is the first method to build the two dimensional device. Firstly, a mask was drawn as shown in Figure 4.4, in which the substrate glass is a circular platewith 12 cm diameter and 0.55 mm height. The width of the electrodes is 120 μm. The distance between opposite electrodes is 100 μm for P0, 170 μm for R0, and 200μm for P02 and R02.

There are two materials for the electrodes. For the electrodes made of the copper, a layer of the chrome is deposited between the substrate glass and the electrodes. The other material is platinum. For platinum electrodes, the titanium is deposited between the substrate and the electrodes. Then a layer of positive photoresist was spin coated on the metal film. After a process of soft baking, the film with photoresist is exposed to the aligner with the mask and developed by using the developer. Finally, we etch away the parts of the metal coating without the protection of the photoresist, and an array of the electrodes is formed when the rest of the photoresist is removed, please see Figure 4.5 and 4.6.

The second method is using the eraser as the substrate and a thin blade as the electrodes to build the dielectrophoresis device. The eraser is a 2cm 

2 cm  1.15 cm cuboid, and it was cut four paths with the knife. The width

of the blade tip is 20 μm, and the triangular thin blades were buried along the four paths as four electrodes. The distance between two opposite electrodes is about one to two times of the thickest part of the blade which is about 80 μm.

In these handmade electrodes, the major problem of this method is that the tip of the thin blade is curved since the rectangular blade was processed to a trapezoid blade (see Figure 4.7).

To improve the disadvantage of the blade-electrodes as shown in Figure 4.8. In which, the blade tip in (b) is straighter than the blade tip in (a).

This feature can provide more symmetricity when four blade consist a dielectrophoretic device. (c) is the acupuncture needles. It is obvious to see that there is no any warp at the tip of the needle. The third method built the device with the electrode by the acupuncture needles. The similar process with the second method was applied. The acupuncture needles were obtained from WUJIANG CITY CLOUD & DRAGON MEDICAL DEVICE CO., LTD., and its length is 3.6 cm and its diameter is ~160 μm. And the distance of the opposite electrodes is about 150 ~ 300 μm. In this design, the thin blade in the second design was replaced by the needle. The advantage of this design is that the acupuncture needle is very straight, and there is no any warp at the tip. So the acupuncture needles could be directly used in the fabrication of the dielectrophoretic device without any extra manufacturing. As a result, the configuration of four needle-electrodes can be more symmetric. The more

symmetric, the more possibility to succeed (see Figure 4.9) in the following tests. The symmetricity means that the opposite electrodes should be aligned to each other (see Figure 4.10).

4.2 Signal generator and testing

We used a signal generator as the power supply to the electrodes, and it help to design a control program with assist software called Labview. The signal generator is NI USB-6343 (see Figure 4.11), which is made by National Instrument company. The maximum sampling rate of USB-6343 is 900 kS/s. There are four analog output channels on USB-6343. With the four analog output channels being used and the limitation of the signal generator, the maximum sampling frequency of the electrodes is up to 225 kHz, and the frequency of the electric field which must be less than a half of the sampling rate is 112.5 kHz. As a result, the maximum frequency of programs with the switch in the program is 56.25 kHz, because there are eight virtual channels in the program. To check the accuracy of the wave signal generated by NI USB-6343 with the program code we deigned, we used an oscilloscope to measure the sine wave signal generated by the NI USB-6343. This measurement showed an important result that the jagged edge became much obvious while the control frequencies was increased (see Figure 4.12). The real output amplitude was 5.2 Volts, but it was exactly 5 Volts in the setting.

From the above measurement, we decided the frequency which we used in the experiment was at the interval of 10 kHz to 30 kHz. Finally, we used the following three sequences as discussion, the sequences which were designed by us in the LabView to run the dielectrophoresis test.

The rotational sequence which is shown as Figure 4.13 is a simple program which can achieve the traveling-waved dielectrophoresis. There are an upper white blank is frequency, the lower blank is the amplitude, and output waveform window in (a). There are front panel and block diagram in the Labview. In the front panel, we can enter the desired frequency and the amplitude. When the program is running, the wave diagram will be displayed in the right hand side window which is called output waveform in the program. The block diagram is the designed program code. The frequency and the amplitude are input to the second column which is called simulate signal blocks. Blocks from the top block to the bottom block in the second column represent electrodes with phase 0, 90, 180 , and 270 , and they also represent the channels from the first to the last of analog output.

For separated parameters program, we can apply different frequency and the amplitude on each electrode (see Figure 4.14 and 4.15). In Figure 4.15, (1) is the switch that can input true or false, and it is the controller for (3). (2) is the input parameters, including, frequency and amplitude. (3) is the signal settings. From the top to the bottom indicate 0⁰, 90⁰, 180⁰, and 270⁰. There

are two cases, true and false. It is decided by (1). The dielectrophoretic field in the false case makes particles rotating counterclockwise, the dielectrophoretic field in the true case makes particles rotating clockwise. (4) is the output setting for the device and displaying the waveform graph.

Here are the blanks in the front panel, and each block can input the required frequency and the amplitude to every electrode. For the third column, there are two cases. The program will switch between this two cases depending on the switch bottom in the front panel is on or off. When the switch is off, the program will run the false case. In the false case, the particle will rotate counterclockwise. In the other hand, the program will run the true case. In the true case, the phase sequence changes from ( 0 , 90 , 180 , and 270   ) to （ 0 , 270 , 180 , and 90    ）, which means the particle will rotate clockwise.

In the rectangular shifting path program as shown in the Figure 4.16, there are a time counter and a case selector which has eight cases. In Figure 4.16, (1) is the time counter shows the elapsed time on the front panel and inputs elapsed time to (2). (2) shows 8 intervals of time. In every interval the output amplitude is set to make the specimen travel a rectangular path. In this program, there is also a switch to control the direction of the rotation. The time counter is set as a maximum 1000 seconds with the reset bottom. It also shows the elapsed time in the front panel, and it inputs the elapsed time to the

case selector. There are eight cases in the case selector, and the standard for different case is the elapsed time. The case will be executed when the elapsed time is (1) 0 s or other, (2) 21 s ~ 30 s, (3) 31 s ~ 40 s, (4) 41 s ~ 60 s, (5) 61 s

~ 80 s, (6) 81 s ~ 100 s, (7) 101 s ~ 110 s, (8) 111 s ~ 120 s. These eight stages represent the square path designed for the particle.

4.3 Rotational test

The rotational test is a process for proving the feasibility of three types of the dielectrophoretic device designed previous. For experiment, we used an optical microscope with a charge-coupled device (CCD) to capture the image.

The experiment arrangement is shown as the Figure 4.17. The first device is a common design which was crafted by the standard manufacturing process of the MEMS. Here the R02 device was applied to do the experiment; the R02 device was produced by standard procedure of MEMS; the R02 device is a device with rectangular electrodes; and the distance of the opposite electrodes is 200 μm. The amplitude of voltage and the frequency of rotation were firstly setup by 5 V and 20 kHz, and they were applied to the four electrodes. The result of the rotating test by using a R02 device with Cu-electrodes is shown as the Figure 4.18. The particles started to move at the very first second when the signal was applied to the electrodes. The rotation was initiated after the particles translated to the center area of the device. Generally, the rotation

was considered as a constant velocity motion for particles rotate for n cycles (n is a natural number). The velocity of the motion was not a constant if we considered the rotating angle did not equal to 360n, (nZ) . This phenomenon was caused by the angle between the effective dipole and the electric field. Then we tuned the frequency to 25, 30, and 35 kHz. The same phenomenon was existing for every case. Next, we replace the Cu-electrodes by the Pt-electrodes. Because the reduction potential of the copper is smaller than the redox potential of the platinum. So the stability of the exam became better. Result of the test with Pt-electrodes is shown in the Figure 4.19. Then we drew an angular velocity-frequency diagram as Figure 4.20. According to the dielectrophoretic theory, the test result will not affect by using electrodes which were made of different materials. But there were differences between the results by using Cu-electrodes and Pt-electrodes. The ratios ( _Cu _Pt) of the angular velocity by using Cu-electrodes and Pt-electrodes become greater with the frequency increasing. The ratio is 0.78 at 15 kHz, and the ratio becomes 0.89 at 35 kHz.

Now, we assumed the viscous torque can be written as,

T_viscous  8r3 (4.1)

And the torque induced by dielectrophoresis is as following,

 1 2 3 ³ ^*  3

The equation of particle’s rotational motion is assumed by

Equation (4.3) can be written as a function of Eq. (4.1) and (4.2),

We can get a relation between the angular velocity and the imaginary part of the Clausius-Mossotti factor as Figure 4.21. By comparing the experiment results and the calculation results, we can determine ^Im^K^* ^ ^{ }^0.0185for low concentration of the Aspergillus Niger at 20 kHz. Following the above procedure, we calculate ^{Im K} ^* ^  for different frequency (see Figure 4.22).

On the other hand, two other devices relative to the eraser substrate and the acupuncture needles electrode were studied. The eraser substrate based device was built by the thin blade and the eraser. We cut a rectangular thin blade into trapezoid. There would be a warp at the tip of the trapezoid thin

blade after the manufacture. To treat the warp, we tried to heat and then hammer the blade. After we applied a treatment to the blade, the blade became straighter. The voltage amplitude and the frequency were setup by 5 V and 30 kHz to apply to the blade. Accordingly to the test, the experimental test showed that it existed a dielectrophoretic field, but this configuration was not symmetric enough to trap the particle. The acupuncture needles electrode made device is an improved version modified from the second one. Replacing

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