Investigation of the Charging Characteristics of Micrometer Sized

Jan 8, 2013 - droplet can be used as the droplet actuation method. This work proposed a novel method of investigating the charging characteristics of ...
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Investigation of the Charging Characteristics of Micrometer Sized Droplets Based on Parallel Plate Capacitor Model Yanzhen Zhang, Yonghong Liu,* Xiaolong Wang, Yang Shen, Renjie Ji, and Baoping Cai College of Electromechanical Engineering, China University of Petroleum, Qingdao 266580, People’s Republic of China S Supporting Information *

ABSTRACT: The charging characteristics of micrometer sized aqueous droplets have attracted more and more attentions due to the development of the microfluidics technology since the electrophoretic motion of a charged droplet can be used as the droplet actuation method. This work proposed a novel method of investigating the charging characteristics of micrometer sized aqueous droplets based on parallel plate capacitor model. With this method, the effects of the electric field strength, electrolyte concentration, and ion species on the charging characteristics of the aqueous droplets was investigated. Experimental results showed that the charging characteristics of micrometer sized droplets can be investigated by this method.

1. INTRODUCTION The electrophoretic motion of charged aqueous droplets with diameters of several micrometers has attracted a great deal of scientific and engineering interest. For instance, the stability of emulsion and other colloids system was usually explained by the charging of the dispersed micrometer sized droplets. In industrial applications, such as dehydration of crude oil1−4 and electrostatic spraying,5,6 the charging characteristics of micrometer-sized droplets is of great importance. Recently, especially with the development of microfluidics technology,7,8 lab-on-achip devices,9,10 and the biochemical field,11,12 the actuation of charged droplets has attracted more and more attention. Accurate control of the micrometer-sized droplet is of great importance in the above applications. Generally speaking, electrowetting, or electrowetting on a dielectric (EWOD), and dielelctrophoresis (DEP) are two primarily manipulation methods for moving droplets in a microfluidics device.13 In EWOD, the droplets are manipulated on the arrays of electrodes. The position of droplets can be precisely controlled by adjusting the potential of the electrodes arrays. And the characteristic of this method was a good match for array-based biological and chemical applications. However, the direct contact between the droplets and the surface usually causes contact line pinning and biofouling due to surface contamination. In DEP, the contact between droplets and the surface was avoided. The DEP forces only dependents on the dielectric property of the droplets. However, compared with EWOD, the higher voltage of DEP limited its application. Recently, investigations carried out by Im et al.14,15 and Jung et al.16−18 showed that electrophoresis of charged droplets (ECD) can be an alternative droplet manipulation method. Im et al.14 listed three advantages of ECD over EWOD and DEP. First, unlike the case of EWOD, ECD is free from surface © 2013 American Chemical Society

contamination. Second, the principle of ECD is much simpler and more straightforward. Third, in the case of ECD, the coalescence of the droplet can be easily controlled. To study the motion of a charged droplet under a given electric field, it is necessary to measure how much charge a droplet acquires since the Coulomb force was proportional to the quantity of the electric charge. Generally, the charge transfer of a conductive sphere with a relatively large diameter can be directly measured by an oscilloscope,19,20 electrometer,14 or Faraday cup. For a macroscopic droplet moving in an immiscible liquid, the quantity of the charge of a droplet can be indirectly determined by image analysis.14,21,22 In this method, the moving of a charged droplet was recorded by a high speed camera and the Coulomb force was assumed to be balanced by the hydrodynamic drag force. The charge of a droplet can be estimated based on Newtonian laws of motion. However, accurate determination of the hydrodynamic drag force was very difficult; therefore, the accuracy of this method cannot be assured.14,23 Furthermore, in the case of micrometer-sized droplets (diameter smaller than 100 μm), it is very difficult to record the motion of such a small droplet by camera without a specially developed device; this increases the difficulty of the measurement. Alternatively, the generation of such a small discrete droplet was another problem. Generally, discrete droplets with diameters larger than several hundreds of micrometers can be obtained by micropipet; for droplets smaller than several tens of micrometers, it is very difficult to generate by micropipet. Received: September 20, 2012 Revised: December 25, 2012 Published: January 8, 2013 1676

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The charging characteristics of an aqueous droplet of several hundreds of micrometers in size have been studied experimentally by many researchers14,15 commonly with the above-mentioned methods. Im et al.14 investigated the charging characteristics of the droplets ranged from 264 to 615 μm with the help of an electrometer, and compared the results obtained by electrometer with the results obtained by image analysis. Their research indicated that the measurement accuracy of the electrometer cannot be assured due to the extremely small electric charge carried by the droplets, whereas the measured results obtained by image analysis was more uniform and consistent with the actual value. The results reported by Im et al.14 indicated that the electric charge of a droplet with a diameter of several hundreds micrometers cannot be directly detected by electrometer due to the measurement accuracy of the present measurement device. Apparently, it was more unrealistic to directly detect the electric charge of a droplet with diameter of several tens or several micrometers. The charging characteristics of droplets with diameters of several tens or several micrometers were rarely reported due to the difficulty of both optical observation and generation of such small discrete droplets. The size of the droplets is of important biological significance since the size of the living cells, DNA, and viruses are all in micrometer size, or even small. Furthermore, in the other industry application, such as dehydration of crude oil1−4 and electrostatic spraying,5,6 it is of great industrial value to investigate the charging characteristics of micrometer-sized droplets. In this paper, we proposed a novel method of investigation the charging characteristics of micrometer sized droplets. This new method is expected to be a powerful tool to accelerate the evolution of the microfluids, chemical, biological and other related applications.

Figure 1. Illustration of the charging behavior of the micrometer sized droplets in the parallel plate capacitor, a, without insulated layer and b, with insulated layer. The droplets between the electrode plates and the insulated layer have been amplified for illustration.

1 1 1 1 = + + Cb C1 C2 C3 C1 = C3 =

C2 =

ε0εrS d

(3)

ε0εeS d − 2t

(4)

where Cb is the capacitance of the capacitor shown in Figure1b; εi and εe are the relative permittivity of the insulated layer and emulsion, respectively; t and d − 2t is the thickness of insulated layer and emulsion, respectively. From eqs 2, 3, and 4, the value of Cb can be expressed as follows:

2. PRINCIPLE Since the charge quantity of the single droplet with diameter smaller than several tens micrometers is too small to be directly detected by oscilloscope, electrometer and Faraday cup, a capacitive measurement instrument was developed in this work to measure the charging characteristics of the micrometer-sized droplets. Different from the previous work14 in which a discrete droplet was generated by a micropipet, in our case, a large amount of droplets were obtained by dispersing water into oil. This process was called emulsification and was performed by a homogenizer. For a perfect parallel plate capacitor, the capacitance can be expressed as follows: C=

ε0εiS t

(2)

Cb =

ε0εiεeS 2tεe + (d − 2t )εi

(5)

Since the value of Cb can be detected by the capacitance measurement device, and the values of ε0, εi, t, S, and d were already known, the relative permittivity of the emulsion can be calculated by solving eq 5, εe =

εi(d − 2t )C b ε0εiS − 2tC b

(6)

For the capacitor with bare electrodes, as shown in Figure 1a, the capacitance can be expressed by the following equation according to the definition of capacitance,

(1)

Ca =

where ε0 is the vacuum permittivity, εr is the relative permittivity of the material filled between the parallel electrodes, S is the area of the electrodes, and d is the distance between them. For the capacitor shown in Figure 1b, the electrodes were covered by an insulated layer of thickness t, and in the middle was filled by emulsion. According to the definition of the parallel plate capacitor, when the capacitor was filled by multilayer material with different relative permittivity, the capacitor can be treated as a series of multiple parallel plate capacitors. Therefore, for the capacitor shown in Figure 1b, the capacitance can be can be expressed as follows:

Q droplets ε0εeS + d U

(7)

where Ca is the capacitance of the capacitor as shown in Figure 1a, U is the voltage applied on the electrodes, Qdroplets is the quantity of the electric charge consumed by the charging of droplets that contact with the bare electrodes. The value of Qdroplets can be calculated by the following equation,

Q droplets = nQ

(8)

where n is the number of the droplets that can be charged by the bare electrodes and Q is the charge of single droplet. 1677

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For a perfectly conducting solid sphere of radius a in contact with an electrode, a saturation charge Qtheory equal to the following: Q theory =

π2 (4πa 2)ε0εrE 6

geometry relationship, the number of droplets that are directly opposite to the electrodes can be obtained by dividing 2S (total area of the two electrodes) by l2: ⎛ 4πa3 ⎞−2/3 2S n = 2 = 2S⎜ ⎟ l ⎝ 3Wcon ⎠

(9)

where εr is the relative permittivity of the surrounding medium.24 In our case, the value of εr can be replaced by εe since the capacitor was filled by emulsion, and E can be replaced by U/d. Q theory =

π2 U (4πa 2)ε0εe 6 d

From eqs 6, 7, 8, 9, 10, 11, and 13, the value of η can be derived: η=

(10)

⎛ 4 ⎞−1/3 −7/3 −2/3 ⎜ ⎟ W con π ⎝3⎠ Cad(ε0εiS − 2tC b) − ε0εi(d − 2t )C bS ε0εi(d − 2t )C bS

In eq 10, the acquired charge of the droplets after contact the bare electrode are proportional to their surface area and the electrical field strength. A previous investigation carried out by Im et al.14 showed that the aqueous droplets were less charged than the corresponding perfectly conductive sphere, and the actual charge of an aqueous droplet after contact with an electrode can be expressed by the following equation, Q = ηQ theory

(13)

(14)

As can be seen from eq 14, η is the function of S, t, d, ε0, εi, Wcon, Ca, and Cb, and is independent of the voltage applied on the electrodes, U, and the radius of the droplets, a. In eq 14, the value of S, t, d, ε0, εi, and Wcon was already known, and the value of Ca and Cb can be detected by the capacitance measurement device.

(11)

3. EXPERIMENTAL SECTION

where η is the coefficient and its value is between 0 and 1. In order to determine the value of η, it is first necessary to determine the number of droplets, n, that can be charged by the bare electrodes. In our case, the droplets that are directly opposite the electrodes, the color droplets as illustrated in Figure 1a, were assumed to be charged by the bare electrodes. The rationality of this assumption will be discussed in the following sections. To perform the calculation, the droplets in the emulsion were assumed to have the same size and are uniformly distributed in the emulsion for simplicity. Since accurate determination of the value of n was very difficult, in our case, an approximate estimate was proposed. If we mesh the space between the electrodes into many small uniform cubes and in each cube there is a droplet, as shown in Figure 2,

The instrument made by the authors is shown in Figure 3. The materials of the electrodes are stainless steel. The opposite surface of

Figure 3. a, Illustration and b, picture of the experimental set up. the two electrodes was mirror polished to ensure the parallelism of the two electrodes. The diameters of the electrodes are 110 mm and the distance between them can be adjusted by rotating the cell which is made with Perspex. A digital electrical bridge (TH2828S) was used to measure the capacitance of the parallel plate capacitor. The measurement mechanism of the device was based on the charging characteristic of the capacitor. From the charging time of the capacitor, the value of the capacitance can be determined. The detected voltage was sinusoidal and the RMS value of the voltage can be adjusted between 0 and 1 V. During the measurement, three level of detected voltage was used in the current experiments to investigate the influence of detected voltage. The detected frequency can be adjusted between 0.04 and 200 kHz, according to the value of the capacitance. For a small capacitor, a high detected frequency was adopted since the charging time was very short. In our case, the capacitance of the parallel plate was very small,

Figure 2. Illustration of the distribution of the droplets in the parallel plate capacitor.

then the side length of the cubes can be calculated according to the droplets size and water content of the emulsion.

⎛ 4πa3 ⎞1/3 l=⎜ ⎟ ⎝ 3Wcon ⎠

(12)

where l is the side length of the cube, Wcon is the water content of the emulsion (in volume ratio). In Figure 2, the blue droplets opposite the lower electrodes and the red droplets opposite the upper electrodes were assumed to be charged by the electrodes. According to the 1678

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about several hundreds of pF, therefore, a relatively high detected frequency, 100 kHz, was adopted in order to ensure the measurement accuracy. Water-in-oil emulsions were prepared using, for the oil phase, 82.1 vol % of synthetic transformer oil (provided by ZhongDe Industrial & Trading Co., Ltd., Dongying), and for the water phase, 17.9 vol% of deionized water (provided by College of Chemical Engineering, China University of Petroleum). Stationary tape mainly made up of cellophane was attached on the electrodes surface and used as the insulated layer. The thickness of the insulated layer was 48 μm. The physical property of the transformer oil, deionized water, and stationary tape used in the experiment are summarized in Table 1.

insulated electrodes, the relative permittivity of air and oil can be calculated with eq 6. The results are listed in Table 2. As can Table 2. Comparison of the Measured and Actual (or Predicted) Value of Relative Permittivity of Air, Oil, and Emulsion

Table 1. Physical Property of the Materials property density(g/cm3) (20 °C) viscosity (20 °C) relative permittivity conductivity(μs/cm)

insulated layer

3.95 too small to be measured

oil

water

0.86

1

120 cP 2.36 too small to be measured

1 cP 84 65

relative permittivity

air

oil

emulsion

actual value measured value with insulated electrodes measured value with bare electrodes predicted value

1.00 1.01 1.01

2.36 2.32 2.33

4.2 4.21 4.26

be seen from Table 2, the relative permittivity of air and oil was very close to their actual values. With insulated electrodes, the relative permittivity of the emulsion used in our work was also measured. The measured value was very close to the predicted value with the model of Jakoby and Vellekoop.25 The results listed in Table 2 confirm the feasibility of the method. It should be noted that the relative permittivity of emulsion cannot be measured with bare electrodes due to the direct charging of the droplets contacted with the bare electrodes. The charge of the droplets will increase the energy stored by the capacitor and exaggerate the actual value of the permittivity of emulsion. 4.2. Influence of Electrical Field Strength and Ion Species. Since the maximum RMS value of the detected voltage was 1 V, during this experiment the distance between the electrodes was adjusted to 0.5 mm; therefore, the electrical field strength can be adjusted from 0 to 20 V/cm. The homogenization speed of the emulsions used in this experiment was 5000 r/min. The influence of electrical field strength and ion species on the value of η is shown in Figure 5. As shown in Figure 5, the

The homogenization was performed by a homogenizer (FJ200, with 18 and 12.7 mm of stator and rotor diameters, respectively) with different rotation speed. The micrographs of the emulsion in our experiments were shown in Figure 4. As can be seen from Figure 4, the

Figure 4. Micrograph of the emulsions used in our experiments. a, the rotation speed of the homogenizer was 5000 r/min; b, the rotation speed of the homogenizer was 2000 r/min. droplets’ size distribution was significantly affected by the rotation speed of the homogenizer. In order to stabilize the emulsion, 0.1 wt % of Span80 (provided by Kermel Chemical Reagent Co., Ltd., Tianjin) was added to the oil phase. After homogenization, the emulsion was observed by an optical microscope with the aiming of getting the information of droplets size distribution. All experiments are performed at room temperature (20 °C). Because we are interested in the biochemical applications, we use physiological saline (154 mM NaCl solution), and KCl solution with the same mole concentration to see the effects of different ion species. To examine the concentration effect, we use three different concentrations of NaCl solutions of 1.54, 15.4, and 154 mM. The electrolyte ion species and concentration were the same as those in the literature,14 therefore comparative analysis can be done with the aiming of examining the correctness of our experimental results. According to the reports of Im et al.,14 the value of η was affected by electrical field strength, ion species, and the electrolyte concentration in the aqueous droplet. Detailed discussions are presented bellow.

Figure 5. Influence of electric fields strength and electrolyte ion species on the dimensionless charge of deionized water and electrolyte droplets.

value of η was independent of the electrical field strength. The results of our experiments were consistent with eq 14. With different applied voltage, the value of Ca does not show much difference; so does Cb. This trend was a little different from the report of Im et al.14 who investigated the charging characteristics of droplets with diameter of several hundreds micrometers under relatively high electrical field strength (1.9−5.1 KV/cm). In our case, the electrical field strength was (4−20 V/ cm).

4. RESULTS AND DISCUSSION 4.1. Validation of the Method. In order to validate the feasibility of this method, the relative permittivity of air and oil were measured with bare electrodes and with insulated electrodes, respectively. With bare electrodes, the relative permittivity of air and oil can be derived from eq 1, and with 1679

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The results showed that both the value of η and its deviation of the droplets shown in Figure 4a was a little smaller than those of the droplets shown in Figure 4b. The results were not consistent with eq 14, which showed that the value of η was independent of the droplet sizes. Perhaps this can be explained by the difference of the droplet distribution in the emulsion, which will affect the number of droplets that can be charged by the electrodes.

The results of our experiments showed that the electrolyte droplets were less charged than the deionized water droplets and the difference between different ion species was insignificant. This was consistent with the reports of Im et al.14 Some possible explanations were given by Im et al. from the view of electrochemical reactions. A more detailed explanation is beyond the scope of the present study, and further research is needed to understand the complex electrochemical charging mechanism. 4.3. Influence of Electrolyte Concentration. The influence of electrolyte concentration is shown in Figure 6.

5. COMPARISON WITH HIGH ELECTRICAL FIELD STRENGTH The above experimental results indicated that the influence of electric field strength on the charging characteristics of micrometer-sized droplets was insignificant within the range of 4−20 V/cm. In order to investigate the charging characteristics under higher electrical field strength, for instance several kV/cm, another experimental device, as shown in Figure 8, was

Figure 6. Influence of electric fields strength and electrolyte concentration on the dimensionless charge of deionized water and electrolyte droplets.

Figure 8. Illustration of the experimental set up. The droplets between the electrode plates have been amplified for illustration.

As can be seen from Figure 6, with different electrical field strength, the electrolyte droplets were less charged than deionized water droplets in all cases, regardless of their concentration and electrical field strength. It seems that the quantity of the charge decreases with increasing electrolyte concentration. 4.4. Influence of Droplets Size. The influence of droplets size on the charging characteristics was investigated, and the results are shown in Figure 7. Only qualitative investigation was carried out in our current study since the droplet size cannot be accurately controlled. As shown in Figure 4, the droplet size has a broad distribution.

developed. A high voltage direct current (DC) power supply was connected to the two electrodes of the capacitor through a resister and IGBT (SGL160N60UFD) which was controlled by a single chip (89C52RC). The resistance of the resister was 1000 Ω. An oscilloscope (RIGOL DS5042M) was used to record the waveform of the charging current. Before each measurement, the two electrodes were connected by a metal wire to neutralize the charge carried by the capacitor and the droplets. From the charging waveform, the quantity of electric charge stored by the capacitor and the droplets can be obtained. In our experiment, the breakover time of the IGBT was very short, 5 μs, to avoid the coalescence of droplets in the emulsion. Our previous investigation2,3 showed that the average droplet size can increase one time within only several seconds if the emulsion was subjected to an electrical field of several KV/ cm. The current waveform showed that the charging process of the capacitor can be completed within 5 μs. In this experiment, the distance between the electrodes was increased to 3.16 mm to avoid breakdown since the voltage of the DC power supply was much higher than the detected voltage of the electrical bridge. With bare electrodes, as shown in Figure 1a, the quantity of electric charge stored by the capacitor can be expressed as follows: Q a = Q droplets + Q c

(15)

where Qa is the total charge consumed by droplets and capacitor, and Qc is the charge consumed by capacitor, which can be expressed as follows:

Figure 7. Influence of droplet size on the dimensionless charge of deionized water droplets. 1680

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Article

ε0εeS U d

(16)

With insulated electrode, as shown in Figure 1b, the charge stored by the capacitor can be expressed as follows: Q b = C bU

(17)

where Qb is the electric charge quantity stored by the capacitor, Cb is the capacitance of the capacitor and can be calculated by eq 5. From eqs 6, 8, 10, 11, 13, 15, 16, and 17, the value of η can be expressed as follows: η=

⎛ 4 ⎞−1/3 −7/3 −2/3 ⎜ ⎟ W con π ⎝3⎠ Q a(ε0εidSU − 2tdQ b) − ε0εiSUQ b(d − 2t ) ε0εi(d − 2t )SQ bU

Figure 10. Influence electrolyte ion species on the dimensionless charge of deionized water and electrolyte droplets with high electrical field strength.

(18)

The derivation procedure of eq 18 was similar with that of eq 14 in section 2. In eq18, the value of S, t, d, εi, U, and Wcon are already known; the value of Qa and Qb can be obtained by integrating the current waveform recorded by the oscilloscope. In Figure 9, we compared the typical charging waveforms of the capacitor with bare electrodes and the capacitor with

is very difficult to determine how many droplets were in contact with the electrode at the moment of turning on the circuit. In eq 12, we assumed that the droplets were uniformly distributed and had the same size. However, it was not consistent with the actual case. In eq 13, the droplets that were directly opposite to the electrode were assumed to be charged and discharged by the electrodes. Apparently, the value of n calculated by eq 13 was much larger than the actual case, which will result in a relatively small η value. Alternatively, in the actual case, the sedimentation of the droplets will cause nonuniform distribution of the droplets. Theoretically, the number of droplets that contact the bottom electrode should be larger than that contacting the top electrode due to the sedimentation. This increases the difficulty of accurate determination of the value of n. However, with this method, comparative investigation can be done to research the influence of electrolyte concentration and ion species. For instance, from the results of the current work, we can conclude that the electrolyte droplets were less charged than the deionized water droplets.

Figure 9. Comparison of the typical charging waveforms of the capacitor with and without insulated layer.

6. CONCLUSIONS In this work, a new method of investigating the charging characteristic of micrometer-sized droplets was proposed. On the basis of the simple parallel plate capacitor model, the charging characteristic of micrometer-sized droplets can be determined. The results indicted that the method was very easy to be understood and operated. The main disadvantage of this method was the difficulty of accurately determining the number of droplets that can be charged by the bare electrodes. The current calculation method in this work exaggerates the value of n and as a consequence results in an η value smaller than the actual case. Further research is still needed to modify this method. The current research is expected to provide a powerful investigational method for elucidating the charging characteristics of micrometer-sized droplets.

insulted electrodes. As can be seen from Figure 9, with bare electrodes, the current was much bigger than the case of insulated electrodes. The value of η that is shown in Figure 5 was remeasured by this method with high electrical field strength and the results are shown in Figure 10. As can be seen from Figure 10, apart from the larger deviation of the results, the value of η does not show a significant difference from that shown in Figure 5. This indicated that the method proposed in this work can be used to investigate the charging characteristics of micrometer-sized droplets. It should be noted that, in all of the experimental cases, an aqueous droplet is less charged than the perfect conductor, about 15−25% of the theoretical maximum. In our present study, the value of η is much smaller than that reported by Im et al.14 (40−70%). Perhaps this can be explained by the calculation method of the number of droplets that can be charged by the electrodes. In the actual case, only the droplets that contacted with the electrodes can be charged. However, it

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ASSOCIATED CONTENT

S Supporting Information *

Four tables showing the average value and standard deviation of Q/Qtheory presented in Figures 5, 6, 7, and 10. This material is available free of charge via the Internet at http://pubs.acs.org. 1681

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AUTHOR INFORMATION

Corresponding Author

*Tel: 85-0546-8392303; fax: 86-0546-8393620; e-mail: [email protected], [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

The work is partially supported by Chinese National Natural Science Foundation (Grant No. 51275529), Incubation Programme of Excellent Doctoral Dissertation of China University of Petroleum (Grant No. LW120301A), Science and Technology Development Plan of Qingdao City (Grant No. 12-1-4-7-(2)-jch), and Taishan Scholar Construction Project of Shandong Province (Grant No. TS20110823).

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