30
2. THICK-ELECTRODE DEP FOR SINGLE-CELL 3D ROTATION
2.3.2 DESIGN AND SIMULATION OF 3D ROTATIONAL STRUCTURE OF
“ARMILLARY SPHERE”
Chip structure
Although the above-mentioned open structure can realize 3D rotation of single cells, single-cell
loading is nontrivial. In order to improve the single-cell loading eciency, a microchip combining
the thick electrodes and microchannel is proposed, as shown in Figure 2.9. e materials of four
vertical thick electrodes are C-PDMS, and the bottom electrode is transparent electrode ITO. For
single-cell loading, a V-shape single-cell capture structure is designed in the microchannel.
PDMS
Cell
C-PDMS
SU-8
Pillar
ITO
Glass
1
4
5
3
z
y
x
2
Figure 2.9: Schematic diagram of the single-cell 3D rotational chip structure.
Working procedures
Figure 2.10 shows the working procedures: (a) inject the cell solution and capture one single cell
using the V-shape pillars as the trap site; (b) using a back ow to release the captured cell from the
trap site, and when the cell ow to the electrode chamber, an electrical signal can be applied to the
two thick electrodes. When the resulting nDEP force and Stokes force are balanced, the cell is kept
in the chamber; (c-e) after the position of the cell in the chamber is stabilized, 3D rotation of the
cell is achieved by applying dierent signal congurations on the electrodes; (f) recovering the cell
by ushing the ow and stopping the electrical signals.
31
(a) (b) (c)
(d)
(e) (f)
Trap Release and Fix Rotation about Z-Axis
Rotation about X-Axis Rotation about Y-Axis Recycle
Figure 2.10: Chip working procedure diagram.
Electrode shape design
e DEP force and torque are proportional to ∇E
2
and E
2
, respectively, and are related to the
shape of the electrode. Figure 2.11(a‒c) shows three typical electrode geometries (circular, square,
and sharped) with the same microchannel width (200 µm). V
1
= 10sin(ωt), V
2
= 10sin(ωt+π/2),
V
3
= 10sin(ωt+π), and V
4
= 10sin(ωt+3π/2) are applied to the four thick electrodes, and the bot-
tom electrode is oating. Assuming ε
m
= 100ε
0
, R
cell
= 6 µm, Re[K
CM
] = 0.5, Figure 2.11(d) is the
average strength distribution of the electric eld over a period along the line A-A corresponding to
the three structures. e electric eld generated by the sharped electrode has the highest average
strength, which means the generated torque is the largest.
e DEP force generated by the two electrodes is analyzed. V
3
= 10sin(ωt), V
4
= 10sin(ωt+π)
are applied to the electrodes 3, 4, and the remaining two electrodes and the bottom electrode are
oating. Figure 2.11(e) shows the distribution of DEP forces along the cut line A-A. It can be found
that the sharp electrode produces the greatest DEP force, approximately twice that of the circular
and square electrodes. us, the sharp electrode is selected as the electrode geometry.
2.3 THICKELECTRODE MULTIELECTRODE CHIP DESIGN
32
2. THICK-ELECTRODE DEP FOR SINGLE-CELL 3D ROTATION
(a) Round
ITO
5
14
2
C-PDMS
3
SquareSharp
(d)
(e)
(b) (c)
8
7
6
5
4
50
40
30
20
10
0
Round
Square
Sharp
Round
Square
Sharp
E
ms
(V/m)
F
DEP
(pN)
-200 -100 100 2000
Along the Cutline A-A (µm)
-200 -100 100 2000
Along the Cutline A-A (µm)
Figure 2.11: Comparison of electric eld and DEP force of dierent shapes of electrodes: (a–c) top
view of electrode with three typical shapes; (d) electric eld strength along the line A-A (Vp-p = 10
V); and (e) along the line A-A e distribution of the DEP force on (Vp-p = 10 V).
Single-cell V-shape capture structure design
e V-shape trap structure placed in the microchannel is used to capture a single cell. Under the
laminar ow, a single cell will be trapped at the V-shape trap structure. Once a single cell is cap-
tured, the ow resistance at the V-shaped trap structure will increase and the remaining cells will
ow away from both sides. For the captured cell, back ow is used to push it away from the trap
site and transfer it to the electrode chamber.
e microchannel size is 200 μm×160 μm wide, the V-shape structure is 15 μm × 15 μm ×
25 μm, and the gap of V-shape is 10 μm. Because the cells are soft, the cell at the trap site would be
deformed easily by the ow force and squeezed out of the gap. On the other hand, it is necessary
to avoid too much shear force generated by the uid to aect the cell. e shear force of the ow
acting on the cell is estimated to be 0.076 dyne/cm
2
at a ow rate of 20 μm/s. According to the
literature, the eect of this shear force on the cell can be negligible.
33
Single-cell capture positioning simulation
After single-cell capture, the cell is transferred to the electrode chamber using back ow, and the
location of the cell in the chamber can be determined in two ways. e rst method uses visual
feedback to observe the position of the cell in real time, and stops the micropump immediately
when the cell moves into the chamber. However, this method has delay time and the cell easily
ows out of the electrode chamber. e second method uses the DEP force to balance the stokes
force. When back ow pushes the trap cell into the electrode chamber, an electrical signal is applied
to the two thick electrodes on the right side, which creates a DEP force between the two electrodes.
Figure 2.12(a) is a simulation of the electric eld strength (Vp-p = 10 V, f = 100 kHz). Figure
2.12(b) shows the distribution of DEP forces along the A-A cutline at dierent voltage amplitudes.
Assuming cell ow rate 40 μm/s, the stokes force is about 24 pN. It is possible to estimate the po-
sition at which the DEP force equal to stokes force. e larger the voltage amplitude, the more the
balance position is to the left. For example, when the voltage amplitude is 10 V, the balance position
of the cell is approximately at the center of the chamber.
(a) (b)
100
50
0
-50
-100
-100 100
×10
14
5
4
3
2
1
0
0
-100 1000
A-A Cutline (µm)
75
50
25
0
10 V
5 V
2 V
F
DEP
(pN)
(µm)
(µm)
∇
E
2
(V
2
/m
3
)
Figure 2.12: Simulation results of DEP force: (a) simulation of electric eld strength; and (b) the dis-
tribution of DEP force on A-A cutline.
3D rotational electric eld simulation
Horizontal rotation
Applying the same amplitude and frequency electrical signals (Vp-p = 10 V, f = 1 MHz) with a
phase shift of 90° on the four C-PDMS thick electrodes can generate a horizontally rotational elec-
tric eld in the chamber, causing the cell to do in-plane rotation. Figure 2.13 shows the electric eld
distribution simulation of the electrode chamber. Figure 2.13(a) shows that the electric eld in the
chamber rotates clockwise in one signal period. Figure 2.13(b) shows the electric eld in the cham-
ber rotates counterclockwise in one signal period once reversing the signals to the four electrodes.
2.3 THICKELECTRODE MULTIELECTRODE CHIP DESIGN
34
2. THICK-ELECTRODE DEP FOR SINGLE-CELL 3D ROTATION
(a)
(b)
Figure 2.13: Simulation of horizontal rotational electric eld: (a) clockwise rotation about the Z-axis;
and (b) counterclockwise rotation about the Z-axis.
Vertical rotation
In order to achieve vertical rotation, it is necessary to ensure that there is a phase shift between the
electrical signals applied to the two thick electrodes and the bottom electrode. Figure 2.14 shows
the variation of the electric eld at dierent time (Vp-p = 10 V, f = 1 MHz). In one period, the
electric eld in the vertical direction rotates clockwise, as shown in Figure 2.14(a). e direction of
cell rotation can be changed by adjusting the sequence of phase shift, as shown in Figure 2.14(b).
(a)
(b)
Figure 2.14: Simulation of vertical rotational electric eld (about Y-axis).
Changing the electrical signal conguration on the electrodes enables the electric eld in
the chamber to rotate about the X-axis. Figure 2.15 shows the change in electric eld at dierent
time (Vp-p = 10 V, f = 1 MHz). In one period, the electric eld in the vertical direction rotates
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