G RID DENSITY - MATHEMATICAL MODEL AND NUMEICAL METHOD 16

CHAPTER 2 MATHEMATICAL MODEL AND NUMEICAL METHOD 16

2.3 G RID DENSITY

The meshing elements and accuracy of the numerical model was determined by the testing of grid density. The convergence criteria of

the left and right interfaces, which is the pumping pressure for the motion of the liquid droplet. According to Fig. 2-9, the pressure difference reached a stable value, 650 N/m², at a grid density of 150,000 cells/mm³, which was used in the simulation.

Fig. 2-1 Illustration of Electrical Double Layer [2]

Fig. 2-3 Illustration of basic model used to deduce equations [14]

Fig. 2-4 Equivalent circuit of EWOD in the parallel plates [1]

Fig. 2-5 Illustration of deducing pressure difference

Fig. 2-6 Illustration of droplet moved by different pressure

Fig. 2-7 Views of X, Y and Z directions of droplet cutting [9]

(a) Actual interface

(b) SLIC

Fig. 2-8 Schematic diagram of free surface reconstructions: (a) actual interface; (b) SLIC approximation; (c) PLIC approximation

Fig. 2-9 SIMPLEC algorithms

Fig. 2-10 Evolution of the pressure difference against grid density (case 05)

CHAPTER 3 ELECTRODE DESIGNS AND DEVICE PROCESS

It is well-known that for EWOD, the drag of droplet is greater when the channel height becomes smaller. In order to solve this problem, a set of new shape of electrodes with extended rectangles was designed. The difference between the new and original electrodes can be seen in Fig. 3-1, in which the original one is square, whereas the new one is interdigitated with an “extended rectangle”. According to Eq. (2.22), the large pressure difference can move the droplet fancily. So the first step is to design the electrode that can generate large pressure difference. Consequently, the electrode shape and channel height are also needed to take into consideration. The comparison of the original electrodes with new ones will be discussed in next chapter.

3.1 Designs of electrode arrangements

All designed types of electrodes are illustrated in Fig. 3-2. There are nine types of electrodes with different widths of extended electrode, various areas of extended electrode and specific numbers of extended electrode. All of them are summarized in Table 3-1. Fig. 3-3 shows the arrangements of different electrodes, in which the first group is A1and A2, the second group is A3 and A4, the third group is A5 and A6, and the forth group is A7 and A8.

For instance, the first group stands for the kind of electrode array in one-dimension, such as A1A2A1A2…. Similarly, the other three groups have the same meaning of first group, such as A3A4A3A4…, A5A6A5A6… , A7A8A7A8…, etc..

Table 3-1 Electrode shapes

The experimental equipments consist of the contact angle goniometer, microscope, CCD camera and controlled circuit (microcontroller). The schematic configurations are shown in Fig. 3-4. The contact angle goniometer, whose base is on a XYZ platform, is used to measure contact angle on the hydrophobic layer (Teflon layer). The microscope is used to observe droplet motion, such as droplet moving, cutting, velocity and so on, recorded by CCD camera (30 frames/second) and subsequently transferred to the computer. The controlled circuit uses the input of digital signal to control electrodes, switching on or off on the EWOD device, which will be illustrated as follows. The photolithographic mask for EWOD device is shown in Fig.3-5.

3.2.1 Process of EWOD device

A metal layer of 200/800

A

^o Cr/Au was evaporated on glass substrate by E-beam Evaporator. After etching process and re-clean step of glass, SiNx thin film 3000

A

^o is deposited as the dielectric layer of EWOD by PECVD.

The next step, photolithography is used to open the bonding pads, and dielectric layer on the bonding pads is removed by dilute buffered oxide etchant (BOE). At last, Dupont Teflon, diluted with 3M FC-77, is spun on the glass by spin coater to complete the fabrication.

Followings are the detailed recipe for fabrication of the above process, which is shown in Fig. 3-6 as well. The top plate process is illustrated in Fig.3-7. Figure 3-8 shows the SEM photo of EWOD device.

(I) Glass substrate process

1. Clean substrate in Caro acid ( H2SO4 : H2O2 = 3 : 1) at 120^o

C

for 600 secs Æ Immerse the substrate in the deionized (D.I.) water for 60 secs Æ Blow and dry the substrate by N2 gun Æ Put soft bake on hot plate at 100^o

C

for 180 sec.

2. Metal evaporation, E-beam Evaporator, Cr/Au 200/800

A

^o .

3. Clean the glass in Acetone (ACE) with ultrasonic vibrator for 900 sec.

4. Soft bake on hot plate at 100^o

^C

for 180 sec.

5. Spin coat HMDS, 4000 rpm for 40 sec.

6. Soft bake on hot plate at 100^o

^C

for 180 sec.

7. Spin coat Shipley S1818 PR, 500 rpm for 15sec, 4000 rpm for 30sec.

8. Soft bake on hot plate at 100^o

^C

for 180 sec.

9. Exposure, Single-Side Mask Aligner.

10. Develop with Shipley MF 315 developer around 20 sec to window above bonding pads.

11. Hard bake on hot plate at 120^o

^C

for 600 sec.

12. Wet etching in potassium iodine solution to remove the Au for 4~8 sec.

13. Wet etching in Chromium Photomask Etchant to remove the Cr for 5 sec.

14. Clean the glass in Acetone (ACE) with ultrasonic vibrator for 300 sec, remove the photoresist.

15. Soft bake on hot plate at 100^o

^C

for 180 sec.

16. Deposit the Si3N4 by PECVD.

17. Spin coat diluted Teflon AF on the EWOD devices, 500 rpm for 15 sec, 3000 rpm for 30 sec.

18. Hard bake on hot plate, 110^o

^C

for 600 sec, 160^o

^C

for 1200 sec, and 260^o

^C

for 1800 sec.

(II) Silicon wafer substrate process

1. Clean substrate in Caro acid ( H2SO4 : H2O2 = 3 : 1) at 120^o

C

for 600 sec Æ Immerse the substrate in the deionized (D.I.) water for 60 sec Æ Blow the substrate dry by N2 gun Æ Soft bake on hot plate at 100^o

C

for 180 sec.

2. Deposit SiO2 (3000

^A

^o ) and SiNx (3000

^A

^o ) on the Si-wafer by PECVD.

3. Metal evaporation, E-beam Evaporator, Cr/Au 200/800

^A

^o .

4. Clean the glass in Acetone (ACE) with ultrasonic vibrator for 900 sec.

5. Soft bake on hot plate at 100^o

^C

for 180 sec.

6. Spin coat HMDS, 4000 rpm for 40 sec.

7. Soft bake on hot plate at 100^o

^C

for 180 sec.

8. Spin coat Shipley S1818 PR, 500 rpm for 15sec, 4000 rpm for 30sec.

9. Soft bake on hot plate at 100^o

^C

for 180 sec.

10. Exposure, Single-Side Mask Aligner.

11. Develop with Shipley MF 315 developer around 20 sec to window above bonding pads.

12. Hard bake on hot plate at 120^o

^C

for 600 sec.

13. Wet etching in potassium iodine solution to remove the Au for 4~8 sec.

14. Wet etching in Chromium Photomask Etchant to remove the Cr for 5 sec.

15. Clean the glass in Acetone (ACE) with ultrasonic vibrator for 300 sec, remove the photoresist.

16. Soft bake on hot plate at 100^o

^C

for 180 sec.

17. Deposit the Si3N4 by PECVD.

18. Spin coat diluted Teflon AF on the EWOD devices, 500 rpm for 15 sec, 3000 rpm for 30 sec.

19. Hard bake on hot plate, 110^o

^C

for 600 sec, 160^o

^C

for 1200 sec, and 260^o

^C

for 1800 sec.

(III) Top plate process

1. Clean the ITO glass in Acetone (ACE) with ultrasonic vibrator for 600 sec.

2. Spin coat diluted Teflon AF (

1000Α) on the ITO glass, 500 rpm for 5 sec, 500 rpm for 15 sec, 3000rpm for 5sec and 3000 for 40sec.

3. Hard bake on hot plate, 110^o

^C

for 600 sec, 160^o

^C

for 1200 sec, and 260^o

^C

for 1800 sec.

3.2.2 Measurement of contact angles

Measurements of the contact angle change by EWOD were made in a DI water droplet using Contact Angle Goniometer (MagicDrop, USA). The 10ul droplet was placed on a 3000 Å dielectric layer of silicon nitride coated with 1000 Å Teflon. A wire was penetrated into the droplet from the top, and the ac potentials with 1 K, 3K, 5K, 7K and 9K Hz, were applied between the liquid and the electrode underneath the dielectric layers. The contact angle was changed from 116° to 76°. The dielectric layers of nitride and Teflon formed two plate capacitors in series. The capacitance of a single capacitor is given by,

r 0

c d

=ε ε

(3.1) where c is the capacitance per unit area. The equivalent capacitance of two

The dielectric constant (^ε^r) of 3000 Å nitride and 1000 Å Teflon is 7.8 and 2, respectively. The equivalent capacitance of the nitride and Teflon layers can be obtained by Eq. (3.1) and (3.2). Fig. 3-9 shows the comparison of the experimental and theoretical contact angles based on Eq. (2.14). The contact angle parabolically decreases as the applied potential increases until it is saturated between 65° and 80°. The reason for the saturation is not clearly understood as of today. In any case, there exists a limitation in the contact angle change by EWOD, beyond which the higher potential can no longer decrease the contact angle any further. In addition, the Lippmann-Young’s equation does not consider the proceeding of the droplet. However, the droplet is advancing by the applied voltage. In order to produce larger pressure difference and to fit the simulation conditions, the voltage 100 AC with 3K or 5K Hz is used in the experiments. If a large voltage (> 110V) is applied to droplet, it will cause hydrolysis easier. Due to the limitation of microcontroller, the offset of voltage is set to 50V.

0.08mm 0 .08mm

A1 A2 A3

A4 A5 A6

A7 A8 A9 Fig. 3-2 Different shapes of electrode

Fig. 3-3 Array of different electrodes for one-dimension

(a) Contact angle goniometer (b) Microscope and CCD came

(a)

(b)

(c)

(d)

Fig. 3-5 (a) The pattern of 1-D photolithographic mask; (b)(c)(d) The pattern of pictures of EWOD control electrodes

（a）Acid washing （b）Metal deposition (Cr/Au)

(e) Nitride deposition (f) Spin coat Teflon

(Ⅰ) Glass substrate process Si3N4

S1818

Glass Au 800

A

Cr 200

A

Teflon 1000

A

Si wafer

（a）MRCA (Modified RCA Clean) （b）SiO2 and SiNx deposition

（c）Metal deposition (Cr/Au) (d) Photolithography (EWOD pattern)

(e) Ache-down (Au/Cr) (f) Nitride deposition

(g) Spin coat Teflon

Si3N4 3000

Å

SiO₂ 3000

Å

Cr 200

A

Au 800

A

S1818

Si3N4

Teflon 1000

A

(a) ITO glass (b) Spin coat Teflon Fig. 3-7 Illustration of top plate process

Fig. 3-8 The SEM photo of EWOD device

Si3N4 3000

A

SiO2 3000

A

Cr 200

A

Silicon Au 800

A

ITO glass

Teflon 1000

A

ITO glass

Fig. 3-9 Measurement of contact angle

CHPATER 4

RESULTS AND DISCUSSION

In this chapter, it will firstly present the simulation results that show the variations of droplet shapes under different pressure due to the electrode arrangement, the mean moving velocity of droplet and the time needed from one pattern to another while droplet is in the moving or cutting state. For experiments, it presents that a nano-liter droplets is created by different designs of square-, interdigiated- (2323) and interdigitated-electrode (5656).

Finally, a comparison between numerical and experimental results for moving droplet is given.

4.1 Simulation

4.1.1 Simulation parameters

The initial conditions are the droplet location, droplet volume (radius of droplet) and initial velocity of droplet. In order to further simplify the problem, it assumes that the droplet radius is fixed at 0.3 mm for each simulation case. Because the channel height is one of the varying parameters, the resultant droplet volume (

π r

²×

h

) is also changed. The corresponding values are list in Table 4-1.

Table 4-1 Volume of droplet (radius is 0.3 mm)

Channel height (h;

μ m

) 20 35 70

Volume (nl) 5.655 9.896 19.792

Boundary conditions are the contact angles, which were obtained by experimental measurements under applied voltage. Other properties, which

are listed in Table 4-2, are composed of the gap between adjacent patterns, surface tension, gas viscosity, gas density, liquid viscosity and liquid density.

In this study, the varying parameters are the channel height and the arrangement of electrodes, which were discussed briefly in the previous section. Consequently, the droplet location in Z direction in Table 4-2 is a function of channel height. The arrangement of electrodes was described in last chapter.

Table 4-2 Simulation properties

droplet location (m) X=1.5E-4, Y=2.4E-4, Z=variable, 1E-5, 1.75E-5 and 3.5E-5

radius of droplet (m) 3E-4

initial velocity of droplet (m/s) Vx=0, Vy=0 and Vz=0

contact angle 80°( wettability); 115°(non wettability)

electrode size (mm²)

0.5 X 0.48 (2323) 0.5 X 0.475 (5656) 0.5 X 0.5 (square)

main electrode area (mm²) 0.144

channel height (

μ m

) Variable (20, 35 and 70)

gap of adjacent patterns (

μ m

) 20

surface tension (N/m) 0.719

gas viscosity (air) (

Kg

m

⋅

s

) 1.846E-5

gas density (air) (

Kg

/ m³) 1.1614

liquid viscosity (DI water) (

Kg

m

⋅

s

) 8.9E-4

In this work, 16 simulation cases, which are based on the combinations of newly designed electrodes mentioned in Section 3-1, for both droplet moving and cutting. They are discussed as follows.

4.1.2 Droplet moving

In this section, the resultant mean velocities (

V

₁ ) and pressure differences (ΔP₁) for each case are presented in Table 4-3 while the droplet moves among adjacent electrodes. In this table, “a” represents the area sum of the extended rectangles and “A” total electrode area, whose representations can be seen graphically in Fig. 4-1. P1 is the initial pressure, P2 the instantaneous pressure as droplet starts to move and P3 the steady pressure as the droplet finish the movement. T and W are the time of moving among adjacent electrodes and the width of extended rectangle, respectively.

Table 4-3 16 cases of droplet moving simulations

20 a1=0.016 A1=0.176 13.291 0.0316 1896 1023 1755 873

2 35 0.016 0.176 21.032 0.01997 1145 695 1063 450

Figure 4-2 shows moving droplet shape at 0.0076805s from the top view for case 1 (channel height = 20

μ m

) together with the instantaneous velocity and pressure distributions at the middle plane. Note that the colored part is the wetting area, where the voltage is applied by electrode to generate the driving force for droplet moving. The dash lines represent the locations of head and tail interface (between liquid and gas), respectively. It can be seen that the minimum droplet velocity occurs at the tail interface whereas the maximum one is in the middle part, where an electrode wetting is under the way, instead of the head interface. It indicates that the front part of droplet is decelerated because the droplet head is going to stop due to no wetting as the next electrode is shut down at that instant. On the other hand, the rear part is accelerated since this part is subjecting to an electrode wetting.

The two concave gas velocity profiles just ahead of the head interface and behind the tail interface are resulted from the continuity condition with a sudden density change between two phases. The phenomenon implies that the droplet head pushes the air ahead of it and the tail drags the air behind it.

Because the air is stagnant away from the droplet, this explains why air velocity profiles exhibit the concave shapes.

It can be seen that the largest pressure inside droplet occurs adjacent to the tail whereas the smallest one is at head. It indicates that the front part of droplet is in hydrophilic area and the rear one is in hydrophobic area (see Fig.

4-2). Because the front half part of droplet is in the hydrophilic area, the pressure between liquid and gas decreases. However, the droplet can move forward due to pressure gradient between head and tail.

Figure 4-3 shows head and tail pressures and velocities of droplet as a function of time for case 1. Remind that the head and tail are at the locations mentioned in Fig. 4-2. The time history is divided into three regimes, such

as I, II and III for interpretation. In regime I, it is from when the droplet starts to move to the instant when its head touches the electrode without voltage (no wetting; position 1). Regime II, the droplet head moves from the position 1 to position 2, where the droplet is moved due to the inertia from previous wetting area. Regime III, the droplet head moves from the position 2 to position 3, where the droplet stops to move completely.

It can be seen that the velocity of droplet head increases with a decrease of pressure from 0.000284s to 0.00386s, indicating that the droplet starts moving into the electrode with applied voltage. From 0.00386s to 0.006583s, it shows the opposite trend that the head velocity decreases with a rise of pressure, implying that the droplet tail is dragged by head to cause itself to slow down. However, the head pressure of droplet is smaller than that of tail in the regime I. A sudden peak occurs for tail velocity at 0.004967s, it is because that the resistance exerted by the plates initially retards the movement of droplet tail as the droplet head starts to move when electrode wetting is on.

When the momentum of the front part of droplet is strong enough to overcome the drag force, it cause the tail to move forward suddenly then slow down by the hitting the front part of droplet that leads to velocity peak. At the 0.008074s, a peak of head velocity appears because the head arrives at electrode without voltage, making it hard to move forward. After that, the instantaneous head velocity increases acutely again because the interface in the neighborhood of head is still moving to squeeze it to move forward suddenly.

In the regime II, the pressures of head and tail oscillate very randomly.

droplet. For the tail, its velocity pattern shows stable relatively.

In regime III, all the head pressure of droplet is smaller than that of tail one, implying that the droplet stops to move. Although the head droplet is not moving, the tail droplet still moves and compresses the head one, causing the head velocity to shake.

Figure 4-4 shows the moving droplet shape at 0.004412s from the top view for case 3 (channel height = 70

μ m

) together with the instantaneous velocity and pressure distributions at the middle plane. Comparing Fig. 4-4 with Fig. 4-2, both droplet heads are at the same position, however, the droplet length of Fig. 4-2 is longer. It is because that the smaller channel height possesses the greater flow resistance such that it causes the droplet to move more difficultly.

Figure 4-5 shows the variations of pressures and velocities for head and tail of droplet in case 3 with time. It also can divide into three regimes, which are similar to those in Fig. 4-3. The different between Fig. 4-3 and Fig.

4-5 is no sudden peaks for pressure and velocity in Fig. 4-5. The higher channel height has the lower flow resistance, so that the droplet can move more easily and the peristalsis behavior due to the middle part of droplet which pushes the head and drags the tail to move forward is not obvious.

From the both figures, the influence of flow resistance on different channel heights for droplet can be checked.

The illustrations of droplet moving for interdigitated electrodes (2323), interdigitated electrodes (5656) and square electrodes at channel height 35

μ m

are shown in Fig. 4-6. It is can be seen that the shape of droplet moving is influenced by electrode design and that the interdigitated electrode (2323) has the longest wetting curve in the front part of droplet, so that it has the largest pressure difference to move droplet. The droplet shapes of interdigitated

electrode (5656) and square electrode are similar while droplet starts to move, because the numbers of extended rectangle for interdigitated electrode is too much and its form is like a square electrode. When droplet arrives at middle electrode, the designs of interdigitated electrode have longer wetting curve than that of square electrode. It proves that the design of interdigitated electrode brings function into full play.

4.1.2.1 Comparison between the interdigitated electrodes and square electrodes

Firstly, it needs to prove the interdigitated electrode can generate a greater pressure difference than square electrodes. Therefore, case-5, case-14 and case-16 in Table 4-3 are used to make a comparison. The curve of droplet touching the next electrode is shown in Fig. 4-7, which the touching length of interdigitated electrode (2323) is longer than others. These cases have the same channel height (35 m

μ

). The design of interdigitated electrodes has another advantage that the droplet can occupy the more area of adjacent electrode while moving to next electrode, as shown in Fig. 4-8. Observably, the pressure difference of case-05 and case-14 is larger than that of case-16.

The same results are also found in the groups of (case-1, 15), (case-4, 15) (case-11, 15), (case-14, 15) (case-2, 5), (case-5, 7), (case-5, 8), (case-5, 10), and (case-5, 12), therefore, it can conclude that the new electrode is meaningful.

different channel height. The gap of case-1 is 20 m

μ

, case-2 35 m

μ

and case-3 70 m

μ

, respectively. It can be seen that the pressure difference increases with the decrease of channel height, as shown in Table 4-4. The reason is that, the resultant droplet volume is decreased, the cohesion increased, consequently, and the drag of droplet is increased as the channel height becomes smaller. Therefore, it needs more pressure difference to drive the droplet. From Eq. (2.22),

Δ can demonstrates that these simulation results are good enough, since the three cases (group (case-4, -5, -6), (case-11, -12), (case-13, -14) and (case-15, 16)) tend to exhibit the same phenomenon, which the pressure difference is increased as the channel height decreases.

However, the droplet might stop moving in the experiment as the channel height so small that the drag is probably larger than the driving force. The drag is including particle, uneven surface of device, air drag and much more.

在文檔中改善EWOD 元件於產生奈升級液滴之研究 (頁 45-0)