- Email: [email protected]
Numerical simulation of particle concentration in dielectrophoretic flow for high voltage applications
Accepted Manuscript Title: Numerical Simulation of Particle Concentration in Dielectrophoretic Flow for High Voltage Applications Author: Hong-Pil Jeon Jong-Chul Lee PII: DOI: Reference:
S0025-5408(14)00264-5 http://dx.doi.org/doi:10.1016/j.materresbull.2014.05.007 MRB 7451
To appear in:
MRB
Received date: Revised date: Accepted date:
3-8-2013 6-4-2014 2-5-2014
Please cite this article as: Hong-Pil Jeon, Jong-Chul Lee, Numerical Simulation of Particle Concentration in Dielectrophoretic Flow for High Voltage Applications, Materials Research Bulletin http://dx.doi.org/10.1016/j.materresbull.2014.05.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Numerical Simulation of Particle Concentration in Dielectrophoretic Flow for High Voltage Applications (Program number: Fr-P100, abstract number: 0573)
a
ip t
Hong-Pil Jeona,* and Jong-Chul Leeb Graduate School of Automotive Engineering, Gangneung-Wonju National University,
School of Mechanical and Automotive Engineering, Gangneung-Wonju National
us
b
cr
Wonju 220-711, Korea
University, Wonju 220-711, Korea
Corresponding author: Prof. Jong-Chul Lee, E-mail: [email protected]
Highlights
d
Graphical abstract
M
Tel: (+82-33) 760-8766, Fax: (+82-33) 760-8761
an
*
Ac ce pt e
► The dielectrophoretic flow with particle concentration was calculated. ► The flow along the boundary was caused by p-DEP from left to right. ► The particles should be accumulated inside vortices and near electrodes. ► The electrical breakdown of a dielectric liquid might be controlled. Abstract
A numerical simulation of magnetic nanoparticles in a liquid dielectric was developed to model dielectrophoretic flows for high voltage applications, e.g. transformers, capacitors, high voltage cables, and switchgears. From previous research, we found that the dielectric breakdown voltage of a transformer oil-based magnetic fluid was affected positively or negatively according to the amount of magnetic nanoparticles under the official testing condition of dielectric fluids. In order to understand these phenomena for enhancing the dielectric characteristics of the fluid
1 Page 1 of 14
finally, magnetic particles were visualized experimentally and numerically in a fluidic chip consisting of a microchannel and electrodes. In this study, we investigated the dielectrophoretic flow and the particle concentration in the microfluidic system with the different applied voltage for enhancing the electrical breakdown characteristics of a
cr
ip t
liquid dielectric used for high voltage applications.
KEYWORDS: A. magnetic materials, A. nanostructures, D. dielectric properties, D.
an
1. Introduction
us
electrical properties, D. magnetic properties.
M
As a dielectric material in liquid state for high voltage applications, e.g. transformers, capacitors, high voltage cables, and switchgears, the main purpose of a liquid dielectric
d
is to endure electric fields as high as possible or to quench electric discharges as fast as
Ac ce pt e
possible [1]. The dielectric breakdown voltage (DBV) is a measure of a liquid dielectric ability to withstand a high electric field stress without breaking down [2]. Magnetic fluid is a stable colloidal mixture contained magnetic nanoparticles (MNPs) coated with a surfactant [3]. It was found recently that the addition of magnetic nanoparticles could increase the dielectric breakdown voltage of the fluid, if the condition of the added particles in the fluid was in balance with that of keeping down the initiation and propagation of electrical streamers [4-6]. In order to explain the phenomenon for increasing DBV with adding MNPs, which was direct conflict with conventional wisdom regarding the breakdown of dielectric liquids, Hwang et al. with MIT [7] tried to explain the reason of the phenomena with the concept of electron scavengers of magnetic nanoparticles by computations. But they
2 Page 2 of 14
showed only the trend of initiation and propagation of electrical streamers only with a spherical particle for computations [8]. We have tried to verify the phenomena with the integration of dielectrophoresis (DEP) and microfluidic system for the characterization of micro/nano particles
ip t
experimentally [9] and numerically [10]. Particle movement towards regions of high
cr
electric field intensities is called positive DEP (p-DEP) and occurs when the interior of the particle is more permissive to the field [11]. Positive DEP force traps particles in
us
regions with strong electric field gradients, while negative DEP (n-DEP) force repels them from such regions [12]. However, it was very difficult to visualize the particles
an
motion in-situ using the microfluidic system, which was made up of a microchannel and
M
electrodes. Therefore, we have been developing a simplified unified model for estimating the dielectrophoretic activity of magnetic nanoparticles using a commercial
d
multiphysics program, COMSOL Multiphysics [13].
Ac ce pt e
In this study, we numerically simulate the dielectrophoretic flow and the particle concentration in the microfluidic system with the different applied voltage. Furthermore, the virtual images of MNPs under the different DEP force are investigated for affecting the electrical breakdown characteristics of a liquid dielectric with adding MNPs.
2. Methodology
The computational domain, which is modeled according to a fabricated chip (50mm×20mm) used for visualizing magnetic nanoparticles in [9], consists of two cylindrical electrodes, a 2 mm-long microchannel filled with magnetic fluids and PDMS (polydimethylsiloxane) around a channel as shown in Fig. 1. The width and the height
3 Page 3 of 14
of a 500 ㎛–long microchannel located in the middle of the channel are 50 ㎛ and 5 ㎛, respectively. In order to compute MNP’s trajectory in the microfluidic system under an electric potential, we have to calculate first the electrostatic field and the flow field,
ip t
sequentially. The electric field distribution in the system described by the Laplace
cr
equation with appropriate boundary conditions will provide the potential distribution in
the computational domain. This potential distribution is used to calculate the DEP force
2
(1)
M
3
an
FDEP 2 rp m Re K E
us
acting on particles as shown in Eq. (1).
where m is the permittivity of the base fluid and K ( ) the Clausius-Mossotti factor at
Ac ce pt e
d
frequency given by
*
K
p m *
*
p 2 m
(2)
*
where p * and m * are the complex permittivities ( * j / ) of the particle and fluid, respectively. The magnetic nanoparticles with high polarizability compared to the base fluid ( Re K 0 ) undergo positive DEP (pDEP) and are moved toward regions containing large E
2
which are typically near the edges of electrodes. Because DEP
force is proportional to the gradient of square of the electrical field strength, the higher potential applied at the electrodes generates the stronger DEP force with fluid flow.
4 Page 4 of 14
Fluidic forces for incompressible viscose liquids are described by the Navier-Stokes equation as shown in Eq. (3). And to simulate the deflection and sedimentation of the magnetic nanoparticles in a microfluidic chip, the Lagrange equation for moving
? ? ? ? u ? ? u u p 2 u f t
cr
? f Ap ? ? ? ? u f u p u f u p f 2
?
us
dt
CD
(4)
an
pV p
? du p
(3)
ip t
particles must be solved as shown in Eq. (4) [14].
?
M
where is the fluid density, u the velocity vector, p the pressure, the molecular
d
viscosity, f (FDEP) the dielectrophoretic force, V the volume and CD the flow resistance.
Ac ce pt e
The indices f and p stand for fluid and particle. The material properties such as relative permittivity and density for computations are shown in Table 1. Especially, the permittivity of a transformer oil based magnetic fluid, which has 0.065% of the volume concentration of magnetic nanoparticles as shown in [9], is interpolated from the values of OT-4 and EFH-1 produced by the manufacturers for the analysis of electric field.
3. Results and discussion In order to calculate the dielectrophoretic flow and the particle concentration in the microfluidic system with three different applied voltages (2.5 kV, 10kV and 20 kV), we set this complex problem by a set of coupled nonlinear equations as shown in Eqs. (3)
5 Page 5 of 14
and (4) and solved the coupled electric and flow fields in a microfluidic system by advanced CFD methods as mentioned in the previous section. Since DEP force is proportional to the gradient of square of the electrical field strength, it is found that there are the typical four points having the relative high-value of DEP force around the
ip t
edges of the microfluidic system as shown in Fig. 2. It should be because the edge of the
cr
channel is electrically the triple point, which has three different permittivities such as
the fluid, the electrode and PDMS. And the electric field gradient E [V/m2] and E
2
us
are high relatively near these triple points. The maximum DEP forces from
an
computations are 4.8 nN, 11.1 nN and 305 nN at three different voltages, 2.5 kV, 10 kV and 20 kV, respectively. And these are p-DEP forces in which the particles direct to the
M
local field gradient maximum. The volume concentration of MNPs is 0.065%, which is enough to cause the dielectrophoretic flow of the base fluid by p-DEP force to MNPs.
d
The direction of DEP flow is from left to right along the upper and the lower boundaries
Ac ce pt e
of the microfluidic system by p-DEP force to MNPs. As there is no inlet or outlet in the microfluidic system, the hydrodynamic pressure is increased near the right-hand side of the channel and causes the reverse flow from right to left along the centerline of the system [13].
Streamlines and velocity vectors for three different voltages are shown in Fig. 3. We can find the four vortices near the electrodes. The magnitude of a vortex is proportional to the applied voltage. Therefore, the spacing between the electrode and the vortex is smaller when the applied voltage is higher. The relationship between the vortex and the voltage should play an important role to analysis the electrical breakdown characteristics of a liquid dielectric with adding MNPs because there are the conductive MNPs in the vortices according the dielectrophoretic flow of the base fluid. The
6 Page 6 of 14
conductive MNPs in the vortices might be electron scavengers as mentioned in [7], and increase the electrical breakdown characteristics of a liquid dielectric. However, the increased DBV with adding MNPs should be limited by the
ip t
aggregation of MNPs. There are two regions where most MNPs exist in the microfluidic system. Those are the inner region of vortex and the edge space near electrode as shown
cr
in Fig. 4. The MNPs inside the vortices could go a little closer to the electrodes due to the stronger dielectrophoretic flow in case of increasing the applied voltage. And the
us
MNPs could experience more continuous collisions with the upper part of electrodes
an
and should be accumulated there easier when the applied voltage goes up. The bridge of MNPs between two regions should decrease the electrical breakdown characteristics of
M
a liquid dielectric. Finally, it is concluded that the electrical breakdown characteristics of a liquid dielectric might be controlled by adding MNPs and causing dielectrophoretic
Ac ce pt e
d
flow, which could be used for high voltage applications.
4. Conclusions
In this study, we numerically simulated the dielectrophoretic flow and the particle concentration in the microfluidic system with the different applied voltage. And the virtual images of MNPs under the different DEP force were investigated for affecting the electrical breakdown characteristics of a liquid dielectric with adding MNPs. It was found that the direction of DEP flow was from left to right along the upper and the lower boundaries of the microfluidic system by p-DEP force to MNPs. And the reverse flow from right to left along the centerline of the system was generated by the hydrodynamic pressure. These flows caused the vortices near the electrodes and set MNPs inside the vortices. These conductive MNPs in the vortices might be electron
7 Page 7 of 14
scavengers to increase the electrical breakdown characteristics of a liquid dielectric. However, in case of increasing the applied voltage, the MNPs inside the vortices could go a little closer to the electrodes due to the stronger dielectrophoretic flow, and be attached to those positioned at the upper part of electrodes. These bridges of MNPs
ip t
between two regions should decrease the electrical breakdown characteristics of a liquid
cr
dielectric.
us
Acknowledgements
This research was supported by Basic Science Research Program through the National
an
Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and
M
Technology(NRF-2010-0023506) and by the Agency for Defense Development through
Ac ce pt e
d
Chemical and Biological Defense Research Center.
References
[1] R. E. Hebner, Measurements of Electrical Breakdown in Liquids: Plenum, New York (1988), p. 519.
[2] U. Gafvert, A. Jaksts, C. Tornkvist, and L.Walfridsson, "Electrical Field Distribution in Transformer Oil", IEEE Trans. Electr. Insul. 27 (1992), p. 647. [3] S. Odenbach, Colloidal Magnetic Fluids: Basics, Development and Application of Ferrofluids, Springer-Verlag, Berlin, Heidelberg (2009). [4] V. Segal, A. Hjorstberg, A. Rabinovich, D. Nattrass, and K. Raj, "AC(60 Hz) and
8 Page 8 of 14
Impulse Breakdown Strength of a Colloidal Fluid Based on Transformer Oil and Magnetite Nanonparticles", IEEE International Symposium on Electrical Insulation, Arlington, Virginia, USA, June 7-10, 1998, p. 619. [5] J. Kudelcik, P. Bury, P. Kopcansky, and M. Timko, "Dielectric Breakdown in
ip t
Mineral Oil ITO 100 Based Magnetic Fluid", Physics Procedia 9 (2010), p. 78.
cr
[6] J. C. Lee, H. S. Seo, and Y. J. Kim, "The Increased Dielectric Breakdown Voltage
Journal of Thermal Sciences 62 (2012), p.29.
us
of Transformer Oil-Based Nanofluids by an External Magnetic Field", International
[7] J. G. Hwang, M. Zahn, and F. M. O'Sullivan, L. A. A. Pettersson, O. Hjortstam, and
an
R. Liu, "Effects of Nanoparticle Charging on Streamer Development in
M
Transformer Oil-Based Nanofluids", Journal of Applied Physics 107 (2010), 014310.
d
[8] F. M. O'Sullivan, "A Model for the Initiation and Propagation of Electrical
Ac ce pt e
Streamers in Transformer Oil and Transformer Oil Based Nanofluids", Ph.D. Thesis, Massachusetts Institute of Technology, 2007. [9] J. C. Lee, W. H. Lee, S. H. Lee, and S. Y. Lee, "Positive and Negative Effects of Dielectric Breakdown in Transformer Oil Based Magnetic Fluids", Materials Research Bulletin 47 (2012), 2984.
[10]J. C. Lee and S. Lee, "Dielectrophoresis-Magnetophoresis Force Driven Magnetic Nanoparticle Movement in Transformer Oil Based Magnetic Fluids", J. Nanosci. Nanotechnol. 13(9) (2013), p. 6179. [11]C. Zhang, K. Khoshmanesh, A. Mitchell, and K. Kalantar-zadeh, "Dielectrophoresis for Manipulation of Micro/Nano Particles in Microfluidic Systems", Anal. Bioanal. Chem. 396 (2010), p. 401.
9 Page 9 of 14
[12]Y. Kang and D. Li, "Electrokinetic Motion of Particles and Cells in Microchannels", Microfluid Nanofluid 6 (2009), p. 431. [13]H. S. Seo, S. Lee, and J. C. Lee, "Simplified Unified Model for Estimating the Dielectrophoretic Activity of Magnetic Nanoparticles Aimed at Enhancing the
ip t
Dielectric Characteristics of Transformer Oil ", J. Nanosci. Nanotechnol. In-press.
cr
[14]COMSOL Multiphysics User Guide, V.4.3a, Solving the Model-The Linear System Solver.
us
[15]C. D. James, J. McClain, K. R. Pohl, N. Reuel, K. E. Achyuthan, C. J. Bourdon, K. Rahimian, P. C. Galambos, G. Ludwig, and M. S. Derzon, "High-Efficiency
an
Magnetic Particle Focusing Using Dielectrophoresis and Magnetophoresis in a
Ac ce pt e
d
045015.
M
Microfluidic Device", Journal of Micromechanics and Microengineering 20 (2010),
Figure Captions
Fig. 1 (a) Schematic diagram of the microfluidic system. (b) Meshed simulation geometry.
Fig. 2 The computational results of dielectrophoretic force [nN] for three different voltages. (a) 2.5 kV. (b) 10 kV. (c) 20 kV. Fig. 3 The computational results of streamlines and velocity vectors for three different voltages. (a) 2.5 kV. (b) 10 kV. (c) 20 kV. Fig. 4 The computational results of particle trajectories for three different voltages. (a) 2.5 kV. (b) 10 kV. (c) 20 kV.
10 Page 10 of 14
d Ac ce pt e
(b)
M
an
us
cr
ip t
(a)
Figure 1
11 Page 11 of 14
ip t
(a)
an
us
cr
(b)
d
M
(c)
Ac ce pt e
Figure 2
12 Page 12 of 14
(a)
us
cr
ip t
(b)
an
(c)
Ac ce pt e
d
M
Figure 3
13 Page 13 of 14
(a)
cr
ip t
(b)
an
us
(c)
Ac ce pt e
d
M
Figure 4
Table 1. Material properties for the computations of electric and flow fields. Magnetic fluid (0.065%)
Transformer oil
Magnetic nanoparticle Electrode (Fe3O4, 20nm)
Density (ρ) [kg/m3]
-
837
4800
-
-
Relative permittivity (ε)
2.208
2.2
14.5
1
12.1
PDMS
14 Page 14 of 14
S0025-5408(14)00264-5 http://dx.doi.org/doi:10.1016/j.materresbull.2014.05.007 MRB 7451
To appear in:
MRB
Received date: Revised date: Accepted date:
3-8-2013 6-4-2014 2-5-2014
Please cite this article as: Hong-Pil Jeon, Jong-Chul Lee, Numerical Simulation of Particle Concentration in Dielectrophoretic Flow for High Voltage Applications, Materials Research Bulletin http://dx.doi.org/10.1016/j.materresbull.2014.05.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Numerical Simulation of Particle Concentration in Dielectrophoretic Flow for High Voltage Applications (Program number: Fr-P100, abstract number: 0573)
a
ip t
Hong-Pil Jeona,* and Jong-Chul Leeb Graduate School of Automotive Engineering, Gangneung-Wonju National University,
School of Mechanical and Automotive Engineering, Gangneung-Wonju National
us
b
cr
Wonju 220-711, Korea
University, Wonju 220-711, Korea
Corresponding author: Prof. Jong-Chul Lee, E-mail: [email protected]
Highlights
d
Graphical abstract
M
Tel: (+82-33) 760-8766, Fax: (+82-33) 760-8761
an
*
Ac ce pt e
► The dielectrophoretic flow with particle concentration was calculated. ► The flow along the boundary was caused by p-DEP from left to right. ► The particles should be accumulated inside vortices and near electrodes. ► The electrical breakdown of a dielectric liquid might be controlled. Abstract
A numerical simulation of magnetic nanoparticles in a liquid dielectric was developed to model dielectrophoretic flows for high voltage applications, e.g. transformers, capacitors, high voltage cables, and switchgears. From previous research, we found that the dielectric breakdown voltage of a transformer oil-based magnetic fluid was affected positively or negatively according to the amount of magnetic nanoparticles under the official testing condition of dielectric fluids. In order to understand these phenomena for enhancing the dielectric characteristics of the fluid
1 Page 1 of 14
finally, magnetic particles were visualized experimentally and numerically in a fluidic chip consisting of a microchannel and electrodes. In this study, we investigated the dielectrophoretic flow and the particle concentration in the microfluidic system with the different applied voltage for enhancing the electrical breakdown characteristics of a
cr
ip t
liquid dielectric used for high voltage applications.
KEYWORDS: A. magnetic materials, A. nanostructures, D. dielectric properties, D.
an
1. Introduction
us
electrical properties, D. magnetic properties.
M
As a dielectric material in liquid state for high voltage applications, e.g. transformers, capacitors, high voltage cables, and switchgears, the main purpose of a liquid dielectric
d
is to endure electric fields as high as possible or to quench electric discharges as fast as
Ac ce pt e
possible [1]. The dielectric breakdown voltage (DBV) is a measure of a liquid dielectric ability to withstand a high electric field stress without breaking down [2]. Magnetic fluid is a stable colloidal mixture contained magnetic nanoparticles (MNPs) coated with a surfactant [3]. It was found recently that the addition of magnetic nanoparticles could increase the dielectric breakdown voltage of the fluid, if the condition of the added particles in the fluid was in balance with that of keeping down the initiation and propagation of electrical streamers [4-6]. In order to explain the phenomenon for increasing DBV with adding MNPs, which was direct conflict with conventional wisdom regarding the breakdown of dielectric liquids, Hwang et al. with MIT [7] tried to explain the reason of the phenomena with the concept of electron scavengers of magnetic nanoparticles by computations. But they
2 Page 2 of 14
showed only the trend of initiation and propagation of electrical streamers only with a spherical particle for computations [8]. We have tried to verify the phenomena with the integration of dielectrophoresis (DEP) and microfluidic system for the characterization of micro/nano particles
ip t
experimentally [9] and numerically [10]. Particle movement towards regions of high
cr
electric field intensities is called positive DEP (p-DEP) and occurs when the interior of the particle is more permissive to the field [11]. Positive DEP force traps particles in
us
regions with strong electric field gradients, while negative DEP (n-DEP) force repels them from such regions [12]. However, it was very difficult to visualize the particles
an
motion in-situ using the microfluidic system, which was made up of a microchannel and
M
electrodes. Therefore, we have been developing a simplified unified model for estimating the dielectrophoretic activity of magnetic nanoparticles using a commercial
d
multiphysics program, COMSOL Multiphysics [13].
Ac ce pt e
In this study, we numerically simulate the dielectrophoretic flow and the particle concentration in the microfluidic system with the different applied voltage. Furthermore, the virtual images of MNPs under the different DEP force are investigated for affecting the electrical breakdown characteristics of a liquid dielectric with adding MNPs.
2. Methodology
The computational domain, which is modeled according to a fabricated chip (50mm×20mm) used for visualizing magnetic nanoparticles in [9], consists of two cylindrical electrodes, a 2 mm-long microchannel filled with magnetic fluids and PDMS (polydimethylsiloxane) around a channel as shown in Fig. 1. The width and the height
3 Page 3 of 14
of a 500 ㎛–long microchannel located in the middle of the channel are 50 ㎛ and 5 ㎛, respectively. In order to compute MNP’s trajectory in the microfluidic system under an electric potential, we have to calculate first the electrostatic field and the flow field,
ip t
sequentially. The electric field distribution in the system described by the Laplace
cr
equation with appropriate boundary conditions will provide the potential distribution in
the computational domain. This potential distribution is used to calculate the DEP force
2
(1)
M
3
an
FDEP 2 rp m Re K E
us
acting on particles as shown in Eq. (1).
where m is the permittivity of the base fluid and K ( ) the Clausius-Mossotti factor at
Ac ce pt e
d
frequency given by
*
K
p m *
*
p 2 m
(2)
*
where p * and m * are the complex permittivities ( * j / ) of the particle and fluid, respectively. The magnetic nanoparticles with high polarizability compared to the base fluid ( Re K 0 ) undergo positive DEP (pDEP) and are moved toward regions containing large E
2
which are typically near the edges of electrodes. Because DEP
force is proportional to the gradient of square of the electrical field strength, the higher potential applied at the electrodes generates the stronger DEP force with fluid flow.
4 Page 4 of 14
Fluidic forces for incompressible viscose liquids are described by the Navier-Stokes equation as shown in Eq. (3). And to simulate the deflection and sedimentation of the magnetic nanoparticles in a microfluidic chip, the Lagrange equation for moving
? ? ? ? u ? ? u u p 2 u f t
cr
? f Ap ? ? ? ? u f u p u f u p f 2
?
us
dt
CD
(4)
an
pV p
? du p
(3)
ip t
particles must be solved as shown in Eq. (4) [14].
?
M
where is the fluid density, u the velocity vector, p the pressure, the molecular
d
viscosity, f (FDEP) the dielectrophoretic force, V the volume and CD the flow resistance.
Ac ce pt e
The indices f and p stand for fluid and particle. The material properties such as relative permittivity and density for computations are shown in Table 1. Especially, the permittivity of a transformer oil based magnetic fluid, which has 0.065% of the volume concentration of magnetic nanoparticles as shown in [9], is interpolated from the values of OT-4 and EFH-1 produced by the manufacturers for the analysis of electric field.
3. Results and discussion In order to calculate the dielectrophoretic flow and the particle concentration in the microfluidic system with three different applied voltages (2.5 kV, 10kV and 20 kV), we set this complex problem by a set of coupled nonlinear equations as shown in Eqs. (3)
5 Page 5 of 14
and (4) and solved the coupled electric and flow fields in a microfluidic system by advanced CFD methods as mentioned in the previous section. Since DEP force is proportional to the gradient of square of the electrical field strength, it is found that there are the typical four points having the relative high-value of DEP force around the
ip t
edges of the microfluidic system as shown in Fig. 2. It should be because the edge of the
cr
channel is electrically the triple point, which has three different permittivities such as
the fluid, the electrode and PDMS. And the electric field gradient E [V/m2] and E
2
us
are high relatively near these triple points. The maximum DEP forces from
an
computations are 4.8 nN, 11.1 nN and 305 nN at three different voltages, 2.5 kV, 10 kV and 20 kV, respectively. And these are p-DEP forces in which the particles direct to the
M
local field gradient maximum. The volume concentration of MNPs is 0.065%, which is enough to cause the dielectrophoretic flow of the base fluid by p-DEP force to MNPs.
d
The direction of DEP flow is from left to right along the upper and the lower boundaries
Ac ce pt e
of the microfluidic system by p-DEP force to MNPs. As there is no inlet or outlet in the microfluidic system, the hydrodynamic pressure is increased near the right-hand side of the channel and causes the reverse flow from right to left along the centerline of the system [13].
Streamlines and velocity vectors for three different voltages are shown in Fig. 3. We can find the four vortices near the electrodes. The magnitude of a vortex is proportional to the applied voltage. Therefore, the spacing between the electrode and the vortex is smaller when the applied voltage is higher. The relationship between the vortex and the voltage should play an important role to analysis the electrical breakdown characteristics of a liquid dielectric with adding MNPs because there are the conductive MNPs in the vortices according the dielectrophoretic flow of the base fluid. The
6 Page 6 of 14
conductive MNPs in the vortices might be electron scavengers as mentioned in [7], and increase the electrical breakdown characteristics of a liquid dielectric. However, the increased DBV with adding MNPs should be limited by the
ip t
aggregation of MNPs. There are two regions where most MNPs exist in the microfluidic system. Those are the inner region of vortex and the edge space near electrode as shown
cr
in Fig. 4. The MNPs inside the vortices could go a little closer to the electrodes due to the stronger dielectrophoretic flow in case of increasing the applied voltage. And the
us
MNPs could experience more continuous collisions with the upper part of electrodes
an
and should be accumulated there easier when the applied voltage goes up. The bridge of MNPs between two regions should decrease the electrical breakdown characteristics of
M
a liquid dielectric. Finally, it is concluded that the electrical breakdown characteristics of a liquid dielectric might be controlled by adding MNPs and causing dielectrophoretic
Ac ce pt e
d
flow, which could be used for high voltage applications.
4. Conclusions
In this study, we numerically simulated the dielectrophoretic flow and the particle concentration in the microfluidic system with the different applied voltage. And the virtual images of MNPs under the different DEP force were investigated for affecting the electrical breakdown characteristics of a liquid dielectric with adding MNPs. It was found that the direction of DEP flow was from left to right along the upper and the lower boundaries of the microfluidic system by p-DEP force to MNPs. And the reverse flow from right to left along the centerline of the system was generated by the hydrodynamic pressure. These flows caused the vortices near the electrodes and set MNPs inside the vortices. These conductive MNPs in the vortices might be electron
7 Page 7 of 14
scavengers to increase the electrical breakdown characteristics of a liquid dielectric. However, in case of increasing the applied voltage, the MNPs inside the vortices could go a little closer to the electrodes due to the stronger dielectrophoretic flow, and be attached to those positioned at the upper part of electrodes. These bridges of MNPs
ip t
between two regions should decrease the electrical breakdown characteristics of a liquid
cr
dielectric.
us
Acknowledgements
This research was supported by Basic Science Research Program through the National
an
Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and
M
Technology(NRF-2010-0023506) and by the Agency for Defense Development through
Ac ce pt e
d
Chemical and Biological Defense Research Center.
References
[1] R. E. Hebner, Measurements of Electrical Breakdown in Liquids: Plenum, New York (1988), p. 519.
[2] U. Gafvert, A. Jaksts, C. Tornkvist, and L.Walfridsson, "Electrical Field Distribution in Transformer Oil", IEEE Trans. Electr. Insul. 27 (1992), p. 647. [3] S. Odenbach, Colloidal Magnetic Fluids: Basics, Development and Application of Ferrofluids, Springer-Verlag, Berlin, Heidelberg (2009). [4] V. Segal, A. Hjorstberg, A. Rabinovich, D. Nattrass, and K. Raj, "AC(60 Hz) and
8 Page 8 of 14
Impulse Breakdown Strength of a Colloidal Fluid Based on Transformer Oil and Magnetite Nanonparticles", IEEE International Symposium on Electrical Insulation, Arlington, Virginia, USA, June 7-10, 1998, p. 619. [5] J. Kudelcik, P. Bury, P. Kopcansky, and M. Timko, "Dielectric Breakdown in
ip t
Mineral Oil ITO 100 Based Magnetic Fluid", Physics Procedia 9 (2010), p. 78.
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[6] J. C. Lee, H. S. Seo, and Y. J. Kim, "The Increased Dielectric Breakdown Voltage
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[7] J. G. Hwang, M. Zahn, and F. M. O'Sullivan, L. A. A. Pettersson, O. Hjortstam, and
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R. Liu, "Effects of Nanoparticle Charging on Streamer Development in
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Transformer Oil-Based Nanofluids", Journal of Applied Physics 107 (2010), 014310.
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[8] F. M. O'Sullivan, "A Model for the Initiation and Propagation of Electrical
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Streamers in Transformer Oil and Transformer Oil Based Nanofluids", Ph.D. Thesis, Massachusetts Institute of Technology, 2007. [9] J. C. Lee, W. H. Lee, S. H. Lee, and S. Y. Lee, "Positive and Negative Effects of Dielectric Breakdown in Transformer Oil Based Magnetic Fluids", Materials Research Bulletin 47 (2012), 2984.
[10]J. C. Lee and S. Lee, "Dielectrophoresis-Magnetophoresis Force Driven Magnetic Nanoparticle Movement in Transformer Oil Based Magnetic Fluids", J. Nanosci. Nanotechnol. 13(9) (2013), p. 6179. [11]C. Zhang, K. Khoshmanesh, A. Mitchell, and K. Kalantar-zadeh, "Dielectrophoresis for Manipulation of Micro/Nano Particles in Microfluidic Systems", Anal. Bioanal. Chem. 396 (2010), p. 401.
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[12]Y. Kang and D. Li, "Electrokinetic Motion of Particles and Cells in Microchannels", Microfluid Nanofluid 6 (2009), p. 431. [13]H. S. Seo, S. Lee, and J. C. Lee, "Simplified Unified Model for Estimating the Dielectrophoretic Activity of Magnetic Nanoparticles Aimed at Enhancing the
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Dielectric Characteristics of Transformer Oil ", J. Nanosci. Nanotechnol. In-press.
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[14]COMSOL Multiphysics User Guide, V.4.3a, Solving the Model-The Linear System Solver.
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[15]C. D. James, J. McClain, K. R. Pohl, N. Reuel, K. E. Achyuthan, C. J. Bourdon, K. Rahimian, P. C. Galambos, G. Ludwig, and M. S. Derzon, "High-Efficiency
an
Magnetic Particle Focusing Using Dielectrophoresis and Magnetophoresis in a
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045015.
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Microfluidic Device", Journal of Micromechanics and Microengineering 20 (2010),
Figure Captions
Fig. 1 (a) Schematic diagram of the microfluidic system. (b) Meshed simulation geometry.
Fig. 2 The computational results of dielectrophoretic force [nN] for three different voltages. (a) 2.5 kV. (b) 10 kV. (c) 20 kV. Fig. 3 The computational results of streamlines and velocity vectors for three different voltages. (a) 2.5 kV. (b) 10 kV. (c) 20 kV. Fig. 4 The computational results of particle trajectories for three different voltages. (a) 2.5 kV. (b) 10 kV. (c) 20 kV.
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(b)
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an
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(a)
Figure 1
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(a)
an
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(b)
d
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(c)
Ac ce pt e
Figure 2
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(a)
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(b)
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(c)
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Figure 3
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Figure 4
Table 1. Material properties for the computations of electric and flow fields. Magnetic fluid (0.065%)
Transformer oil
Magnetic nanoparticle Electrode (Fe3O4, 20nm)
Density (ρ) [kg/m3]
-
837
4800
-
-
Relative permittivity (ε)
2.208
2.2
14.5
1
12.1
PDMS
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