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Jiachen Wuzhang1 Yongxin Song1 Runzhe Sun1 Xinxiang Pan1 Dongqing Li2 1 Department
of Marine Engineering, Dalian Maritime University, Dalian, P. R. China 2 Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, Canada
Received February 3, 2015 Revised May 11, 2015 Accepted June 4, 2015
Research Article
Electrophoretic mobility of oil droplets in electrolyte and surfactant solutions Electrophoretic mobility of oil droplets of micron sizes in PBS and ionic surfactant solutions was measured in this paper. The experimental results show that, in addition to the applied electric field, the speed and the direction of electrophoretic motion of oil droplets depend on the surfactant concentration and on if the droplet is in negatively charged SDS solutions or in positively charged hexadecyltrimethylammonium bromide (CTAB) solutions. The absolute value of the electrophoretic mobility increases with increased surfactant concentration before the surfactant concentration reaches to the CMC. It was also found that there are two vortices around the oil droplet under the applied electric field. The size of the vortices changes with the surfactant and with the electric field. The vortices around the droplet directly affect the drag of the flow field to the droplet motion and should be considered in the studies of electrophoretic mobility of oil droplets. The existence of the vortices will also influence the determination and the interpretation of the zeta potential of the oil droplets based on the measured mobility data. Keywords: Charge redistribution / Droplet electrophoresis / Electrophoretic mobility / Ionic surfactant / Vortex interaction DOI 10.1002/elps.201500062
1 Introduction Electrophoresis is one of the powerful analytical methods in many fields, such as petroleum industry, biochemistry, and biomedical engineering. For example, it can be used to characterize the surface electrokinetic properties of particles and cells without causing damage to the particles and cells [1]. The CE technology has been widely used for separation of biological molecules such as proteins [2]. Under an electric field, a charged particle in a bulk aqueous electrolyte solution will move relative to the surrounding liquid. Such motion is referred to as the electrophoresis. Electrophoresis is typically characterized by the particle velocity, ve p =
E εr εo p for a thin electric double layer
(1)
or by electrophoretic mobility (velocity per unit applied electric field), e p =
εr εo p ve p = , E
(2)
where p is the zeta potential of the particle; E is the applied electric field; εr εo is the dielectric constant of the liquid; and is the viscosity of the liquid. Equation (1) is usually referred to as the Smoluchowski equation. Electrophoretic mobility is an important parameter and can be used to calculate the surface charge and zeta potential of a solid particle
Correspondence: Professor Dongqing Li, Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON N2L3G1, Canada E-mail: [email protected]
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based on the electrokinetic theory and the Smoluchowski equation. Because of the importance of the electrophoretic mobility, extensive theoretical, and experimental studies have been carried out with respect to its theoretical interpretation and the measurement methods [3–10]. It should be noted, however, that the Smoluchowski equations such as Eqs. (1) and (2) are valid only for solid particles with a thin Electrical Double Layer (EDL) and low zeta potential. For droplet electrophoresis, many studies have also been reported [11–19] since the Quincke experiments [20]. Booth [12] was the first to theoretically study the electrophoresis of spherical fluid droplets in electrolyte solutions. He derived a general formula for the electrophoreitic mobility of bubbles and droplets, assuming a symmetrical charge distribution on the surface. The formula, however, disagrees with the experiments [21]. Taylor [22] measured the electrophoretic mobility of decalin droplets in aqueous media and calculated the zeta potential from the measured mobility by modifying the Smoluchowski equation with several parameters, such as ion cloud relaxation, surface conductivity, and droplet phase viscosity. They found that these parameters have little effects on the mobility. Later, Levine and O’Brien [16] developed a theory about the electrophoretic motion of a charged mercury drops in aqueous electrolyte solution. They found that the polarization effect can enhance the electrophoresis of the mercury drop. By extending the electrophoresis model for a solid spherical particle, Ohshima [13] showed that the fluid nature of the interphase boundary sharply differentiates drops from solids.
Colour Online: See the article online to view Figs. 1–8 in colour
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The model, however, is applicable only to drops that have a much higher conductivity than the supporting electrolyte. Baygents and Saville [17] computed the electrophoretic mobility as a function of the zeta potential and several other parameters for both conducting and nonconducting droplets. They found that the -potential alone is not sufficient to characterize the surface. However, their implicit assumption of the weak-field approximation is problematic for micron-size droplets [23]. Droplet electrophoresis was recently studied by V. Knecht et al. who found that the calculated electrophoretic mobility does not always reflect the net charge or electrokinetic potential of a suspended liquid droplet based on their molecular dynamics simulation results [24]. Huang et al. [25] theoretically investigated the electrophoretic motion of a liquid droplet in a cylindrical pore, taking account of the double layer polarization and the droplet viscosity effects. They found that the lower the viscosity of the droplet is, the greater the electrophoretic velocity is. Also, the polarization effect will slow down the droplet movement in general. Ory Schnitzer [26] developed a coarse-grained macroscale model for electrophoretic motion of a bubble in order to overcome the shortcomings of thin-double layer assumption. However, they neglected the adsorption of salt ions and adopted uniform surface-charge density assumption. Furthermore, oil droplet electrophoresis phenomena become more complicated when ionic surfactants are adsorbed at the oil-water interface. The adsorbed surfactants will change the EDL structure, alter lateral transport of ions behind the shear plane [27]. Researches on rising air bubble [28–31] and droplets [28, 29] in gravity or pressure driven flows showed that the surfactant molecules will be swept to the rear of the droplet and form a so-called “stagnant cap” due to the hydraulic drag force. Electrophoresis behavior of oil droplets in surfactant containing electrolyte solutions was also reported. Sarah A. Nespolo et al. [32] considered the hydrodynamic mobility effect when converting the measured electrophoretic mobility values to zeta potentials. In order to examine the extent to which the standard electrokinetic model is a good approximation, R. Barchini studied the electrokinetic properties of SDS-stabilized oil droplets of submicron size and derived zeta potential with O’Brien and White theory [33] but without considering the hydrodynamics effect. They found some challenging questions when applying the theory to highly charged colloidal particles. As discussed above, the majority of these studies focus on the influence of the electrokinetic or hydrodynamic properties of the interface on droplet mobility as well as the interpretation of the electrokinetic potential and the validity of the Smoluchowski equation [34]. In the literature, there are some data on the elelctrophoretic mobility of oil droplets. Barchini et al. studied the electrokinetic properties of surfactantstabilized silicon oil droplets (276576 nm in diameter) in SDS solution. They found that the magnitude of mobility is between 57 × 10−4 cm2 V−1 .s−1 [27]. Electrophoretic mobilities of 5.35.75 × 10−4 cm2 V−1 .s−1 for decane droplet in SDS (with varying concentrations) and 10−3 NaNO3 mixture solution were also reported [32]. Marinova et al. measured C 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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the electrophoretic mobility of xylene droplet as a function of pH at a fixed NaCl concentration. Specifically, the mobility is between 58 × 10−4 cm2 V−1 .s−1 for a varying 69 pH values [35]. It should be noted that most of the droplet diameters are in the submicron range. Submicron oil droplets are generally considered as hard spheres [36]. Currently, there is little data on mobility of micron-sized oil droplets. It should be realized that the surface charges or the adsorbed surfactants on a droplet surface are mobile, while the surface charges or the adsorbed surfactants on solid particle surface are immobile. This is a key difference between an oil droplet and a solid particle in electrophoresis. Will the mobile surface charges on an oil droplet influence the electrophoretic motion of the droplet under different electric fields? Will ionic surfactants absorbed at the oil droplet surface influence the electrophoretic mobility of an oil droplet? Will the mobile surface charges and the absorbed surfactants have any effects on the flow field around the droplet? Very little is known in these regards. In this paper, the electrophoretic mobility of oil droplets in PBS and ionic surfactant solutions were studied under different concentrations of ionic surfactants and different electric fields. The flow field around the droplet was also examined by using 1 m polystyrene tracing particles. It was found that two vortices near the droplet were formed. The observed smaller mobility under stronger electric field under the same surfactant concentration can be explained by the increasing effects of the vortices with the electric field. While forming circulating flows inside a droplet has been reported before, this paper demonstrates first time the vortices formed outside the droplets in both PBS and surfactant solutions. The finding of the vortices near a droplet can help to understand the complicate electrophoretic behavior of droplets. The effects of the vortices should be considered before zeta potential and surface charge can be calculated from the measured electrophoretic mobility.
2 Materials and methods 2.1 System setup and sample preparation Figure 1 shows the experimental system that includes a microfluidic chip, a DC power supply (CSI3003 × 3,Circuit Specialists,Mesa,AZ) and an inverted optical microscope image system (Ti-E, Nikon) with a progressive CCD camera (DSQi1Mc, Nikon). The experiments of electrophoretic motion of oil droplets were conducted in a microfluidic chip with a straight microchannel as shown in Fig. 1. The microfluidic chip was fabricated by bonding a PDMS plate with a glass substrate (25.66 × 75.47 × 1.07 mm, CITOGLAS, China) using a plasma cleaner (HARRICK PLASMA). The master for making the microchannel on the PDMS plate was fabricated by using a negative photo-resist (SU-8 2025, MicroChem Co., Newton, MA) on a silicon wafer substrate (4” N/PHOS, Montco Silicon Technology Inc., Spring City, PA). The channel is 190 m wide, 1.2 cm long, and 25 m in www.electrophoresis-journal.com
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Figure 1. A schematic diagram of the experimental system.
height. There are two wells at the ends of the microchannel (not shown in Fig. 1). The wells (2 cm in diameter) are used as the solution reservoirs and for inserting electrodes to apply electric field along the channel. The oil droplets in surfactants solutions of different concentrations were obtained by mixing 10 L Soya-bean oil (Jin Longyu AE, Jinhai Food Industry Company, China) with 1.5 mL surfactant solutions. In this study, two ionic surfactants, SDS (⬎99% purity, Shanghai Bioengineering Company, China) and CTAB (⬎99% purity, Tianjing Damao Chemical Company, China), were used. To prepare the surfactant solutions, a certain amount of SDS or CTAB was added to the 7.5 mM sodium borate buffer solution (PBS). Afterwards, 10 L oil was added to the surfactant solution and was mixed for 23 min with a vortex hand mixer (Lab dancer, M7-15US12R-F, IKA Company, Germany). 2.2 Measurement of the mobility The electrokinetic movement of oil droplets was measured in the microfluidic chip placed on the observation stage of the microscope. To begin the experiments, the microfluidic chip was primed first with PBS buffer solution. Then 10 L oil sample solution was added into the inlet well. The liquid levels in the inlet and outlet wells were carefully balanced by adding a certain amount of the sample solution in the wells by using a digital micro-pipette. Afterwards, Pt electrodes were inserted in the wells and an electric field was applied to transport the oil droplets in the channel. In the meantime, the oil droplet motion was recorded by the CCD camera (DSQi1Mc, Nikon) of the inverted optical microscope imaging system (Ti-E, Nikon). The camera was operated in a video mode at a frame rate of 11.4 frames per second. The reading error in determining the cell position is about ±2 pixels that correspond to actual dimension of ±5.4 m. The microscope imaging system was also equipped with specific software that can determine the size of the droplets. In order to keep the C 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
same conditions for measuring the mobility, we only used the oil droplets moving near the central line of the channel to calculate the mobility. In this way, the same conditions, including the same distance away from the channel all, were kept. To minimize the influence of static hydraulic pressure on the movement of the oil droplets, two approaches were adopted. First, relatively larger wells were used to minimize the back pressure driven flow generated by the EOF. Secondly, only the droplet movement of the first 1020 s after applying the electric field was recorded and used for calculating the electrophoresis mobility. Under each set of conditions (e.g. surfactant concentration and electric field), the velocity of a droplet of a certain size was measured and then its electrophoresis mobility was calculated. For each size, at least five droplets of the same size were measured; each data point reported in the figures of this paper is the average value of these results.
2.3 Observation of the flow field around a droplet The flow field around an oil droplet was visualized by using 1 m tracing particles (Fluka, Shanghai, China). In practice, it is very difficult to observe and visualize the flow field around a moving droplet with tracing particles, especially when the droplet is very small and moves very fast. In this study, therefore, we studied the flow field around a relative larger droplet that was fixed in a position in the middle of the channel. Fixing the droplet position in a microfluidic channel was achieved by the following approach: an oil droplet was placed on the bottom surface of the PDMS microfluidic channel (80 m in height, open to the air and without plasma treatment) without the solution first; then the solution (with 1 m tracing particles) was added into the channel with a pipette. Afterwards, a glass slide treated by a plasma cleaner (HARRICK PLASMA) is covered on the microfluidic channel. Finally, www.electrophoresis-journal.com
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Figure 2. Dependence of oil droplet velocity on surfactant concentration under an electric field of 41.7 V/cm for droplets with different diameters (39 m), (A) in SDS solution, (B) in CTAB solution. (V > 0: moving toward positivie side of the applied electric field; V < 0: moving toward negative side of the applied electric field).
different electric fields were applied and the trajectories of the trace particles around an oil droplet were recorded by the CCD camera (DS-Qi1Mc, Nikon) of the inverted optical microscope imaging system (Ti-E, Nikon).
3 Results and discussion
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of the negative surface charges on the droplets. This is indicated by the positive velocity value ( 70 m/s) shown in both Fig. 2A and B (0 mM). For the droplets in SDS (an anionic surfactant) solutions, as shown in Fig. 2A, the droplets still moved toward the positive side of the applied electric field and the velocity increases with the increase in SDS concentration. Beyond 4 mM concentration, the velocity approaches an essentially constant value. This is likely due to saturated adsorption of SDS at the channel walls and on the droplet surfaces. Realizing that the net motion of an oil droplet in this case is determined by both the EOF of the solution in the microchannel (toward the negative side of the electric field) and the electrophoresis of the oil droplet (toward the positive side of the electric field), the final constant velocity indicates the balance of these two driving forces. As regards to the oil droplets in CTAB (a cationic surfactant) solution (Fig. 2B), in contrast, the droplets sharply reversed the moving direction once CTAB was added (from about 70 m/s to −20 m/s). This can be understood by the fact that adsorption of CTAB molecules carrying positive charges on the channel walls and the droplet surface will reverse both the direction of EOF and the direction of droplet electrophoresis. Beyond the CMC, the adsorption of CTAB surfactant molecules at the channel walls and at the droplet surfaces reaches saturation; the opposite motions of EOF in the channel and droplet electrophoresis are balanced; thus the velocity of the droplets will not change with the increase of CTAB concentration as clearly shown in Fig. 2B. From Fig. 2, it can also be noticed that there is no obvious difference in the velocity of the droplets of different diameters. This means that the electrokinetic movement of the oil droplets is not size dependent. For the following sections, therefore, we will analyze the elelctrokinetic movement only for droplets of approximately 3 m in diameter. Figure 3 shows the dependence of droplet velocity on the applied electric field with different surfactant concentrations for 3 m oil droplets. It is clear that the droplet velocity increases with the electric field. In Fig. 3A, the droplet velocity in 6 mM SDS solution increases by 75.88% when the electric field is increased from 25.8 to 41.7 V/cm. For CTAB solution, as shown in Fig. 3B, the velocity in 0.5 mM CTAB solution increases about 36.3% when the electric field is increased from 25.8 to 41.7 V/cm. Because the movement of a droplet is the combination of the EOF of the bulk solution and the electrophoresis of the droplet, and thus the electrophoretic velocity of the droplets is given by:
3.1 Electrophoretic mobility
Vep = V − VEOF .
Figure 2 shows the dependence of oil droplet velocity on surfactant concentration under an electric field of 41.7 V/cm for droplets with different diameters (39 m). In this figure, zero surfactant concentration means that the oil droplets were in pure PBS solution without any surfactants. When the oil droplets were in PBS buffer solution, the droplets moved toward the positive side of the applied electric field because
Where Vep is the electrophoresis velocity of the droplet, V is the measured droplet velocity, and VEOF is the electroosmotic flow of the bulk solution in the channel. Theoretically, Vep and VEOF can be calculated by:
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(3)
Vep = ep · E
(4)
VEOF = EOF · E .
(5)
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120 Mobility (10-4cm2V-1.s-1)
10
V (μm.s-1)
100 80 60 40 0
2 4 6 Concentration (mM)
9 8 7 6 5
8
0
A
70
2
4 6 Concentration (mM)
8
A
6.0
25.8V/cm 41.7V/cm
25.8V/cm 41.7V/cm
4.0
Mobility (10-4cm2V-1.s-1)
50 V (μm.s-1)
25.8 V/cm 41.7V/cm
11
25.8V/cm 41.7V/cm
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30 10 -10
2.0 0.0
-2.0
-30 0.0
0.5
1.0 1.5 2.0 Concentration (mM)
-4.0
2.5
B
0.0
Figure 3. Dependence of droplet velocity on the applied electric field in different surfactant concentrations for 3 m oil droplets. (A) In SDS solution and (B) in CTAB solution (V > 0: moving toward positive side of the applied electric field; V < 0: moving toward negative side of the applied electric field).
Where ep and EOF are the electrophoresis mobility and the electroosmotic mobility, respectively. Combining the above equations yields: ep =
V − EOF . E
(6)
Table 1 summarizes the electroosmotic mobility of SDS and CTAB solutions in PDMS channel as reported in the published papers [30, 31]. Using the values in Table 1, experimentally measured droplet velocity data (such as shown in Fig. 2), and using Eq. (6), the electrophoretic mobility of the oil droplets can be obtained and is shown in Fig. 4. Figure 4 shows the dependence of the electrophoretic mobility on surfactant concentration. Under the two electric fields used in the experiments, the electrophoretic mobility for the droplets in PBS solution is about 5.3 [(m/s).(V/cm)], which is larger comparing with the mobility of a nanometer-sized silicon oil droplet (276 nm in diameter) in water/SDS solution as reported by Barchini [32]. C 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
0.5
1.0 1.5 Concentration (mM)
2.0
2.5
B
Figure 4. Dependence of the electrophoretic mobility on surfactant concentration with different applied electric fields. (A) In SDS solution and (B) in CTAB solution.
From Fig. 4, it is obvious that the absolute value of mobility increases with the increasing surfactant concentration. This increased mobility is due to the adsorption of surfactant at the oil droplet surface and hence the increased surface charge density. The adsorption of surfactants at the oil droplet surface will reach maximum when the surfactant concentration reaches to the CMC. Correspondingly, the mobility will become constant beyond the CMC. It should be noted that under the same surfactant concentration, however, the mobility is smaller in an electric field of 41.7 V/cm than that in a 25.8 V/cm electric field. For example, the mobility is increased by about 4.5% when the electric field is reduced from 41.7 V/cm to 25.8 V/cm for the oil droplets in 6 mM SDS solution. For oil droplet electrophoretic mobility, it has been generally accepted that the EDL polarization effect will slow down the droplet motion somewhat. In the cases of this study, the observed smaller electrophoretic mobility under larger electric field and the same surfactant concentration cannot be explained by the polarization effect for the following reasons. www.electrophoresis-journal.com
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Table 1. Electroosmotic mobility of SDS and CTAB solutions in PDMS channels as reported in reference papers [30, 31] ( > 0: flowing in the opposite direction to the electric field; < 0: flowing in the same direction with the electric field). (A) In SDS solution. (B) In CTAB solution
(A) Concentration (mM) Mobility (, 10−4 cm2 /V·s) (B) Concentration (mM) Mobility (, 10−4 cm2 /V·s)
0 –3.70
1 –6.30
2 –6.60
3 –6.80
4 –6.85
6 –7.00
0 –3.70
0.5 2.72
1.0 3.11
1.5 3.26
2.0 3.43
2.5 3.50
8 –7.10
Firstly, the zeta potential of the oil droplets in PBS is estimated to be within −50 to −70 mV [35, 37, 38]. Theoretically, the characteristic thickness of EDL (1/) is 3 nm for a 10−2 M NaCl solution. Since the NaCl concentration in PBS solution is larger than 10−2 M, 1/ is less than 3 nm in this study. Accordingly, a will be larger than 1000 for a 3 m oil droplet in PBS solution (a is the particle radius). Therefore, the EDL polarization effect on-mobility can be ignored. Secondly, even if the polarization effect exists, the counter electric field induced by the swept counterions can be considered as the same under the same surfactant concentration, due to the very large a. Furthermore, the measured mobility may be related to the observed vortices around the droplets. Because the mobile surface charges at droplet surface can be redistributed under the influence of the externally applied electric field, the nonuniform distribution of the surface charges may result in nonuniform EOF around the droplets, and hence affect the electrophoretic mobility of the droplets. Therefore, the dependence of electrophoretic behavior of oil droplets on electric field may arise from the redistribution of the mobile surface charges on the liquid–liquid interfaces as discussed below. 3.2 Vortices near the droplet Figures 5–7 shows the flow field around an oil droplet in different solutions (PBS, SDS, and CTAB solutions) under the two different electric fields. The pictures were obtained by superposing a series of consecutive images of the moving trace particles around the droplet. These pictures clearly show that there are two vortices around the oil droplet in all of the solutions. For comparison, solid (polystyrene) particles were tested under the same conditions; there were no vortices around the solid particles. As observed under the microscope, for the droplet in PBS and SDS solutions, the directions of the vortex on the lower side and the vortex on the upside are clockwise and counterclockwise, respectively. In contrast, the vortex directions are reversed for the droplet in CTAB solution. This corresponds well to the EOF flow directions at the oil-water interface in PBS, SDS, and CTAB solutions. In addition, there are differences in the size of vortices under different electric fields in surfactant solutions. The size of the vortices also increases slightly with the increase of the electric field.
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Figure 5. Vortices around an oil droplet in the PBS solution under different electric fields, (A) E1 = 25.8 V/cm, (B) E2 = 41.7 V/cm.
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Figure 6. Vortices around an oil droplet in SDS solution (5 mM) under different electric fields, (A) E1 = 25.8 V/cm, (B) E2 = 41.7 V/cm.
A possible explanation of the formation of the vortices is the redistribution of the mobile surface charges on the droplet surface, as illustrated in Fig. 8. Without the externally applied electric field, the surface charges of the oil droplets in an electrolyte or surfactant solution generally will be evenly distributed. When an electric field is applied, the mobile surface charges will be attracted to one side of the droplet due to the electrostatic attraction force. As a result, one section of the droplet surface has more surface charges (A1 ) and the rest of droplet surface has no or less surface charges (A2 ). For the flow field around the droplet, consequently, there are two boundary conditions: slip velocity (EOF velocity) boundary on surface A1 and no slip velocity for surface A2 due to the absence of surface charges. The EOF from the surface A1 will hit the stationary liquid on the surface A2 , is forced to move away from the surface A2 and results in a flow circulation, i.e. a vortex near the droplet. The EOF velocity will increase with C 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Figure 7. Vortices around an oil droplet in CTAB solution (0.5 mM) under different electric fields, (A) E1 = 25.8 V/cm, (B) E2 = 41.7 V/cm.
E
EOF
A1
A2
Figure 8. A schematic diagram of the redistribution of surface charges and vortex formation under different electric fields (E2 > E1 ).
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the increasing electric field and surface charge density, consequently, the vortices will also be size dependent on the electric field and surface charge density (surfactant concentration in this study). For the droplets in PBS and SDS solutions, the surface charges are negative and thus one clockwise vortex on the lower side and one counterclockwise vortex on the upside will be formed. However, for droplets in the positively charged surfactant CTAB solutions, if the CTAB molecules make the surface charge to be positive, the EOF flow direction on the droplet surface will be reversed under the same electric field direction. As a result, the directions of the vortices will also be reversed. This was confirmed by the observation under the microscope. A direct consequence of the vortices on the two sides of the droplet is to increase the flow resistance and hence reduce the droplet motion. As discussed above, the formation of the vortices may be caused by the redistribution of the mobile surface charges on the droplet surface. Increase of the applied electric field will reduce the surface area A1 that has concentrated surface charges, and increase the surface area A2 that has no or less surface charges. Therefore, the vortices around the droplet will increase with the applied electric field. Stronger vortices will slow down the motion of the droplets; consequently, the measured mobility will decrease with the increasing electric field. This is in agreement with the experimental results of the smaller mobility under a higher electric field, as is shown in Fig. 4.
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tions under the externally applied electric field. The finding of the vortices near a droplet can help to understand the electrophoretic behavior of droplets. Furthermore, the effects of the vortices should be considered and analyzed before zeta potential and surface charge can be calculated from the measured electrophoretic mobility values of oil droplets in electrolyte and surfactant solutions. The authors wish to thank the financial support of the Fundamental Research Funds for the Central Universities (3132014336), Liaoning Science Foundation (2014025020), and Liaoning Excellent Talent Supporting Plan (LJQ2014050) from China to Y. S., the Natural Sciences and Engineering Research Council of Canada through a research grant to D. L., the support from Dalian Maritime University to D. L., and the financial support from the University 111 project of China under Grant No. B08046 is greatly appreciated. The authors have declared no conflict of interest.
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4 Concluding remarks
[4] Russel, W. B., Saville, D. A., Schowalter, W. R., Colloidal Dispersions, Cambridge University Press, UK 1989.
Electrophoretic mobility of oil droplets of micron sizes in PBS and ionic surfactant solutions was measured in this paper. The electrophoretic mobility was obtained by using the conventional electrophoresis theory and by measuring the moving velocity of the droplet by a microscope image analysis system. The experimental results show that the ionic surfactants absorbed at the oil droplet surface can increase the electrophoretic mobility of an oil droplet before the surfactant concentration reaches to the CMC. Under the same surfactant concentration, the mobility, however, is smaller under stronger electric field. Unlike a solid particle, it was found that there are two vortices around the droplets. The formation of the vortices may be caused by the redistribution of the mobile surface charges on the droplet surfaces under the influence of the externally applied electric field. The vortices on the sides of the droplets will generate additional flow resistance to the motion of the droplets and hence affect the electrophoretic mobility of the droplets. As the size of the vortices increases with the electric field, the effects of the vortices on the electrophoretic mobility of the droplets will also increase with the electric field. While circulating flows inside a droplet have already been demonstrated, this paper firstly demonstrates two vortices formed around droplets in both PBS and surfactant solu-
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[34] Dukhin, S. S., Derjaguin, B. V., Electrokinetic phenomena in Surface and Colloid Science, Vol. 7, Wiley, New York 1974.
[24] Knecht, V., Risselada, H. J., Mark, A. E., Marrink, S. J., J. Colloid Interface Sci. 2008, 318, 477–486. [25] Cheng-Hsuan, H., Eric, L., J. Phys. Chem. C 2012, 116, 15058−15067. [26] Ory, S., Itzchak, F., Ehud, Y., Mech. J. Fluid. 2014, 753, 49–79. [27] Barchini, R., Saville, D. A., Langmuir 1996, 12, 1442–1445. [28] Clift, R., Grace, J. R., Weber, M. E., Bubbles, Drops, Particles, Academic Press, New York, 1978. [29] Griffith, R. M., Chem. Eng. Sci. 1962, 17, 1057–1070.
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[35] Marinova, K. G., Alargova, R. G., Denkov, N. D., Velev, O. D., Petsev, D. N., Ivanov, I. B., Borwankar, R. P., Langmuir 1996, 12, 2045–2051. [36] Delgado, A. V., Interfacial Electrokinetics and Electrophoresis. CRC Press, New York, 2001. [37] Linggen, K., James, K. B., Robert, J. H., Colloids Surf. B Biointerfaces 2003, 27, 11–21. [38] Jyh-Ping, H., Anca, N., J. Colloid Interface Sci. 2003, 259, 374–381.
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Jiachen Wuzhang1 Yongxin Song1 Runzhe Sun1 Xinxiang Pan1 Dongqing Li2 1 Department
of Marine Engineering, Dalian Maritime University, Dalian, P. R. China 2 Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, Canada
Received February 3, 2015 Revised May 11, 2015 Accepted June 4, 2015
Research Article
Electrophoretic mobility of oil droplets in electrolyte and surfactant solutions Electrophoretic mobility of oil droplets of micron sizes in PBS and ionic surfactant solutions was measured in this paper. The experimental results show that, in addition to the applied electric field, the speed and the direction of electrophoretic motion of oil droplets depend on the surfactant concentration and on if the droplet is in negatively charged SDS solutions or in positively charged hexadecyltrimethylammonium bromide (CTAB) solutions. The absolute value of the electrophoretic mobility increases with increased surfactant concentration before the surfactant concentration reaches to the CMC. It was also found that there are two vortices around the oil droplet under the applied electric field. The size of the vortices changes with the surfactant and with the electric field. The vortices around the droplet directly affect the drag of the flow field to the droplet motion and should be considered in the studies of electrophoretic mobility of oil droplets. The existence of the vortices will also influence the determination and the interpretation of the zeta potential of the oil droplets based on the measured mobility data. Keywords: Charge redistribution / Droplet electrophoresis / Electrophoretic mobility / Ionic surfactant / Vortex interaction DOI 10.1002/elps.201500062
1 Introduction Electrophoresis is one of the powerful analytical methods in many fields, such as petroleum industry, biochemistry, and biomedical engineering. For example, it can be used to characterize the surface electrokinetic properties of particles and cells without causing damage to the particles and cells [1]. The CE technology has been widely used for separation of biological molecules such as proteins [2]. Under an electric field, a charged particle in a bulk aqueous electrolyte solution will move relative to the surrounding liquid. Such motion is referred to as the electrophoresis. Electrophoresis is typically characterized by the particle velocity, ve p =
E εr εo p for a thin electric double layer
(1)
or by electrophoretic mobility (velocity per unit applied electric field), e p =
εr εo p ve p = , E
(2)
where p is the zeta potential of the particle; E is the applied electric field; εr εo is the dielectric constant of the liquid; and is the viscosity of the liquid. Equation (1) is usually referred to as the Smoluchowski equation. Electrophoretic mobility is an important parameter and can be used to calculate the surface charge and zeta potential of a solid particle
Correspondence: Professor Dongqing Li, Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON N2L3G1, Canada E-mail: [email protected]
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based on the electrokinetic theory and the Smoluchowski equation. Because of the importance of the electrophoretic mobility, extensive theoretical, and experimental studies have been carried out with respect to its theoretical interpretation and the measurement methods [3–10]. It should be noted, however, that the Smoluchowski equations such as Eqs. (1) and (2) are valid only for solid particles with a thin Electrical Double Layer (EDL) and low zeta potential. For droplet electrophoresis, many studies have also been reported [11–19] since the Quincke experiments [20]. Booth [12] was the first to theoretically study the electrophoresis of spherical fluid droplets in electrolyte solutions. He derived a general formula for the electrophoreitic mobility of bubbles and droplets, assuming a symmetrical charge distribution on the surface. The formula, however, disagrees with the experiments [21]. Taylor [22] measured the electrophoretic mobility of decalin droplets in aqueous media and calculated the zeta potential from the measured mobility by modifying the Smoluchowski equation with several parameters, such as ion cloud relaxation, surface conductivity, and droplet phase viscosity. They found that these parameters have little effects on the mobility. Later, Levine and O’Brien [16] developed a theory about the electrophoretic motion of a charged mercury drops in aqueous electrolyte solution. They found that the polarization effect can enhance the electrophoresis of the mercury drop. By extending the electrophoresis model for a solid spherical particle, Ohshima [13] showed that the fluid nature of the interphase boundary sharply differentiates drops from solids.
Colour Online: See the article online to view Figs. 1–8 in colour
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The model, however, is applicable only to drops that have a much higher conductivity than the supporting electrolyte. Baygents and Saville [17] computed the electrophoretic mobility as a function of the zeta potential and several other parameters for both conducting and nonconducting droplets. They found that the -potential alone is not sufficient to characterize the surface. However, their implicit assumption of the weak-field approximation is problematic for micron-size droplets [23]. Droplet electrophoresis was recently studied by V. Knecht et al. who found that the calculated electrophoretic mobility does not always reflect the net charge or electrokinetic potential of a suspended liquid droplet based on their molecular dynamics simulation results [24]. Huang et al. [25] theoretically investigated the electrophoretic motion of a liquid droplet in a cylindrical pore, taking account of the double layer polarization and the droplet viscosity effects. They found that the lower the viscosity of the droplet is, the greater the electrophoretic velocity is. Also, the polarization effect will slow down the droplet movement in general. Ory Schnitzer [26] developed a coarse-grained macroscale model for electrophoretic motion of a bubble in order to overcome the shortcomings of thin-double layer assumption. However, they neglected the adsorption of salt ions and adopted uniform surface-charge density assumption. Furthermore, oil droplet electrophoresis phenomena become more complicated when ionic surfactants are adsorbed at the oil-water interface. The adsorbed surfactants will change the EDL structure, alter lateral transport of ions behind the shear plane [27]. Researches on rising air bubble [28–31] and droplets [28, 29] in gravity or pressure driven flows showed that the surfactant molecules will be swept to the rear of the droplet and form a so-called “stagnant cap” due to the hydraulic drag force. Electrophoresis behavior of oil droplets in surfactant containing electrolyte solutions was also reported. Sarah A. Nespolo et al. [32] considered the hydrodynamic mobility effect when converting the measured electrophoretic mobility values to zeta potentials. In order to examine the extent to which the standard electrokinetic model is a good approximation, R. Barchini studied the electrokinetic properties of SDS-stabilized oil droplets of submicron size and derived zeta potential with O’Brien and White theory [33] but without considering the hydrodynamics effect. They found some challenging questions when applying the theory to highly charged colloidal particles. As discussed above, the majority of these studies focus on the influence of the electrokinetic or hydrodynamic properties of the interface on droplet mobility as well as the interpretation of the electrokinetic potential and the validity of the Smoluchowski equation [34]. In the literature, there are some data on the elelctrophoretic mobility of oil droplets. Barchini et al. studied the electrokinetic properties of surfactantstabilized silicon oil droplets (276576 nm in diameter) in SDS solution. They found that the magnitude of mobility is between 57 × 10−4 cm2 V−1 .s−1 [27]. Electrophoretic mobilities of 5.35.75 × 10−4 cm2 V−1 .s−1 for decane droplet in SDS (with varying concentrations) and 10−3 NaNO3 mixture solution were also reported [32]. Marinova et al. measured C 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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the electrophoretic mobility of xylene droplet as a function of pH at a fixed NaCl concentration. Specifically, the mobility is between 58 × 10−4 cm2 V−1 .s−1 for a varying 69 pH values [35]. It should be noted that most of the droplet diameters are in the submicron range. Submicron oil droplets are generally considered as hard spheres [36]. Currently, there is little data on mobility of micron-sized oil droplets. It should be realized that the surface charges or the adsorbed surfactants on a droplet surface are mobile, while the surface charges or the adsorbed surfactants on solid particle surface are immobile. This is a key difference between an oil droplet and a solid particle in electrophoresis. Will the mobile surface charges on an oil droplet influence the electrophoretic motion of the droplet under different electric fields? Will ionic surfactants absorbed at the oil droplet surface influence the electrophoretic mobility of an oil droplet? Will the mobile surface charges and the absorbed surfactants have any effects on the flow field around the droplet? Very little is known in these regards. In this paper, the electrophoretic mobility of oil droplets in PBS and ionic surfactant solutions were studied under different concentrations of ionic surfactants and different electric fields. The flow field around the droplet was also examined by using 1 m polystyrene tracing particles. It was found that two vortices near the droplet were formed. The observed smaller mobility under stronger electric field under the same surfactant concentration can be explained by the increasing effects of the vortices with the electric field. While forming circulating flows inside a droplet has been reported before, this paper demonstrates first time the vortices formed outside the droplets in both PBS and surfactant solutions. The finding of the vortices near a droplet can help to understand the complicate electrophoretic behavior of droplets. The effects of the vortices should be considered before zeta potential and surface charge can be calculated from the measured electrophoretic mobility.
2 Materials and methods 2.1 System setup and sample preparation Figure 1 shows the experimental system that includes a microfluidic chip, a DC power supply (CSI3003 × 3,Circuit Specialists,Mesa,AZ) and an inverted optical microscope image system (Ti-E, Nikon) with a progressive CCD camera (DSQi1Mc, Nikon). The experiments of electrophoretic motion of oil droplets were conducted in a microfluidic chip with a straight microchannel as shown in Fig. 1. The microfluidic chip was fabricated by bonding a PDMS plate with a glass substrate (25.66 × 75.47 × 1.07 mm, CITOGLAS, China) using a plasma cleaner (HARRICK PLASMA). The master for making the microchannel on the PDMS plate was fabricated by using a negative photo-resist (SU-8 2025, MicroChem Co., Newton, MA) on a silicon wafer substrate (4” N/PHOS, Montco Silicon Technology Inc., Spring City, PA). The channel is 190 m wide, 1.2 cm long, and 25 m in www.electrophoresis-journal.com
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General
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Figure 1. A schematic diagram of the experimental system.
height. There are two wells at the ends of the microchannel (not shown in Fig. 1). The wells (2 cm in diameter) are used as the solution reservoirs and for inserting electrodes to apply electric field along the channel. The oil droplets in surfactants solutions of different concentrations were obtained by mixing 10 L Soya-bean oil (Jin Longyu AE, Jinhai Food Industry Company, China) with 1.5 mL surfactant solutions. In this study, two ionic surfactants, SDS (⬎99% purity, Shanghai Bioengineering Company, China) and CTAB (⬎99% purity, Tianjing Damao Chemical Company, China), were used. To prepare the surfactant solutions, a certain amount of SDS or CTAB was added to the 7.5 mM sodium borate buffer solution (PBS). Afterwards, 10 L oil was added to the surfactant solution and was mixed for 23 min with a vortex hand mixer (Lab dancer, M7-15US12R-F, IKA Company, Germany). 2.2 Measurement of the mobility The electrokinetic movement of oil droplets was measured in the microfluidic chip placed on the observation stage of the microscope. To begin the experiments, the microfluidic chip was primed first with PBS buffer solution. Then 10 L oil sample solution was added into the inlet well. The liquid levels in the inlet and outlet wells were carefully balanced by adding a certain amount of the sample solution in the wells by using a digital micro-pipette. Afterwards, Pt electrodes were inserted in the wells and an electric field was applied to transport the oil droplets in the channel. In the meantime, the oil droplet motion was recorded by the CCD camera (DSQi1Mc, Nikon) of the inverted optical microscope imaging system (Ti-E, Nikon). The camera was operated in a video mode at a frame rate of 11.4 frames per second. The reading error in determining the cell position is about ±2 pixels that correspond to actual dimension of ±5.4 m. The microscope imaging system was also equipped with specific software that can determine the size of the droplets. In order to keep the C 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
same conditions for measuring the mobility, we only used the oil droplets moving near the central line of the channel to calculate the mobility. In this way, the same conditions, including the same distance away from the channel all, were kept. To minimize the influence of static hydraulic pressure on the movement of the oil droplets, two approaches were adopted. First, relatively larger wells were used to minimize the back pressure driven flow generated by the EOF. Secondly, only the droplet movement of the first 1020 s after applying the electric field was recorded and used for calculating the electrophoresis mobility. Under each set of conditions (e.g. surfactant concentration and electric field), the velocity of a droplet of a certain size was measured and then its electrophoresis mobility was calculated. For each size, at least five droplets of the same size were measured; each data point reported in the figures of this paper is the average value of these results.
2.3 Observation of the flow field around a droplet The flow field around an oil droplet was visualized by using 1 m tracing particles (Fluka, Shanghai, China). In practice, it is very difficult to observe and visualize the flow field around a moving droplet with tracing particles, especially when the droplet is very small and moves very fast. In this study, therefore, we studied the flow field around a relative larger droplet that was fixed in a position in the middle of the channel. Fixing the droplet position in a microfluidic channel was achieved by the following approach: an oil droplet was placed on the bottom surface of the PDMS microfluidic channel (80 m in height, open to the air and without plasma treatment) without the solution first; then the solution (with 1 m tracing particles) was added into the channel with a pipette. Afterwards, a glass slide treated by a plasma cleaner (HARRICK PLASMA) is covered on the microfluidic channel. Finally, www.electrophoresis-journal.com
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Figure 2. Dependence of oil droplet velocity on surfactant concentration under an electric field of 41.7 V/cm for droplets with different diameters (39 m), (A) in SDS solution, (B) in CTAB solution. (V > 0: moving toward positivie side of the applied electric field; V < 0: moving toward negative side of the applied electric field).
different electric fields were applied and the trajectories of the trace particles around an oil droplet were recorded by the CCD camera (DS-Qi1Mc, Nikon) of the inverted optical microscope imaging system (Ti-E, Nikon).
3 Results and discussion
Electrophoresis 2015, 36, 2489–2497
of the negative surface charges on the droplets. This is indicated by the positive velocity value ( 70 m/s) shown in both Fig. 2A and B (0 mM). For the droplets in SDS (an anionic surfactant) solutions, as shown in Fig. 2A, the droplets still moved toward the positive side of the applied electric field and the velocity increases with the increase in SDS concentration. Beyond 4 mM concentration, the velocity approaches an essentially constant value. This is likely due to saturated adsorption of SDS at the channel walls and on the droplet surfaces. Realizing that the net motion of an oil droplet in this case is determined by both the EOF of the solution in the microchannel (toward the negative side of the electric field) and the electrophoresis of the oil droplet (toward the positive side of the electric field), the final constant velocity indicates the balance of these two driving forces. As regards to the oil droplets in CTAB (a cationic surfactant) solution (Fig. 2B), in contrast, the droplets sharply reversed the moving direction once CTAB was added (from about 70 m/s to −20 m/s). This can be understood by the fact that adsorption of CTAB molecules carrying positive charges on the channel walls and the droplet surface will reverse both the direction of EOF and the direction of droplet electrophoresis. Beyond the CMC, the adsorption of CTAB surfactant molecules at the channel walls and at the droplet surfaces reaches saturation; the opposite motions of EOF in the channel and droplet electrophoresis are balanced; thus the velocity of the droplets will not change with the increase of CTAB concentration as clearly shown in Fig. 2B. From Fig. 2, it can also be noticed that there is no obvious difference in the velocity of the droplets of different diameters. This means that the electrokinetic movement of the oil droplets is not size dependent. For the following sections, therefore, we will analyze the elelctrokinetic movement only for droplets of approximately 3 m in diameter. Figure 3 shows the dependence of droplet velocity on the applied electric field with different surfactant concentrations for 3 m oil droplets. It is clear that the droplet velocity increases with the electric field. In Fig. 3A, the droplet velocity in 6 mM SDS solution increases by 75.88% when the electric field is increased from 25.8 to 41.7 V/cm. For CTAB solution, as shown in Fig. 3B, the velocity in 0.5 mM CTAB solution increases about 36.3% when the electric field is increased from 25.8 to 41.7 V/cm. Because the movement of a droplet is the combination of the EOF of the bulk solution and the electrophoresis of the droplet, and thus the electrophoretic velocity of the droplets is given by:
3.1 Electrophoretic mobility
Vep = V − VEOF .
Figure 2 shows the dependence of oil droplet velocity on surfactant concentration under an electric field of 41.7 V/cm for droplets with different diameters (39 m). In this figure, zero surfactant concentration means that the oil droplets were in pure PBS solution without any surfactants. When the oil droplets were in PBS buffer solution, the droplets moved toward the positive side of the applied electric field because
Where Vep is the electrophoresis velocity of the droplet, V is the measured droplet velocity, and VEOF is the electroosmotic flow of the bulk solution in the channel. Theoretically, Vep and VEOF can be calculated by:
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(3)
Vep = ep · E
(4)
VEOF = EOF · E .
(5)
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120 Mobility (10-4cm2V-1.s-1)
10
V (μm.s-1)
100 80 60 40 0
2 4 6 Concentration (mM)
9 8 7 6 5
8
0
A
70
2
4 6 Concentration (mM)
8
A
6.0
25.8V/cm 41.7V/cm
25.8V/cm 41.7V/cm
4.0
Mobility (10-4cm2V-1.s-1)
50 V (μm.s-1)
25.8 V/cm 41.7V/cm
11
25.8V/cm 41.7V/cm
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30 10 -10
2.0 0.0
-2.0
-30 0.0
0.5
1.0 1.5 2.0 Concentration (mM)
-4.0
2.5
B
0.0
Figure 3. Dependence of droplet velocity on the applied electric field in different surfactant concentrations for 3 m oil droplets. (A) In SDS solution and (B) in CTAB solution (V > 0: moving toward positive side of the applied electric field; V < 0: moving toward negative side of the applied electric field).
Where ep and EOF are the electrophoresis mobility and the electroosmotic mobility, respectively. Combining the above equations yields: ep =
V − EOF . E
(6)
Table 1 summarizes the electroosmotic mobility of SDS and CTAB solutions in PDMS channel as reported in the published papers [30, 31]. Using the values in Table 1, experimentally measured droplet velocity data (such as shown in Fig. 2), and using Eq. (6), the electrophoretic mobility of the oil droplets can be obtained and is shown in Fig. 4. Figure 4 shows the dependence of the electrophoretic mobility on surfactant concentration. Under the two electric fields used in the experiments, the electrophoretic mobility for the droplets in PBS solution is about 5.3 [(m/s).(V/cm)], which is larger comparing with the mobility of a nanometer-sized silicon oil droplet (276 nm in diameter) in water/SDS solution as reported by Barchini [32]. C 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
0.5
1.0 1.5 Concentration (mM)
2.0
2.5
B
Figure 4. Dependence of the electrophoretic mobility on surfactant concentration with different applied electric fields. (A) In SDS solution and (B) in CTAB solution.
From Fig. 4, it is obvious that the absolute value of mobility increases with the increasing surfactant concentration. This increased mobility is due to the adsorption of surfactant at the oil droplet surface and hence the increased surface charge density. The adsorption of surfactants at the oil droplet surface will reach maximum when the surfactant concentration reaches to the CMC. Correspondingly, the mobility will become constant beyond the CMC. It should be noted that under the same surfactant concentration, however, the mobility is smaller in an electric field of 41.7 V/cm than that in a 25.8 V/cm electric field. For example, the mobility is increased by about 4.5% when the electric field is reduced from 41.7 V/cm to 25.8 V/cm for the oil droplets in 6 mM SDS solution. For oil droplet electrophoretic mobility, it has been generally accepted that the EDL polarization effect will slow down the droplet motion somewhat. In the cases of this study, the observed smaller electrophoretic mobility under larger electric field and the same surfactant concentration cannot be explained by the polarization effect for the following reasons. www.electrophoresis-journal.com
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Table 1. Electroosmotic mobility of SDS and CTAB solutions in PDMS channels as reported in reference papers [30, 31] ( > 0: flowing in the opposite direction to the electric field; < 0: flowing in the same direction with the electric field). (A) In SDS solution. (B) In CTAB solution
(A) Concentration (mM) Mobility (, 10−4 cm2 /V·s) (B) Concentration (mM) Mobility (, 10−4 cm2 /V·s)
0 –3.70
1 –6.30
2 –6.60
3 –6.80
4 –6.85
6 –7.00
0 –3.70
0.5 2.72
1.0 3.11
1.5 3.26
2.0 3.43
2.5 3.50
8 –7.10
Firstly, the zeta potential of the oil droplets in PBS is estimated to be within −50 to −70 mV [35, 37, 38]. Theoretically, the characteristic thickness of EDL (1/) is 3 nm for a 10−2 M NaCl solution. Since the NaCl concentration in PBS solution is larger than 10−2 M, 1/ is less than 3 nm in this study. Accordingly, a will be larger than 1000 for a 3 m oil droplet in PBS solution (a is the particle radius). Therefore, the EDL polarization effect on-mobility can be ignored. Secondly, even if the polarization effect exists, the counter electric field induced by the swept counterions can be considered as the same under the same surfactant concentration, due to the very large a. Furthermore, the measured mobility may be related to the observed vortices around the droplets. Because the mobile surface charges at droplet surface can be redistributed under the influence of the externally applied electric field, the nonuniform distribution of the surface charges may result in nonuniform EOF around the droplets, and hence affect the electrophoretic mobility of the droplets. Therefore, the dependence of electrophoretic behavior of oil droplets on electric field may arise from the redistribution of the mobile surface charges on the liquid–liquid interfaces as discussed below. 3.2 Vortices near the droplet Figures 5–7 shows the flow field around an oil droplet in different solutions (PBS, SDS, and CTAB solutions) under the two different electric fields. The pictures were obtained by superposing a series of consecutive images of the moving trace particles around the droplet. These pictures clearly show that there are two vortices around the oil droplet in all of the solutions. For comparison, solid (polystyrene) particles were tested under the same conditions; there were no vortices around the solid particles. As observed under the microscope, for the droplet in PBS and SDS solutions, the directions of the vortex on the lower side and the vortex on the upside are clockwise and counterclockwise, respectively. In contrast, the vortex directions are reversed for the droplet in CTAB solution. This corresponds well to the EOF flow directions at the oil-water interface in PBS, SDS, and CTAB solutions. In addition, there are differences in the size of vortices under different electric fields in surfactant solutions. The size of the vortices also increases slightly with the increase of the electric field.
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Figure 5. Vortices around an oil droplet in the PBS solution under different electric fields, (A) E1 = 25.8 V/cm, (B) E2 = 41.7 V/cm.
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Figure 6. Vortices around an oil droplet in SDS solution (5 mM) under different electric fields, (A) E1 = 25.8 V/cm, (B) E2 = 41.7 V/cm.
A possible explanation of the formation of the vortices is the redistribution of the mobile surface charges on the droplet surface, as illustrated in Fig. 8. Without the externally applied electric field, the surface charges of the oil droplets in an electrolyte or surfactant solution generally will be evenly distributed. When an electric field is applied, the mobile surface charges will be attracted to one side of the droplet due to the electrostatic attraction force. As a result, one section of the droplet surface has more surface charges (A1 ) and the rest of droplet surface has no or less surface charges (A2 ). For the flow field around the droplet, consequently, there are two boundary conditions: slip velocity (EOF velocity) boundary on surface A1 and no slip velocity for surface A2 due to the absence of surface charges. The EOF from the surface A1 will hit the stationary liquid on the surface A2 , is forced to move away from the surface A2 and results in a flow circulation, i.e. a vortex near the droplet. The EOF velocity will increase with C 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Figure 7. Vortices around an oil droplet in CTAB solution (0.5 mM) under different electric fields, (A) E1 = 25.8 V/cm, (B) E2 = 41.7 V/cm.
E
EOF
A1
A2
Figure 8. A schematic diagram of the redistribution of surface charges and vortex formation under different electric fields (E2 > E1 ).
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the increasing electric field and surface charge density, consequently, the vortices will also be size dependent on the electric field and surface charge density (surfactant concentration in this study). For the droplets in PBS and SDS solutions, the surface charges are negative and thus one clockwise vortex on the lower side and one counterclockwise vortex on the upside will be formed. However, for droplets in the positively charged surfactant CTAB solutions, if the CTAB molecules make the surface charge to be positive, the EOF flow direction on the droplet surface will be reversed under the same electric field direction. As a result, the directions of the vortices will also be reversed. This was confirmed by the observation under the microscope. A direct consequence of the vortices on the two sides of the droplet is to increase the flow resistance and hence reduce the droplet motion. As discussed above, the formation of the vortices may be caused by the redistribution of the mobile surface charges on the droplet surface. Increase of the applied electric field will reduce the surface area A1 that has concentrated surface charges, and increase the surface area A2 that has no or less surface charges. Therefore, the vortices around the droplet will increase with the applied electric field. Stronger vortices will slow down the motion of the droplets; consequently, the measured mobility will decrease with the increasing electric field. This is in agreement with the experimental results of the smaller mobility under a higher electric field, as is shown in Fig. 4.
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tions under the externally applied electric field. The finding of the vortices near a droplet can help to understand the electrophoretic behavior of droplets. Furthermore, the effects of the vortices should be considered and analyzed before zeta potential and surface charge can be calculated from the measured electrophoretic mobility values of oil droplets in electrolyte and surfactant solutions. The authors wish to thank the financial support of the Fundamental Research Funds for the Central Universities (3132014336), Liaoning Science Foundation (2014025020), and Liaoning Excellent Talent Supporting Plan (LJQ2014050) from China to Y. S., the Natural Sciences and Engineering Research Council of Canada through a research grant to D. L., the support from Dalian Maritime University to D. L., and the financial support from the University 111 project of China under Grant No. B08046 is greatly appreciated. The authors have declared no conflict of interest.
5 References [1] Maxwell, P. H., Wiesener, M. S., Chang, G. W., Clifford, S. C., Vaux, E. C., Cockman, M. E., Ratcliffe, P. J., Nature 1999, 399, 271–275. [2] Lumpkin, O. J., Dejardin, P., Zimm, B. H., Biopolymers 1985, 24, 1573–1593. [3] Hunter, R. J., Zeta Potential in Colloid Science, Academic Press Inc., London 1981.
4 Concluding remarks
[4] Russel, W. B., Saville, D. A., Schowalter, W. R., Colloidal Dispersions, Cambridge University Press, UK 1989.
Electrophoretic mobility of oil droplets of micron sizes in PBS and ionic surfactant solutions was measured in this paper. The electrophoretic mobility was obtained by using the conventional electrophoresis theory and by measuring the moving velocity of the droplet by a microscope image analysis system. The experimental results show that the ionic surfactants absorbed at the oil droplet surface can increase the electrophoretic mobility of an oil droplet before the surfactant concentration reaches to the CMC. Under the same surfactant concentration, the mobility, however, is smaller under stronger electric field. Unlike a solid particle, it was found that there are two vortices around the droplets. The formation of the vortices may be caused by the redistribution of the mobile surface charges on the droplet surfaces under the influence of the externally applied electric field. The vortices on the sides of the droplets will generate additional flow resistance to the motion of the droplets and hence affect the electrophoretic mobility of the droplets. As the size of the vortices increases with the electric field, the effects of the vortices on the electrophoretic mobility of the droplets will also increase with the electric field. While circulating flows inside a droplet have already been demonstrated, this paper firstly demonstrates two vortices formed around droplets in both PBS and surfactant solu-
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