3.1. Droplet Dispensing with the Conventional Electrowetting Electrodes
The schematic of the breaking process on conventional EWOD devices is illustrated in
Figure 2a–d, where the extracted liquid is pulled back to the reservoir, and the radius of the neck decreases until it is finally pinched off to generate a droplet. To investigate the volume variation of droplets, experiments were designed with the most widely used conventional electrode arrays, and the results are demonstrated in
Figure 2e. Here, in characterization experiments with an 80 μm gap height, dispensing was attempted 10 times, as this was the maximum that could be dispensed steadily from a reservoir without re-filling. As the reservoir shrank until it was nearly empty, the droplet volume dispensed at 60 V
RMS increased by about 16% relative to the average volume, and the CV reached 5.42%. The monotonous increase of the droplet volume comes mainly from the decrease of the force drawing liquid back to the reservoir.
In practical conditions when the curvatures and voltages are time-dependent, dynamic statuses can be analyzed by two-dimensional hydrodynamic equations. The volume change at the creation site in the pinch-off process can be expressed as a function of the flow rate from the breaking electrode to the creation site. Consequently, the dispensed droplet volume can be calculated by integrating this volume change from the necking start until the droplet pinch-off occurs [
9].
Ideally, to improve the reproducibility of the droplet volume, the parameters in this droplet dispensing process should remain constant for all steps. As the boundary of the liquid extruded from the reservoir meets that of the electrodes applied to the actuation voltage before necking starts, the initial extracted volume can be regarded as constant for droplets dispensed next to each other. Thus, the volume variation comes mainly from the necking process. Unfortunately, the electro-wetting force applied to the droplet is only a function of the applied voltage, the capacitance of the dielectric layer, and the projected length of the liquid boundary. As all other parameters remain constant in the dispensing process, the overall force induced by electro-wetting is in proportion to the length of the liquid boundary on the actuated electrode. When droplets were dispensed continuously without refilling the reservoir, the force pulling the liquid out of the reservoir remained almost the same as the volume of each dispensed droplet changed within a relatively small range, while the draw-back force rapidly decreased as the liquid in the reservoir shrank with the volume of droplets dispensed in this characterization experiment. Consequently, less liquid is drawn back to the reservoir, resulting in the rise of the dispensed droplet volume.
3.2. Square Sub-Electrode Design for Droplet Dispensing
While almost all parameters involved in the dispensing process can affect the droplet volume, the necking process is more important than other steps based on the analysis presented above. Since the volumetric inaccuracy of droplets dispensed consecutively from the non-filling reservoir is mainly due to the uncertainty of the whereabouts of liquids during the necking and splitting process, an intuitive solution is to reduce the size of the splitting electrode to reduce the volume of this portion of liquid [
18,
19].
As illustrated in
Figure 3a–d, the splitting electrode (on which the necking and splitting happen) is segmented into three sub-electrodes. Compared with the traditional microdroplet generation process shown in
Figure 2, the necking process in
Figure 3 is divided into two relatively controllable steps: the volume of liquid above the split electrode is first reduced by grounding the outer splitting sub-electrodes, and the necking process on the center sub-electrode starts after the remaining liquid gets stable. In this way, the volume of the liquid in an unstable necking state is significantly reduced from the entire splitting electrode to one sub-electrode. With a 160 μm gap height, the volume of consecutively dispensed droplets was tested experimentally. When the width of the center sub-electrode is 0.06 mm, 0.36 mm, or 2 mm, the experimental results are shown in
Figure 3f. When the width of the sub-electrode decreases, the volumetric consistency of the dispensed droplets gradually increases. When the width of the sub-electrode is 0.06 mm, the coefficient of variation of the droplet volume decreases to about 0.49%, which is only about 9% of the CV of the traditional electrode structure (5.42%, as shown in
Figure 2). However, factors such as the manufacturing difficulties, the surface tension of the liquid, and the contact angle saturation in electrowetting restrict the further decrease of the sub-electrode size. Narrow sub-electrodes will not only increase the difficulty of device fabrication but also reduce the stability of the device due to the need for a higher driving voltage.
3.3. Dumbbell-Shaped Sub-Electrode Design for Droplet Dispensing
Besides the whereabouts of liquids on splitting electrodes, the exact time and position of the pinch-off cannot be precisely controlled for traditional electrowetting electrode designs [
20]. Herein, a new method is proposed to stabilize the droplet shape and restrict the position of the pinch-off. The illustration and experimental photos of the droplet dispensing process are shown in
Figure 4. The new splitting electrode consists of two outer arcs and a center dumbbell. In this design, the cutting process to pinch off the liquid stretched from the reservoir is divided into two steps: (1) two outer arcs are at first connected to the ground to extract liquid from laterally to the media to form a stable neck on the center dumbbell-shaped sub-electrode, and (2) the center sub-electrode is turned hydrophobic after the liquid gets stable in order to pinch off at the predetermined location, namely the neck. Through this design, the EWOD chip improves the accuracy and consistency of droplet generation from the following aspects: (1) the introduction of sub-electrodes reduces the amount of liquid involved in the subsequent liquid shrinkage and necking process; (2) the profile of the dumbbell-shaped sub-electrode ensures that the liquid above it preferentially shrinks inward in the neck area under the effect of surface tension; (3) since the neck width of the sub-electrode can be extremely small, the reservoir only needs to suck back a very small amount of liquid to induce the pinch-off of liquid at the neck position.
Designs with different neck widths are fabricated with a 240 μm gap height for their effect on the droplet dispensing process. The results are demonstrated in
Figure 5a. The droplet volume still oscillates for ten droplets dispensed from a non-replenishing reservoir, but its amplitude of variation and CV gradually decreases to ±0.5% and 0.38%, respectively, when the neck width is small enough (0.05 mm in this experiment). When the neck width is below 0.10 mm, the droplets dispensed consecutively maintain a high volumetric consistency (coefficient of variation less than 0.5%). When the neck width increases, the volumetric consistency drops rapidly until it reaches the same level as the traditional electrode design (as shown in
Figure 2). As a large volume fluctuation is undesirable, the center dumbbell-shaped sub-electrode should be fabricated with a small neck in order to gain better reproducibility. With a properly chosen neck width, the pinch-off time and position can both be efficiently controlled. Moreover, the necking and pinch-off processes are greatly dependent on the capillary number, which is the ratio between the surface tension and the liquid viscosity. For conditions with small capillary numbers, the necking and pinch-off duration is elongated due to the eliminated Rayleigh–Plateau instability. Thus, the volumetric variation of the liquid in the reservoir has more influence on the volumetric variation of consecutively dispensed droplets.
What is more, the length of the dumbbell-shaped sub-electrode is also changed to verify its effect on the droplet volume variation, and the results are shown in
Figure 5b. Following the results obtained from
Figure 5a, the neck width is set as 0.1 mm, and the length of the breaking electrode changes from 2 mm to 3 mm to 4 mm, while the width remains 2 mm, as demonstrated in
Figure 6. When the length of the dumbbell-shaped sub-electrode gradually increases, the volumetric consistency of the generated water droplets gradually decreases. This result is mainly derived from two aspects: (1) the increase in the length of the dumbbell-shaped sub-electrode represents an increase in the volume of liquid above it during the splitting process; (2) the increase in the aspect ratio of the dumbbell-shaped sub-electrode reduces the curvature of the arcuate boundary and results in increased uncertainty in the pinch-off position. Even so, when the aspect ratio reaches 2, the volumetric consistency (CV = 1.20%) of the dispensed droplets is still much lower than the results when using conventional electrodes.
Moreover, the actuation voltage used in the above experiments is 60 V
rms sinusoidal alternating signals. Therefore, based on the classic Lippmann–Young equation, at the moment when the actuation voltage is applied or removed, the vibration amplitude of liquid will be different: the higher the actuation voltage, the more drastic the vibration of the liquid, the higher the instability in the liquid splitting process, and the worse the volumetric consistency of dispensed droplets. For this purpose, four sinusoidal voltage signals with a frequency of 1 kHz and an amplitude of 60 V
rms, 70 V
rms, 80 V
rms, and 90 V
rms are experimentally tested. The length and width of the driving electrodes are both 2 mm. As shown in
Figure 5c, the experimental results are roughly the same as in the analysis proposed above. Unexpectedly, the coefficient of variation does not increase monotonically with the increase of the magnitude of the actuation voltage, but increases first and then remains unchanged. It is believed that this is caused by the phenomenon of contact angle saturation. At the same time, since the coefficient of variation of droplet volumes has already been decreased to a very small value (when the driving voltage is 60 V
rms, the coefficient of variation is 0.29%), even if the coefficient of variation at 90 V
rms has reached nearly three times that at 60 V
rms, its absolute value is only 0.73%. Moreover, the excitation frequency of ac actuation voltages could also influence the volume variation due to its effect on the Rayleigh–Plateau instability, but thorough research of this effect is beyond the scope of this work.