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Electrophoresis 2015, 36, 731–736
Qian Liang Cunlu Zhao Chun Yang School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore
Received August 19, 2014 Revised November 9, 2014 Accepted November 16, 2014
Research Article
Enhancement of electrophoretic mobility of microparticles near a solid wall— Experimental verification Although the existing theories have predicted enhancement of electrophoretic mobility of microparticles near a solid wall, the relevant experimental studies are rare. This is mainly due to difficulties in experimentally controlling and measuring particle-wall separations under dynamic electrophoretic conditions. This paper reports an experimental verification of the enhancement of electrophoretic mobility of a microparticle moving near the wall of a microchannel. This is achieved by balancing dielectrophoretic and lift forces against gravitational force acting on the microparticle so as to control the gap of particle-wall separation. A simple experimental setup is configured and a fabrication method is developed to measure such separation gap. The experiments are conducted for various particle sizes under different electric field strengths. Our experimental results are compared against the available theoretical predictions in the literature. Keywords: Electrophoretic mobility enhancement / Microchannel wall induced dielectrophoresis / Wall effect on electrophoresis DOI 10.1002/elps.201400405
Additional supporting information may be found in the online version of this article at the publisher’s web-site
1 Introduction In recent years electrokinetic phenomena have been widely used in microfluidic analytical systems for pumping analytes and manipulating (e.g., transport, sorting and separating) micro/nanoparticles and cells. It is known that when a dielectric particle with thin electric double layer (EDL) is electrophoretically transported in an unbounded domain filled with an electrolyte solution, the particle electrophoretic mobility is given by the well-known Smoluchowski equation [1]: = −ε p / , (Here ε , p , and are the dielectric permittivity of solution, the zeta potential of the particle, and the dynamic viscosity of the solution, respectively). Such Smoluchowski equation is no longer valid when the electrophoretic transport of particles is in a bounded domain, for instance, in the vicinity of a solid channel wall. The presence of such solid wall near the particle can cause strong local disturbance of both electric and hydrodynamic flow fields which in turn will alter electrophoretic motion of the particle. In the past decades, a number of stud-
Correspondence: Professor Chun Yang, School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 E-mail: [email protected]
Abbreviations: EDL, electric double layer; EP, electrophoresis
C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ies have examined the wall effects of single or two walls on the electrophoretic transport of micron-sized particles in microchannels. These studies revealed that the electrophoretic mobility strongly depends on particle-wall separation. Specifically, for relatively large particle-wall separations (e.g., the same order of particle diameter), the electrophoretic mobility of particles is decreased by the hydrodynamic viscous retardation [2–5]. For relatively small particle-wall separations (i.e., much smaller than particle diameter), however, the opposite trend is true because of the dominant enhancement of electric stress within the narrow gap between a particle and the wall [2, 5–7]. Although known theoretically for a long time, these interesting predictions have not been quantitatively verified by any experiment mainly due to the difficulties in controlling and measuring particle-wall separations. To our best knowledge, the only relevant experiments by Xuan et al. [7, 8] demonstrated the viscous retardation and nearwall enhancement of electrophoretic transport respectively, but the particle-wall separation necessary for a quantitative verification was unknown in their experiments. In most microfluidic applications, particles tend to sink onto the bottom wall of microfluidic channel due to gravity. With an external electric field applied in parallel to the channel
Colour Online: See the article online to view Figs. 1–3 and 5 in colour.
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wall, the particle experiences a lateral dielectrophoretic (DEP) force that results from the formation of a nonuniform electric field in the particle-wall separation gap [9–12]. In the absence of particle electrophoretic motion and EOF, Young et al. [10] theoretically analyzed such wall-induced DEP force by integrating the Maxwell stress over the particle surface, and they revealed that the DEP force increases with decreasing the particle-wall separation gap. Similarly, without any flow and particle motion Lo and Lei [11] presented a specific microscopy configuration to experimentally confirm the existence of such wall-induced DEP force by balancing it against the buoyancy in an inclined channel. In the presence of electrokinetic flow, the experiments were shown for the DEP force-induced lateral migration of particles in a straight channel [12, 13]. Recently, Kazoe and Yoda [14] reported an experimental study of the effect of external electric field on interfacial dynamics of colloidal particles in a microchannel by using total internal reflection fluorescent microscopy, and they found that there exists a wall-induced force to repel particles away from the channel wall during the electrokinetic transport of submicron polystyrene and silica particles. This is resulted from a combined effect of the aforementioned wall-induced DEP force and the EOF-induced lift force [15]. Based on the theoretical predictions and experimental observations reported in literature, the magnitude of the wall-induced DEP force acting on a particle depends on applied electric field strength and particle-wall separation. Thus, through adjusting such DEP force against the gravitational force, one can accurately modulate the particle-wall separation gap at a microscale level by varying the external electric field. However, such manipulation of particle-wall separations is usually achieved in the vertical direction (i.e., along the channel height direction). This introduces a problem of how to measure the particle-wall separation because most microfluidic measurements relying on conventional microscopy techniques only can provide the information in horizontal plane. More importantly, the measurement of such small particle-wall gap has to be carried out under dynamic conditions in which the particles are in electrokinetic motion within a microchannel. Therefore, it is challenging to determine the micron and/or submicron separation gap between a channel wall and a moving particle. The widely used confocal microscopy [16–19], and total internal reflection microscopy [14, 20–23], though can perform vertical measurements, are much expensive and also suffer from their respective limitations. For example, the confocal microscopy usually captures individual images of order about O(1) s in time scale by reconstructing serial horizontal sections and thus is not suitable for measuring particles in motion [21, 24]. The total internal reflection microscopy only can detect a vertical distance less than 1 m, which is much smaller than the major range of our experimental work reported here. Moreover, all these two techniques work for fluorescent particles only. Motivated by Lo and Lei’s experimental configuration [11], here we report the measurement of the near-wall electrophoretic mobility of microspheres with controlled particlewall separation by adjusting electric field which in turn can C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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generate the channel wall induced DEP force and EOSinduced lift force against gravity force. To achieve such measurement, we also propose a method of fabricating a PDMS microchannel with smooth and flat walls, and then present a simple experimental setup with a conventional optical microscope rotated 90o . This allows for simultaneously measuring the particle electrophoretic mobility and the separation between a particle and the fabricated smooth PDMS wall. Importantly, the dynamic behavior of the particle near-wall electrophoretic motion can be directly observed and assessed by using our experimental setup. The experimental results are used to validate the existing theoretical models of near-wall enhancement of electrophoretic mobility.
2 Materials and methods 2.1 Principle of measuring particle-wall separation gap Consider electrophoretic transport of a charged dielectric particle moving close to the bottom wall of a charged dielectric microchannel filled with an electrolyte solution. In our experiment, the particle motion is observed on the vertical plane (x–z plane) as shown in Fig. 1, where a, b, d, and h denote the particle radius, the distance from the particle center to the bottom wall, the channel height and the particle-wall separation, respectively. Under a DC electric field imposed along the x-coordinate direction, the particle moves horizontally under
Figure 1. A 2D schematic illustration of electrophoretic transport of a microsphere near the bottom wall of a microchannel filled with an electrolyte solution. An electric field E is applied horizontally along the x-coordinate direction, and the lines denote the applied electric field. Along the horizontal x direction the particle is subject to an electrophoresis (EP) force and a hydrodynamic force due to EOF of electrolyte solution. In the sketch, a is the particle radius, h is the particle-wall separation gap and b = a+h. Along the vertical z direction, the particle experiences three forces, including a gravitational force (toward down), a wall-induced dielectrophoretic (DEP) force (toward up) and an EOF-induced lift force (toward up). For an given DC electrical voltage, the two DEP and lift forces can exactly balance the gravitational force such that the particle reaches a vertical equilibrium position with a certain particle-wall separation gap, h while the particle moves horizontally (all dimensions and arrows are not to scale).
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the combined effects of an electrophoresis (EP) force and a hydrodynamic force due to an EOF of electrolyte solution. Meanwhile, along the vertical direction, the particle experiences three forces: first, the gravitational force FG causes the particle to settle down; second, the early described wallinduced DEP force, force FDEP pushes the particle to move up; third, the presence of EOF, which acts like wall sliding, can produce a lubrication pressure within the thin gap between the particle and the wall to lift the particle away from the wall [15]. Such force is termed as lift force, FLift thereafter. Physically, the wall-induced DEP force is scaled to the square of the gradient of electric field, and thus it becomes stronger with increasing the electric field strength. However, the dependence of the EOF-induced life force on electric field is related to two competing effects. On the one hand, the EOF is linearily proportional to the applied DC field strength, suggesting that a larger electric field produces a bigger life force. On the other hand, a larger electric field, which exerts a bigger DEP force, can push the particle away from the wall, resulting in a larger particle-wall gap and hence a smaller life force. Nonetheless, given an applied DC voltage, there exists an equilibrium particle-wall separation where the two upwards DEP and life forces can counterbalance the downwards gravity force. Under such particle-wall separation, the particle electrophoretic motion can be observed and studied. With increasing applied DC voltage, a new balance among the gravity force and the DEP and lift forces will be reestablished, giving rise to a larger particle-wall separation.
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technique, the side wall of SU8 master mould usually is not smooth. Hence, walls of the PDMS channel peeled off from the SU8 mould are rough, which will affect the accuracy of particle-wall separation measurements. To resolve this issue, we developed a protocol for assembling the microfluidic chip to obtain smooth PDMS surfaces which were used as the bottom channel wall in our experiment (see Fig. 2). First, a PDMS slab with a microchannel pattern was fabricated using the standard soft lithography, and then fluid reservoirs were punched at two ends of the channel. Another PDMS slab with smooth surface was also prepared (Fig. 2A). Later the PDMS slab with microchannel pattern was bonded with the smooth surface of another PDMS slab after oxygen plasma treatment (Fig. 2B). Subsequently, the bonded PDMS chip was carefully cut into a cuboid. In order to improve the surface roughness from cutting, the rough surface was placed on a glass slide coated with a thin film of liquid PDMS. After having been baked in an oven at 85°C for 1 h, the liquid PDMS was solidified and incorporated into the rough surface (Fig. 2C). Then the microfluidic chip was peeled off from the glass slide and hence the surface of good quality was obtained. We smoothed all rough surfaces by repeating this procedure. Finally, the microfluidic chip was turned 90o with respect to Fig. 2B and bounded with a glass slide to form the final version of the microfluidic chip. To facilitate the measurement of vertical particle-wall separation, the entire microfluidic chip was turned 90o with respect to Fig. 2C, and observation was performed through an objective lens placed beside the microchip, as illustrated in Fig. 2D.
2.2 Fabrication of microfluidic chip A rectangular PDMS microchannel with dimensions of 2 cm (long) × 250 m (high) × 100 m (wide) for studying particle electrophoretic motion was fabricated using the standard soft lithography. Due to the limitation of the photolithography
2.3 Experimental setup Experimental setup used in the present work is illustrated schematically in Fig. 3. A microscope (Zeiss, Germany)
Figure 2. Schematic illustration of microfluidic chip assembly. (A) The PDMS slab with a microchannel pattern and the smooth PDMS slab are prepared separately. (B) The PDMS slab having microchannel pattern is bonded with the smooth PDMS slab. (C) The bonded two PDMS slabs are turned 90o with respect to (B) and then the side surface is smoothed. (D) The microfluidic chip is placed on the object stage of a microscope. As a result, the smooth PDMS–PDMS interface is employed as the bottom channel wall during our experiment, and the particle-wall separation can be readily observed from the side of the microchip through an objective lens attached to the microscope.
C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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jective lens. The particle-wall separations are measured directly from the captured images with a resolution of 696 × 520 pixels. Particle velocities are then determined by dividing the particle travel distance over the corresponding time interval.
3 Results and discussion
Figure 3. Schematic illustration of the experimental setup. The zoom shows how the microchip is placed and which direction that the measurement is taken.
is laterally turned 90o so that its object stage becomes perpendicular to the table surface. Together with the early assembled microchip, the separation between a moving particle and the smooth bottom wall of the channel can be directly determined with a side-mounted CCD camera. A DC power supply (Stanford Research, USA) is employed to set up a driving electric field. A function generator (Agilent, USA) with an amplifier (EPA-102, Piezo System, USA) is used to output an AC electric field for a short period prior to each test. The motion of particles is recorded as a series of digital images which are later processed and analyzed to obtain the electrophoretic mobility and corresponding particle-wall separations.
2.4 Materials and procedure Polystyrene particles (Duke Scientific, USA) with diameters of 15, 30, and 40 m are used in this work. All particles are suspended in 1 mM sodium bicarbonate (SigmaAldrich, Singapore) buffer solution. A pair of platinum electrodes is placed in each reservoir of the microchannel to generate the driving electric field throughout the microchannel. Before applying electric field, the particles suspended in the channel tend to settle down on the bottom wall because of gravity. The liquid height in two reservoirs is carefully balanced to eliminate possible particle motion due to liquid height difference induced flow. In addition, to avoid the effects of two side walls on particle motion, an AC voltage of 300 V with a frequency of 1 kHz is applied for at least 1 min prior to each measurement such that the particles can be pushed to the center region of the channel by means of DEP forces induced by side walls. Once a required DC voltage is applied, the EP drives the particle toward the anode. Simultaneously, both the bottom wall induced DEP and EOF-induced lift forces repel the particle away from the channel wall. The electrophoretic motion of particles above the bottom wall of microchannel under a DC voltage is observed and recorded with the camera at a speed of 15 frames/s under a 10× ob C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
In this study, we neglect the EDL and van der Waals interactions between particle and bottom wall. The exclusion of these two interactions is based on the fact that the EDL thickness is around 10 nm for 1 mM sodium bicarbonate solution and the van der Waals interaction takes effect only when the separation is within order of 100 nm or smaller. These two length scales are much smaller than the particle-wall separation gaps obtained in our experiment. The snapshot images of electrophoretic motion of 40, 30, and 15 m particles in the microchannel at various values of equilibrium particle-wall separation are presented in Fig. 4A– C, respectively. A typical movie showing the electrophoretic transport of a particle is provided in the supporting material. Due to the limitation of our camera speed, the particle images tend to be a little bit blur due to relatively fast electrophoretic velocities, as shown in the cases of small a/b (corresponding to large particle-wall separations). Since a stronger electric field is required to maintain a larger particle-wall separation gap, higher electrophoretic velocities can be expected for larger particle-wall separations. However, in terms of electrophoretic mobility (the ratio of electrophoretic velocity to electric field strength), it will be shown later that a large particle-wall separation would lead to a lower electrophoretic mobility. Figure 5 depicts the variation of the electrophoretic mobility with nondimensional particle-wall separation, a/b for particles of three different sizes. In the figure, the electrophoretic mobility () of a given particle is normalized by its corresponding r which is the electrophoretic mobility of the particle at the particle-wall separation of a/b ࣈ 0.2. By doing so, the effect of bottom channel wall on particle EP is captured, while the possible effect of side channel walls on particle EP can be eliminated. It is readily identified from the plot that at small particle-wall separations (i.e., 0.85 ⬍ a/b ⬍ 0.95), the measured electrophoretic mobilities are increased significantly. However, for relatively large particle-wall separations (i.e., 0.4 ⬍ a/b ⬍ 0.7), the variation of electrophoretic mobilities is found insignificant, and apparently the electrophoretic mobility becomes less dependent on the particle-wall separation. It should be noted that due to the constrain of the present experimental method and setup, the narrowest particle-wall separation (i.e., the largest a/b) measured in this study is about 5% of the particle radius, corresponding to about a/b = 0.95 for 40 m particles (as shown in Fig. 4). Also limited by image processing, the accuracy of determining the narrow particle-wall gap reduces noticeably with decreasing particle size. For example, the highest value of a/b obtained in the experiment for 30 and 15 m particles are approximately www.electrophoresis-journal.com
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Figure 5. Variation of the normalized particle electrophoretic mobility with nondimensional particle-wall separation, a/b. Note that, a is the particle radius, and b = a + h with h being the particle-wall separation gap. The electrophoretic mobility () of a given particle obtained in the experiment is normalized by its corresponding r which is the electrophoretic mobility of the particle at the particle-wall separation of a/b ࣈ 0.2 approximately.
Figure 4. Snapshot images of the electrophoretic motion of particles at various equilibrial particle-wall separations for (A) 40 m, (B) 30 m, and (C) 15 m particles in a PDMS microchannel. The corresponding applied DC voltages are (A): 550 V, 350 V, 300 V, 250 V, 200 V, 150 V, 70 V, and 30 V; (B): 600 V, 550 V, 450 V, 350 V, 200 V, 100 V, 65 V, and 35 V; (C): 550 V, 450 V, 350 V, 250 V, 200 V, 150 V, 100 V, and 70 V. The blur particle images for the cases of small a/b are attributed to the limited speed of our camera because of relatively fast velocity of particle electrophoretic motion. Note that, a is the particle radius, h is the particle-wall separation gap, and b = a + h.
0.92 and 0.86, respectively. Although further increasing particle size can improve the measurement accuracy and hence can reach higher values of a/b, the motion of larger particles in such 3D microfluidic channel is also subject to the possible effect of side and top walls. Since the present experimental study focuses on examining a single wall effect on the electrophoretic motion of particles near the bottom wall only, particles larger than 40 m are not used in our experiments. As a result, our experimental results did not show the wall effect on particle electrophoretic mobility at extremely small particle-wall gaps, that is, 0.95 ⬍ a/b ⬍ 1. C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
In the literature, a number of theoretical studies have reported the near-wall electrophoretic mobility enhancement of particles in microchannels. Here we compare our experimental results with the theoretical predictions reported by Keh and Anderson [3] and Unni et al. [6]. The former analyzed the near-wall EP of a microsphere parallel to a dielectric plane by using a successive reflection method, and reported an analytical expression for the nearwall electrophoretic velocity of a microsphere as U/Us = 31 (a/b)6 + O((a/b)8 )] , where U [1 − 161 (a/b)3 + 18 (a/b)5 − 256 and Us are particle electrophoretic velocities near the solid wall and in unbounded domains, respectively. The latter studied the electrokinetic transport of a microsphere in a parallel-plane channel via using the Fourier transform wall disturbances, and obtained complex closed-form solutions in terms of infinite series. Then with the boundary collocation method, the unknown coefficients in infinite series are determined numerically. It is seen from Fig. 5 that our experimental results agree well with the predictions in [6]. However, at small particle-wall separations with a/b larger than 0.7, the theoretical predictions by Keh and Anderson show different wall effects on the particle electrophoretic mobility from our experimental observation. This could be due to the fact that the successive reflection method used in Keh and Anderson’s analysis ignores the terms of higher orders than (a/b)6 in the asymptotic formula and thus the enhancement of the wall effect at small particlewall gaps is significantly underestimated. Moreover, Keh and Anderson’s analysis does not consider the particle rotation near the solid wall, and this can be another reason contributing to the discrepancies between the theory and the experiment. Physically, the wall effects on EP are attributed to two competing mechanisms [2]: on the one hand, the narrow gap between a nonconducting particle and the electrically www.electrophoresis-journal.com
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insulating channel wall leads to the enhancement of local electric field because of the conservation of electric current, thereby increasing the local electric field and thus particle velocity; on the other hand, the hydrodynamic interaction between the solid channel wall and the particle retards the fluid flow which in turn slows down the particle motion. The former effect dominates over the latter when the particle is very close to the bottom wall, resulting in increment of electrophoretic mobility due to the dominant enhancement of electric stress within such narrow gap. It should be noted that the viscous retardation effect because of channel wall, however, is hardly to be seen in our present experiment. This could be due to two reasons: first, for the experimental conditions reported in the present investigation, the particle-wall separations are in a range of 0.4 ⬍ a/b ⬍ 0.95. Within such range, the viscous retardation solely due to the bottom channel wall is too weak to be observed. Second, the data presented in Fig. 5 are normalized with a reference electrophoretic mobility r that is the measured electrophoretic mobility of particle transport at a/b ࣈ 0.2, and thus the viscous retardation effect due to the side channel walls has been minimized after the data normalization.
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The authors gratefully acknowledge Tier 1 Academic Research Grant from the Ministry of Education of Singapore to C. Y. and Nanyang Technological University Ph.D. Scholarship to Q.L. The authors have declared no conflict of interest.
5 References [1] Masliyah, J. H., Subir, B., Electrokinetic and colloid transport phenomena, Wiley-Interscience 2006. [2] Anderson, J. L., Annu. Rev. Fluid Mech. 1989, 21, 61–99 [3] Keh, H. J., Anderson, J. L., J. Fluid Mech. 1985, 153, 417–439. [4] Keh, H. J., Chen, S. B., J. Fluid Mech. 1988, 194, 377–390. [5] Yariv, E., Brenner, H., J. Fluid Mech. 2003, 484, 85–111. [6] Unni, H. N., Keh, H. J., Yang, C., Eletrophoresis 2007, 28, 658–664. [7] Xuan, X., Raghibizadeh, S., Li, D., J. Colloid Interface Sci. 2006, 296, 743–748. [8] Xuan, X., Ye, C., Li, D., J. Colloid Interface Sci. 2005, 289, 286–290. [9] Kang, K. H., Kang, Y., Xuan, X., Li, D., Electrophoresis 2006, 27, 694–702.
4 Concluding remarks
[10] Young, E. W. K., Li, D., Langmuir 2005, 21, 12037–12046. [11] Lo, Y. J., Lei, U., Appl. Phys. Lett. 2010, 97, 093702.
In summary, we have presented the first experimental study for quantitative validation of the enhancement of electrophoretic mobility near a solid channel wall. Such validation was realized by using a simple and inexpensive experimental setup and a novel microchip assembly, which allows for simultaneously determining the electrophoretic mobility and particle-wall separation between the channel wall and a moving particle. Our work demonstrated that the enhancement of electrophoretic mobility can be tunable by electrically controlling particle-wall separations via balancing the wall-induced DEP and EOF-induced lift forces against the gravitational force. The experimental results were further compared with two existing analytical models. It was found that our experiments are favorably agreeable with Unni’s model [6] but show a deviation from Keh and Anderson’s model at small particle-wall separations with a/b larger than 0.7. The present work is of practical use since the electrophoretic transport of particles in microfluidic devices is frequently bounded by microchannel structures. Additionally, the reported experimental method can be used for study of hydrodynamic interactions of moving particles and biological cells under well-controlled microenvironments as well as other relevant phenomena involving the control and measurement of particle-wall separations.
C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
[12] Liang, L., Ai, Y., Zhu, J., Qian, S., Xuan, X., J. Colloid Interface Sci. 2010, 347, 142–146. [13] Liang, L., Qian, S., Xuan, X., J. Colloid Interface Sci. 2010, 350, 377–379. [14] Kazoe, Y., Yoda, M., Langmuir 2011, 27, 11481–11488. [15] Bike, S.G., Prieve, D.C. J. Colloid Interface Sci. 1995175 422–434. [16] Dinsmore, A. D., Weeks, E. R., Prasad, V., Levitt, A. C., Weitz, D. A., Appl. Optics 2001, 40, 4152–4159. [17] Semwogerere, D., Weeks, E. R., in: Bowlin, G. L., Wnek, G. (Eds.), Encyclopedia of biomaterials and biomedical engineering, Informa Healthcare London 2005, pp. 1–10. [18] Holmes, D., Morgan, H., Green, N. G., Biosens. Bioelectron. 2006, 21, 1621–1630. [19] Slomka, N., Gefen, A., J. Biomech. 2010, 43, 1806–1816. [20] Fu, L. M., Wang, J. H., Luo, W. B., Lin, C. H., Microfluid. Nanofluid. 2009, 6, 499–507. [21] Joseph, P., Tabeling, P., Phys. Rev. E 2005, 71, 035303 [22] Sadr, R., Yoda, M., Gnanaprakasam, P., Conlisk, A., Appl. Phys. Lett. 2006, 89, 044103. [23] Zettner, C. M., Yoda, M., Exp. Fluids 2003, 34, 115–121. [24] Joseph, P., Cottin-Bizonne, C., Benot, J. M., Ybert, C., Journet, C., Tabeling, P., Bocquet, L., Phys. Rev. Lett. 2006, 97, 156104.
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Electrophoresis 2015, 36, 731–736
Qian Liang Cunlu Zhao Chun Yang School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore
Received August 19, 2014 Revised November 9, 2014 Accepted November 16, 2014
Research Article
Enhancement of electrophoretic mobility of microparticles near a solid wall— Experimental verification Although the existing theories have predicted enhancement of electrophoretic mobility of microparticles near a solid wall, the relevant experimental studies are rare. This is mainly due to difficulties in experimentally controlling and measuring particle-wall separations under dynamic electrophoretic conditions. This paper reports an experimental verification of the enhancement of electrophoretic mobility of a microparticle moving near the wall of a microchannel. This is achieved by balancing dielectrophoretic and lift forces against gravitational force acting on the microparticle so as to control the gap of particle-wall separation. A simple experimental setup is configured and a fabrication method is developed to measure such separation gap. The experiments are conducted for various particle sizes under different electric field strengths. Our experimental results are compared against the available theoretical predictions in the literature. Keywords: Electrophoretic mobility enhancement / Microchannel wall induced dielectrophoresis / Wall effect on electrophoresis DOI 10.1002/elps.201400405
Additional supporting information may be found in the online version of this article at the publisher’s web-site
1 Introduction In recent years electrokinetic phenomena have been widely used in microfluidic analytical systems for pumping analytes and manipulating (e.g., transport, sorting and separating) micro/nanoparticles and cells. It is known that when a dielectric particle with thin electric double layer (EDL) is electrophoretically transported in an unbounded domain filled with an electrolyte solution, the particle electrophoretic mobility is given by the well-known Smoluchowski equation [1]: = −ε p / , (Here ε , p , and are the dielectric permittivity of solution, the zeta potential of the particle, and the dynamic viscosity of the solution, respectively). Such Smoluchowski equation is no longer valid when the electrophoretic transport of particles is in a bounded domain, for instance, in the vicinity of a solid channel wall. The presence of such solid wall near the particle can cause strong local disturbance of both electric and hydrodynamic flow fields which in turn will alter electrophoretic motion of the particle. In the past decades, a number of stud-
Correspondence: Professor Chun Yang, School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 E-mail: [email protected]
Abbreviations: EDL, electric double layer; EP, electrophoresis
C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ies have examined the wall effects of single or two walls on the electrophoretic transport of micron-sized particles in microchannels. These studies revealed that the electrophoretic mobility strongly depends on particle-wall separation. Specifically, for relatively large particle-wall separations (e.g., the same order of particle diameter), the electrophoretic mobility of particles is decreased by the hydrodynamic viscous retardation [2–5]. For relatively small particle-wall separations (i.e., much smaller than particle diameter), however, the opposite trend is true because of the dominant enhancement of electric stress within the narrow gap between a particle and the wall [2, 5–7]. Although known theoretically for a long time, these interesting predictions have not been quantitatively verified by any experiment mainly due to the difficulties in controlling and measuring particle-wall separations. To our best knowledge, the only relevant experiments by Xuan et al. [7, 8] demonstrated the viscous retardation and nearwall enhancement of electrophoretic transport respectively, but the particle-wall separation necessary for a quantitative verification was unknown in their experiments. In most microfluidic applications, particles tend to sink onto the bottom wall of microfluidic channel due to gravity. With an external electric field applied in parallel to the channel
Colour Online: See the article online to view Figs. 1–3 and 5 in colour.
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wall, the particle experiences a lateral dielectrophoretic (DEP) force that results from the formation of a nonuniform electric field in the particle-wall separation gap [9–12]. In the absence of particle electrophoretic motion and EOF, Young et al. [10] theoretically analyzed such wall-induced DEP force by integrating the Maxwell stress over the particle surface, and they revealed that the DEP force increases with decreasing the particle-wall separation gap. Similarly, without any flow and particle motion Lo and Lei [11] presented a specific microscopy configuration to experimentally confirm the existence of such wall-induced DEP force by balancing it against the buoyancy in an inclined channel. In the presence of electrokinetic flow, the experiments were shown for the DEP force-induced lateral migration of particles in a straight channel [12, 13]. Recently, Kazoe and Yoda [14] reported an experimental study of the effect of external electric field on interfacial dynamics of colloidal particles in a microchannel by using total internal reflection fluorescent microscopy, and they found that there exists a wall-induced force to repel particles away from the channel wall during the electrokinetic transport of submicron polystyrene and silica particles. This is resulted from a combined effect of the aforementioned wall-induced DEP force and the EOF-induced lift force [15]. Based on the theoretical predictions and experimental observations reported in literature, the magnitude of the wall-induced DEP force acting on a particle depends on applied electric field strength and particle-wall separation. Thus, through adjusting such DEP force against the gravitational force, one can accurately modulate the particle-wall separation gap at a microscale level by varying the external electric field. However, such manipulation of particle-wall separations is usually achieved in the vertical direction (i.e., along the channel height direction). This introduces a problem of how to measure the particle-wall separation because most microfluidic measurements relying on conventional microscopy techniques only can provide the information in horizontal plane. More importantly, the measurement of such small particle-wall gap has to be carried out under dynamic conditions in which the particles are in electrokinetic motion within a microchannel. Therefore, it is challenging to determine the micron and/or submicron separation gap between a channel wall and a moving particle. The widely used confocal microscopy [16–19], and total internal reflection microscopy [14, 20–23], though can perform vertical measurements, are much expensive and also suffer from their respective limitations. For example, the confocal microscopy usually captures individual images of order about O(1) s in time scale by reconstructing serial horizontal sections and thus is not suitable for measuring particles in motion [21, 24]. The total internal reflection microscopy only can detect a vertical distance less than 1 m, which is much smaller than the major range of our experimental work reported here. Moreover, all these two techniques work for fluorescent particles only. Motivated by Lo and Lei’s experimental configuration [11], here we report the measurement of the near-wall electrophoretic mobility of microspheres with controlled particlewall separation by adjusting electric field which in turn can C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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generate the channel wall induced DEP force and EOSinduced lift force against gravity force. To achieve such measurement, we also propose a method of fabricating a PDMS microchannel with smooth and flat walls, and then present a simple experimental setup with a conventional optical microscope rotated 90o . This allows for simultaneously measuring the particle electrophoretic mobility and the separation between a particle and the fabricated smooth PDMS wall. Importantly, the dynamic behavior of the particle near-wall electrophoretic motion can be directly observed and assessed by using our experimental setup. The experimental results are used to validate the existing theoretical models of near-wall enhancement of electrophoretic mobility.
2 Materials and methods 2.1 Principle of measuring particle-wall separation gap Consider electrophoretic transport of a charged dielectric particle moving close to the bottom wall of a charged dielectric microchannel filled with an electrolyte solution. In our experiment, the particle motion is observed on the vertical plane (x–z plane) as shown in Fig. 1, where a, b, d, and h denote the particle radius, the distance from the particle center to the bottom wall, the channel height and the particle-wall separation, respectively. Under a DC electric field imposed along the x-coordinate direction, the particle moves horizontally under
Figure 1. A 2D schematic illustration of electrophoretic transport of a microsphere near the bottom wall of a microchannel filled with an electrolyte solution. An electric field E is applied horizontally along the x-coordinate direction, and the lines denote the applied electric field. Along the horizontal x direction the particle is subject to an electrophoresis (EP) force and a hydrodynamic force due to EOF of electrolyte solution. In the sketch, a is the particle radius, h is the particle-wall separation gap and b = a+h. Along the vertical z direction, the particle experiences three forces, including a gravitational force (toward down), a wall-induced dielectrophoretic (DEP) force (toward up) and an EOF-induced lift force (toward up). For an given DC electrical voltage, the two DEP and lift forces can exactly balance the gravitational force such that the particle reaches a vertical equilibrium position with a certain particle-wall separation gap, h while the particle moves horizontally (all dimensions and arrows are not to scale).
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the combined effects of an electrophoresis (EP) force and a hydrodynamic force due to an EOF of electrolyte solution. Meanwhile, along the vertical direction, the particle experiences three forces: first, the gravitational force FG causes the particle to settle down; second, the early described wallinduced DEP force, force FDEP pushes the particle to move up; third, the presence of EOF, which acts like wall sliding, can produce a lubrication pressure within the thin gap between the particle and the wall to lift the particle away from the wall [15]. Such force is termed as lift force, FLift thereafter. Physically, the wall-induced DEP force is scaled to the square of the gradient of electric field, and thus it becomes stronger with increasing the electric field strength. However, the dependence of the EOF-induced life force on electric field is related to two competing effects. On the one hand, the EOF is linearily proportional to the applied DC field strength, suggesting that a larger electric field produces a bigger life force. On the other hand, a larger electric field, which exerts a bigger DEP force, can push the particle away from the wall, resulting in a larger particle-wall gap and hence a smaller life force. Nonetheless, given an applied DC voltage, there exists an equilibrium particle-wall separation where the two upwards DEP and life forces can counterbalance the downwards gravity force. Under such particle-wall separation, the particle electrophoretic motion can be observed and studied. With increasing applied DC voltage, a new balance among the gravity force and the DEP and lift forces will be reestablished, giving rise to a larger particle-wall separation.
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technique, the side wall of SU8 master mould usually is not smooth. Hence, walls of the PDMS channel peeled off from the SU8 mould are rough, which will affect the accuracy of particle-wall separation measurements. To resolve this issue, we developed a protocol for assembling the microfluidic chip to obtain smooth PDMS surfaces which were used as the bottom channel wall in our experiment (see Fig. 2). First, a PDMS slab with a microchannel pattern was fabricated using the standard soft lithography, and then fluid reservoirs were punched at two ends of the channel. Another PDMS slab with smooth surface was also prepared (Fig. 2A). Later the PDMS slab with microchannel pattern was bonded with the smooth surface of another PDMS slab after oxygen plasma treatment (Fig. 2B). Subsequently, the bonded PDMS chip was carefully cut into a cuboid. In order to improve the surface roughness from cutting, the rough surface was placed on a glass slide coated with a thin film of liquid PDMS. After having been baked in an oven at 85°C for 1 h, the liquid PDMS was solidified and incorporated into the rough surface (Fig. 2C). Then the microfluidic chip was peeled off from the glass slide and hence the surface of good quality was obtained. We smoothed all rough surfaces by repeating this procedure. Finally, the microfluidic chip was turned 90o with respect to Fig. 2B and bounded with a glass slide to form the final version of the microfluidic chip. To facilitate the measurement of vertical particle-wall separation, the entire microfluidic chip was turned 90o with respect to Fig. 2C, and observation was performed through an objective lens placed beside the microchip, as illustrated in Fig. 2D.
2.2 Fabrication of microfluidic chip A rectangular PDMS microchannel with dimensions of 2 cm (long) × 250 m (high) × 100 m (wide) for studying particle electrophoretic motion was fabricated using the standard soft lithography. Due to the limitation of the photolithography
2.3 Experimental setup Experimental setup used in the present work is illustrated schematically in Fig. 3. A microscope (Zeiss, Germany)
Figure 2. Schematic illustration of microfluidic chip assembly. (A) The PDMS slab with a microchannel pattern and the smooth PDMS slab are prepared separately. (B) The PDMS slab having microchannel pattern is bonded with the smooth PDMS slab. (C) The bonded two PDMS slabs are turned 90o with respect to (B) and then the side surface is smoothed. (D) The microfluidic chip is placed on the object stage of a microscope. As a result, the smooth PDMS–PDMS interface is employed as the bottom channel wall during our experiment, and the particle-wall separation can be readily observed from the side of the microchip through an objective lens attached to the microscope.
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jective lens. The particle-wall separations are measured directly from the captured images with a resolution of 696 × 520 pixels. Particle velocities are then determined by dividing the particle travel distance over the corresponding time interval.
3 Results and discussion
Figure 3. Schematic illustration of the experimental setup. The zoom shows how the microchip is placed and which direction that the measurement is taken.
is laterally turned 90o so that its object stage becomes perpendicular to the table surface. Together with the early assembled microchip, the separation between a moving particle and the smooth bottom wall of the channel can be directly determined with a side-mounted CCD camera. A DC power supply (Stanford Research, USA) is employed to set up a driving electric field. A function generator (Agilent, USA) with an amplifier (EPA-102, Piezo System, USA) is used to output an AC electric field for a short period prior to each test. The motion of particles is recorded as a series of digital images which are later processed and analyzed to obtain the electrophoretic mobility and corresponding particle-wall separations.
2.4 Materials and procedure Polystyrene particles (Duke Scientific, USA) with diameters of 15, 30, and 40 m are used in this work. All particles are suspended in 1 mM sodium bicarbonate (SigmaAldrich, Singapore) buffer solution. A pair of platinum electrodes is placed in each reservoir of the microchannel to generate the driving electric field throughout the microchannel. Before applying electric field, the particles suspended in the channel tend to settle down on the bottom wall because of gravity. The liquid height in two reservoirs is carefully balanced to eliminate possible particle motion due to liquid height difference induced flow. In addition, to avoid the effects of two side walls on particle motion, an AC voltage of 300 V with a frequency of 1 kHz is applied for at least 1 min prior to each measurement such that the particles can be pushed to the center region of the channel by means of DEP forces induced by side walls. Once a required DC voltage is applied, the EP drives the particle toward the anode. Simultaneously, both the bottom wall induced DEP and EOF-induced lift forces repel the particle away from the channel wall. The electrophoretic motion of particles above the bottom wall of microchannel under a DC voltage is observed and recorded with the camera at a speed of 15 frames/s under a 10× ob C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
In this study, we neglect the EDL and van der Waals interactions between particle and bottom wall. The exclusion of these two interactions is based on the fact that the EDL thickness is around 10 nm for 1 mM sodium bicarbonate solution and the van der Waals interaction takes effect only when the separation is within order of 100 nm or smaller. These two length scales are much smaller than the particle-wall separation gaps obtained in our experiment. The snapshot images of electrophoretic motion of 40, 30, and 15 m particles in the microchannel at various values of equilibrium particle-wall separation are presented in Fig. 4A– C, respectively. A typical movie showing the electrophoretic transport of a particle is provided in the supporting material. Due to the limitation of our camera speed, the particle images tend to be a little bit blur due to relatively fast electrophoretic velocities, as shown in the cases of small a/b (corresponding to large particle-wall separations). Since a stronger electric field is required to maintain a larger particle-wall separation gap, higher electrophoretic velocities can be expected for larger particle-wall separations. However, in terms of electrophoretic mobility (the ratio of electrophoretic velocity to electric field strength), it will be shown later that a large particle-wall separation would lead to a lower electrophoretic mobility. Figure 5 depicts the variation of the electrophoretic mobility with nondimensional particle-wall separation, a/b for particles of three different sizes. In the figure, the electrophoretic mobility () of a given particle is normalized by its corresponding r which is the electrophoretic mobility of the particle at the particle-wall separation of a/b ࣈ 0.2. By doing so, the effect of bottom channel wall on particle EP is captured, while the possible effect of side channel walls on particle EP can be eliminated. It is readily identified from the plot that at small particle-wall separations (i.e., 0.85 ⬍ a/b ⬍ 0.95), the measured electrophoretic mobilities are increased significantly. However, for relatively large particle-wall separations (i.e., 0.4 ⬍ a/b ⬍ 0.7), the variation of electrophoretic mobilities is found insignificant, and apparently the electrophoretic mobility becomes less dependent on the particle-wall separation. It should be noted that due to the constrain of the present experimental method and setup, the narrowest particle-wall separation (i.e., the largest a/b) measured in this study is about 5% of the particle radius, corresponding to about a/b = 0.95 for 40 m particles (as shown in Fig. 4). Also limited by image processing, the accuracy of determining the narrow particle-wall gap reduces noticeably with decreasing particle size. For example, the highest value of a/b obtained in the experiment for 30 and 15 m particles are approximately www.electrophoresis-journal.com
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Figure 5. Variation of the normalized particle electrophoretic mobility with nondimensional particle-wall separation, a/b. Note that, a is the particle radius, and b = a + h with h being the particle-wall separation gap. The electrophoretic mobility () of a given particle obtained in the experiment is normalized by its corresponding r which is the electrophoretic mobility of the particle at the particle-wall separation of a/b ࣈ 0.2 approximately.
Figure 4. Snapshot images of the electrophoretic motion of particles at various equilibrial particle-wall separations for (A) 40 m, (B) 30 m, and (C) 15 m particles in a PDMS microchannel. The corresponding applied DC voltages are (A): 550 V, 350 V, 300 V, 250 V, 200 V, 150 V, 70 V, and 30 V; (B): 600 V, 550 V, 450 V, 350 V, 200 V, 100 V, 65 V, and 35 V; (C): 550 V, 450 V, 350 V, 250 V, 200 V, 150 V, 100 V, and 70 V. The blur particle images for the cases of small a/b are attributed to the limited speed of our camera because of relatively fast velocity of particle electrophoretic motion. Note that, a is the particle radius, h is the particle-wall separation gap, and b = a + h.
0.92 and 0.86, respectively. Although further increasing particle size can improve the measurement accuracy and hence can reach higher values of a/b, the motion of larger particles in such 3D microfluidic channel is also subject to the possible effect of side and top walls. Since the present experimental study focuses on examining a single wall effect on the electrophoretic motion of particles near the bottom wall only, particles larger than 40 m are not used in our experiments. As a result, our experimental results did not show the wall effect on particle electrophoretic mobility at extremely small particle-wall gaps, that is, 0.95 ⬍ a/b ⬍ 1. C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
In the literature, a number of theoretical studies have reported the near-wall electrophoretic mobility enhancement of particles in microchannels. Here we compare our experimental results with the theoretical predictions reported by Keh and Anderson [3] and Unni et al. [6]. The former analyzed the near-wall EP of a microsphere parallel to a dielectric plane by using a successive reflection method, and reported an analytical expression for the nearwall electrophoretic velocity of a microsphere as U/Us = 31 (a/b)6 + O((a/b)8 )] , where U [1 − 161 (a/b)3 + 18 (a/b)5 − 256 and Us are particle electrophoretic velocities near the solid wall and in unbounded domains, respectively. The latter studied the electrokinetic transport of a microsphere in a parallel-plane channel via using the Fourier transform wall disturbances, and obtained complex closed-form solutions in terms of infinite series. Then with the boundary collocation method, the unknown coefficients in infinite series are determined numerically. It is seen from Fig. 5 that our experimental results agree well with the predictions in [6]. However, at small particle-wall separations with a/b larger than 0.7, the theoretical predictions by Keh and Anderson show different wall effects on the particle electrophoretic mobility from our experimental observation. This could be due to the fact that the successive reflection method used in Keh and Anderson’s analysis ignores the terms of higher orders than (a/b)6 in the asymptotic formula and thus the enhancement of the wall effect at small particlewall gaps is significantly underestimated. Moreover, Keh and Anderson’s analysis does not consider the particle rotation near the solid wall, and this can be another reason contributing to the discrepancies between the theory and the experiment. Physically, the wall effects on EP are attributed to two competing mechanisms [2]: on the one hand, the narrow gap between a nonconducting particle and the electrically www.electrophoresis-journal.com
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insulating channel wall leads to the enhancement of local electric field because of the conservation of electric current, thereby increasing the local electric field and thus particle velocity; on the other hand, the hydrodynamic interaction between the solid channel wall and the particle retards the fluid flow which in turn slows down the particle motion. The former effect dominates over the latter when the particle is very close to the bottom wall, resulting in increment of electrophoretic mobility due to the dominant enhancement of electric stress within such narrow gap. It should be noted that the viscous retardation effect because of channel wall, however, is hardly to be seen in our present experiment. This could be due to two reasons: first, for the experimental conditions reported in the present investigation, the particle-wall separations are in a range of 0.4 ⬍ a/b ⬍ 0.95. Within such range, the viscous retardation solely due to the bottom channel wall is too weak to be observed. Second, the data presented in Fig. 5 are normalized with a reference electrophoretic mobility r that is the measured electrophoretic mobility of particle transport at a/b ࣈ 0.2, and thus the viscous retardation effect due to the side channel walls has been minimized after the data normalization.
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The authors gratefully acknowledge Tier 1 Academic Research Grant from the Ministry of Education of Singapore to C. Y. and Nanyang Technological University Ph.D. Scholarship to Q.L. The authors have declared no conflict of interest.
5 References [1] Masliyah, J. H., Subir, B., Electrokinetic and colloid transport phenomena, Wiley-Interscience 2006. [2] Anderson, J. L., Annu. Rev. Fluid Mech. 1989, 21, 61–99 [3] Keh, H. J., Anderson, J. L., J. Fluid Mech. 1985, 153, 417–439. [4] Keh, H. J., Chen, S. B., J. Fluid Mech. 1988, 194, 377–390. [5] Yariv, E., Brenner, H., J. Fluid Mech. 2003, 484, 85–111. [6] Unni, H. N., Keh, H. J., Yang, C., Eletrophoresis 2007, 28, 658–664. [7] Xuan, X., Raghibizadeh, S., Li, D., J. Colloid Interface Sci. 2006, 296, 743–748. [8] Xuan, X., Ye, C., Li, D., J. Colloid Interface Sci. 2005, 289, 286–290. [9] Kang, K. H., Kang, Y., Xuan, X., Li, D., Electrophoresis 2006, 27, 694–702.
4 Concluding remarks
[10] Young, E. W. K., Li, D., Langmuir 2005, 21, 12037–12046. [11] Lo, Y. J., Lei, U., Appl. Phys. Lett. 2010, 97, 093702.
In summary, we have presented the first experimental study for quantitative validation of the enhancement of electrophoretic mobility near a solid channel wall. Such validation was realized by using a simple and inexpensive experimental setup and a novel microchip assembly, which allows for simultaneously determining the electrophoretic mobility and particle-wall separation between the channel wall and a moving particle. Our work demonstrated that the enhancement of electrophoretic mobility can be tunable by electrically controlling particle-wall separations via balancing the wall-induced DEP and EOF-induced lift forces against the gravitational force. The experimental results were further compared with two existing analytical models. It was found that our experiments are favorably agreeable with Unni’s model [6] but show a deviation from Keh and Anderson’s model at small particle-wall separations with a/b larger than 0.7. The present work is of practical use since the electrophoretic transport of particles in microfluidic devices is frequently bounded by microchannel structures. Additionally, the reported experimental method can be used for study of hydrodynamic interactions of moving particles and biological cells under well-controlled microenvironments as well as other relevant phenomena involving the control and measurement of particle-wall separations.
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[12] Liang, L., Ai, Y., Zhu, J., Qian, S., Xuan, X., J. Colloid Interface Sci. 2010, 347, 142–146. [13] Liang, L., Qian, S., Xuan, X., J. Colloid Interface Sci. 2010, 350, 377–379. [14] Kazoe, Y., Yoda, M., Langmuir 2011, 27, 11481–11488. [15] Bike, S.G., Prieve, D.C. J. Colloid Interface Sci. 1995175 422–434. [16] Dinsmore, A. D., Weeks, E. R., Prasad, V., Levitt, A. C., Weitz, D. A., Appl. Optics 2001, 40, 4152–4159. [17] Semwogerere, D., Weeks, E. R., in: Bowlin, G. L., Wnek, G. (Eds.), Encyclopedia of biomaterials and biomedical engineering, Informa Healthcare London 2005, pp. 1–10. [18] Holmes, D., Morgan, H., Green, N. G., Biosens. Bioelectron. 2006, 21, 1621–1630. [19] Slomka, N., Gefen, A., J. Biomech. 2010, 43, 1806–1816. [20] Fu, L. M., Wang, J. H., Luo, W. B., Lin, C. H., Microfluid. Nanofluid. 2009, 6, 499–507. [21] Joseph, P., Tabeling, P., Phys. Rev. E 2005, 71, 035303 [22] Sadr, R., Yoda, M., Gnanaprakasam, P., Conlisk, A., Appl. Phys. Lett. 2006, 89, 044103. [23] Zettner, C. M., Yoda, M., Exp. Fluids 2003, 34, 115–121. [24] Joseph, P., Cottin-Bizonne, C., Benot, J. M., Ybert, C., Journet, C., Tabeling, P., Bocquet, L., Phys. Rev. Lett. 2006, 97, 156104.
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