Letter pubs.acs.org/Langmuir
Discrete Electrostatic Charge Transfer by the Electrophoresis of a Charged Droplet in a Dielectric Liquid Do Jin Im,* Myung Mo Ahn, Byeong Sun Yoo, Dustin Moon, Dong Woog Lee, and In Seok Kang Department of Chemical Engineering, Pohang University of Science and Technology, San31 Hyoja-dong, Nam-Gu, Pohang, Gyeongbuk 790-784, South Korea S Supporting Information *
ABSTRACT: We have experimentally investigated the electrostatic charging of a water droplet on an electrified electrode surface to explain the detailed inductive charging processes and use them for the detection of droplet position in a lab-on-a-chip system. The periodic bouncing motion of a droplet between two planar electrodes has been examined by using a high-resolution electrometer and an image analysis method. We have found that this charging process consists of three steps. The first step is inductive charge accumulation on the opposite electrode by the charge of a droplet. This induction process occurs while the droplet approaches the electrode, and it produces an induction current signal at the electrometer. The second step is the discharging of the droplet by the accumulated induced charge at the moment of contact. For this second step, there is no charge-transfer detection at the electrometer. The third step is the charging of the neutralized droplet to a certain charged state while the droplet is in contact with the electrode. The charge transfer of the third step is detected as the pulse-type signal of an electrometer. The second and third steps occur simultaneously and rapidly. We have found that the induction current by the movement of a charged droplet can be accurately used to measure the charge of the droplet and can also be used to monitor the position of a droplet under actuation. The implications of the current findings for understanding and measuring the charging process are discussed.
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INTRODUCTION The electrophoretic motion of charged droplets has attracted a great deal of scientific and engineering interest. The noncoalescence phenomenon of oppositely charged drops in strong electric fields is a widely acknowledged fluid dynamics problem.1,2 For example, storm cloud formation can be explained by the coalescence of charged water drops in free fall.3 In industrial applications, electrically induced droplet motion can be used in the dehydration of petroleum and vegetable oil.4 A better understanding of the behavior of charged droplets in electrohydrodynamic inkjet printing is crucial for accurate control.5,6 The direct charging and the subsequent control of a charged droplet in lab-on-a-chip devices have been actively reported recently.7−14 To study the motion of a charged droplet under a given electric field, it is necessary to measure how much charge a droplet acquires. In classical measurements, the charge transfer from a charged metallic sphere during a capacitive discharge was directly measured with an oscilloscope15,16 with an appropriate RC circuit. The charge was also measured using a Faraday cup, and the two measurements were compared with theoretical predictions. Although the measurement results from a Faraday cup matched the theoretical values well, the measurement with an oscilloscope underestimated the real charges. (Depending on the measurement configuration, the accuracy ranged from 10 to 70% of the theoretical value.16) This underestimation was explained by undetected displace© 2012 American Chemical Society
ment currents by the measurement circuit. Precise measurements of the electric current pulses produced during the discharge also underestimated the real charge value.17 For a small droplet moving in an immiscible liquid, it is possible to measure the charge of a droplet indirectly by image analysis.18,19 In this indirect measurement, the Coulomb force is balanced by the hydrodynamic drag force to estimate the charge of a droplet. Because the charge estimation is largely affected by the size and velocity of a droplet, special care is required for accurate measurements.13 Most of all, depending on the choice of the hydrodynamic drag force (Stokes or Hadamard−Rybczynski), the estimated charge can be different by 33%. Therefore, the accuracy of this method has been a topic of recent discussion.13,20 Recently, both the direct and the indirect methods have been performed to measure the charge of an aqueous droplet acquired by contacting an electrified electrode.13 Except for the fact that the directly measured values are somewhat lower than those of the indirectly estimated values, the two measurements showed good agreement. Aqueous droplets have been found to be less charged than corresponding perfectly conductive spheres. This limiting effect on electrical charging is more significant for an electrolyte droplet, and the effect is positively Received: April 9, 2012 Revised: July 30, 2012 Published: July 31, 2012 11656
dx.doi.org/10.1021/la3014392 | Langmuir 2012, 28, 11656−11661
Langmuir
Letter
emitting diode (LED) light source (10 W). The intensity of light was adjusted to capture the edge of a droplet clearly. Once the outer edge of a droplet was captured from an original image, the inside of the circle was filled to get a spherical solid binary image of a droplet by the LabVIEW image-processing tool kit. The volume of a droplet (radius) was measured from the area of this processed binary image. The center of a droplet is the arithmetic center of mass of the processed binary image, and the velocity was measured by tracking this center. The maximum uncertainty in the optical radius measurement (at the center of the test cell) was lower ( 0. This charging process is detected as a pulse signal (Figure 3d). Therefore, even though the total charge transfer from the electrode to the droplet upon contact is |Q−| + |Q+| (|Q−| for neutralization and | Q+|for charging), the amount of charge detected by the pulsetype signal of the electrometer is just |Q+|, not|Q−| + |Q+|. The charge transfer by the electrophoresis of a charged droplet between two electrodes appears to be a discrete process. (A droplet functions as a discrete charge carrier bouncing back and forth between two electrodes.) However, as shown above, this charge transfer is detected at the electrometer as a continuous function of time that consists of two parts: a pulse-type current upon contact with an electrode and a continuous induced current during the movement of a droplet. Here, the magnitude of the charge transferred for each process is theoretically the same. One point of caution for this charge-transfer process is that the direction of current remains unchanged even though the moving direction of a droplet is alternating. Because the direction of movement and the polarity change at the same time, the direction of the current is maintained throughout the process. That is why the current value is always positive in Figure 2. For a more quantitative description, the charge measurement data from different methods are compared in Figure 4. As expected from Figure 2, the charge data from the pulse-type signals show large variations and have smaller average values than the others. This is supposed to be attributed to the insufficient time resolution of the electrometer because charging occurs within several milliseconds.1,19 However, the charge data from the integration of induction current signals
can see this consistent feature more clearly. Even though the velocities are overlapped for 12 cycles of bouncing motion, the velocity distributions are almost identical, especially in the center region, where the charge of a droplet is estimated. In spite of this consistent electrophoretic motion, the pulsetype signals of current measurement show large variations (3.6 ± 2.0 nA with the minimum 1.53 nA and the maximum 7.84 nA). In addition to the pulse-type signals, we can observe the background signals on the order of nanoamperes between pulses. The average value of these background signals for the positively charged droplet is larger than that for the negatively charged droplet. As a result, the average height of the background signal keeps changing periodically following the bouncing motion of the droplet. Because of the low conductivity of silicone oil, the flow currents are on the order of picoamperes under the same electric field strength (the blue background signal of Figure 2 and also Figure S2 in the Supporting Information). Therefore, the contribution of the direct current through silicone oil to these background signals is negligible. When a charged droplet bounces back from an electrode in the present situation, the total charge transfer upon contact is about twice the charge of a droplet. (Once a positively charged droplet contacts a negative electrode, it is not only neutralized but also negatively charged with a similar amount of charge and vice versa.) However, the charge measured from a pulse-type signal (37 ± 16 pC) is much less than the charge estimated by image analysis (for the positively charged droplet, 94 ± 0.3 pC) and the corresponding perfect conductor (1.07 × 10−10 C). Including the previous work, the maximum observable charge from a pulse-type signal is still slightly smaller than that of the corresponding perfect conductor.13 One possible explanation of the current experimental results is pictorially illustrated in Figure 3. When a water droplet contacts the negative electrode, charging of a droplet occurs as a result of the redistribution of surface charge. Let us denote the charge of the droplet leaving the negative electrode by Q− < 0. This charging process is detected by the electrometer as a 11658
dx.doi.org/10.1021/la3014392 | Langmuir 2012, 28, 11656−11661
Langmuir
Letter
Figure 4. Comparison of the data from different charge measurements of a 1.0 μL water droplet. The charge of a positively charged droplet under 5 kV/cm is (9.4 ± 0.03) × 10−11 C for the image, (3.7 ± 1.6) × 10−11 C for the pulse, and (10.7 ± 0.4) × 10−11 C for induction. Under 3 kV/cm, it is (4.3 ± 0.04) × 10−11 C for the image, (1.4 ± 0.3) × 10−11 C for the pulse, and (6.1 ± 0.1) × 10−11 C for induction. The charge of a negatively charged droplet under 5 kV/cm is (8.1 ± 0.1) × 10−11 C for the image, (3.4 ± 1.5) × 10−11 C for the pulse, and (9.8 ± 0.5) × 10−11 C for induction. Under 3 kV/cm, it is (3.6 ± 0.04) × 10−11 C for the image, (0.9 ± 0.4) × 10−11 C for the pulse, and (5.1 ± 0.1) × 10−11 C for induction. The number of measurements is n = 12 for 5 kV/cm and n = 6 for 3 kV/cm. The error bars represent one standard deviation.
Figure 5. Scaling law of charging for the charges measured by the induction signals, where a is the droplet radius and E is the electric field strength. The average value of positively and negatively charged droplets is used for the scaling law. The reference state is chosen to be a0 = 413 μm and E0 = 3.0 kV/cm, and the resultant charge is Q0 = 2.51 × 10−11 C. For the linear plot, R2 = 0.996.
acquired by direct contact with the electrified electrode. Moreover, the charge measured by the induction current (for a positively charged 1 μL droplet under 5 kV/cm, 1.07 ± 0.04 × 10−10 C) is very close to that of the corresponding perfect conductor (1.07 × 10−10 C). On the basis of this charge measurement result, it appears that at least for a positively charged droplet there is no limiting effect on the charging of a water droplet. At this point, it is necessary to discuss the accuracy of the charge measurement methods described here. As mentioned previously, the accuracy of the indirect image analysis method has been discussed because we have two different choices for the drag force calculation: the Hadamard−Rybczynski drag and the Stokes drag.13 A recent study on this topic20 and the above charge measurement results from induction signals imply that the application of the Stokes drag can be more accurate. The fact that most of the charge on a water droplet is limited to about 70% of that of the corresponding perfect conductor also supports this point 13 (Figure S4 in the Supporting Information). However, if we apply the Stokes law to the results in Figure 4, the estimated charge becomes much larger than that of the perfect conductor (Figure S5 in the Supporting Information). Therefore, further thorough and rigorous studies on the accuracy of the charge measurement methods are definitely needed to shed more light on this issue. From the point of view of small charge measurements, the image analysis or the method of inductive current signal integration is more reliable and consistent than the method based on the pulse-type signal of the charging current. In particular, the current findings on the inductive charge measurement can be a good complementary method to the image analysis because it is more direct and free from inaccuracies caused by the estimation processes. Above all, the induction charge measurement can be useful when the indirect measurement is difficult, such as measuring the amount of charge on an interfacial droplet or on an irregularly shaped particle. There are also some limitations of the inductive charge measurement. Because of noise signals, there is a lower limit for the detectable amount of charge. In the current experimental setup, it is difficult to get the pulse signal under a low electric field (
