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Dielectrophoretic Trapping of Particles at the Three-Phase Contact Line Anil Kumar,† Boris Khusid,‡ and Andreas Acrivos*,† The LeVich Institute, The City College of New York, 140th Street and ConVent AVenue, New York, New York 10031, and New Jersey Institute of Technology, UniVersity Heights, Newark, New Jersey 07102
Dielectrophoresis of suspended polarizable particles is generated by destabilizing a flat interface between two fluids with a spatially uniform ac field. The strong field gradients that are created near the three-phase contact lines of the electrically formed fluid patterns cause the particles to accumulate there and to build a sharp and distinct boundary between regions enriched in and depleted of particles. This straightforward technique does not require the fabrication of complicated electric devices for the dielectrophoretic manipulation and separation of particles. 1. Introduction The electric force, F, exerted by a spatially nonuniform electric field E on a particle immersed in a fluid includes two terms: F ) QE + (P‚∇)E, where Q is the net particle charge and P is the particle dipole moment. The first term in this equation is the well-known electrophoretic force, which causes a charged particle subjected to a direct-current (dc) field to travel along the electric lines, whereas the other term is referred to as the dielectrophoretic force.1 Because the field-induced dipole moment of the particle is proportional to the field strength, the dielectrophoretic force appears, in turn, to be proportional to the square of the applied field. Under the action of an alternating-current (ac) electric field, for which the field strength averaged over the period of the field oscillation vanishes, the timeaverage electrophoretic force also vanishes, whereas the dielectrophoretic force attains a nonzero time-average value, given, for a sphere, by the expression1-4 Fdep ) 3/20fVpRe(β)∇Erms2, where Vp is the particle volume, Erms is the root-mean-square (rms) of the ac field strength, 0 is the vacuum permittivity, f is the dielectric constant of the liquid, and Re(β) is the real part of the relative particle polarization β (a complex value). Re(β) depends on the mismatch between the complex dielectric permittivities of the particle, p* ) ′p - i′′p, and of the fluid, f* ) ′f - i′′f, both taken at the frequency of the applied ac field. In particular, the magnitude and even the sign of Re(β) can be changed by varying the field frequency.3,4 Thus, depending on the sign of Re(β), Fdep moves the particle either toward (positive dielectrophoresis) or away from (negative dielectrophoresis) regions of high field strength. Among a variety of available methods for the manipulation of minute particles in a fluid, dielectrophoresis, which employs ac fields, is currently becoming one of the primary techniques in microdevices because the application of an ac field, at a sufficiently high frequency, suppresses undesirable electrolytic effects as well as electroconvection in the fluid, reduces Joule heating, and employs forces that depend on the relative particle polarizability and are insensitive to the particle charge.2-4 We have also demonstrated recently5,6 that the presence of interparticle interactions can dramatically affect the suspension behavior. As a result, the spatial arrangement of the particles driven by the ac dielectrophoresis forms a sharp and distinct * To whom correspondence should be addressed. E-mail: acrivos@ sci.ccny.cuny.edu. Tel.: (212) 650-8159. Fax: (212) 650-6835. † The City College of New York. ‡ New Jersey Institute of Technology.
boundary between regions enriched in and depleted of particles. This phenomenon involving the formation of a particle concentration front driven by interparticle electric and hydrodynamic interactions suggests the possibility of devising a new method for strongly concentrating particles in focused regions of dielectrophoretic devices. The standard way of generating ac dielectrophoresis is to create an electric field gradient by suitably arranging metallic electrodes in a channel connected to an ac voltage source.1-7 Another possibility is to place electrodes outside the channel and use a constriction of the channel8 or an arrangement of insulating posts across the channel cross section9 to produce a spatially nonuniform field. In this article, we show that a spatially nonuniform field can also be produced by applying a spatially uniform ac field across initially flat interfaces between a suspension and an immiscible fluid, as well as between a suspension and air, which, because of the amplification of electrohydrodynamic disturbances, are reorganized into a regular pattern. In turn, the strong field gradient created near the three-phase contact lines of this pattern causes the suspended polarizable particles to accumulate there and to form a sharp and distinct boundary between regions enriched in and depleted of particles. 2. Experimental Setup and Materials The experimental setup is shown in Figure 1a. A cylindrical cell having insulating walls (cavity diameter ) 1.5 in.) is placed between two horizontal transparent glass electrodes (interelectrode gap L ) 2.3 mm). An ac voltage of rms amplitude 4 kV and frequency 2 kHz is applied to the top electrode, while the bottom electrode is grounded. At this frequency, the undesirable effects of electroconvection, electrolysis, and electrophoresis were found to be insignificant. A 1% (v/v) suspension was prepared by dispersing neutrally buoyant polyalphaolefin spheres (AVEKA, MN, particle size ) 87 µm, particle density ) 0.92 g/cm3) in Mazola corn oil (density ) 0.92 g/cm3, viscosity ) 59.7 cP, and dielectric constant ) 2.87). The particle and corn-oil densities were precisely matched at 23 °C, thereby eliminating any gravitational segregation of the suspension over the experimental time scales. The real part of the relative polarization of polyalphaolefin particles in corn oil, Re(β), equals -0.15 over the frequency range 0.1-3.5 kHz,6 which indicates that the particles should exhibit negative dielectrophoresis in our experiments. Silicone oil (Aldrich, Catalog No. 146153-500G, dielectric constant ) 2.02, density ) 0.963 g/cm3) was chosen as the fluid immiscible with corn oil.
10.1021/ie051151j CCC: $33.50 © 2006 American Chemical Society Published on Web 03/11/2006
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Figure 1. Experimental setup: (a) schematic, (b) initial arrangement of the fluid layers in the interelectrode gap.
Figure 2. Patterns formed in multiphase fluid systems in the 2.3-mm gap following the application of a spatially uniform rms field of 1.7 kV/mm, 2 kHz. The photographs were taken in a plane parallel to the electrodes. The particles are seen as white spots and the particle-free domains as black. (a) Corn oil-silicone oil: Silicone oil columns spanning the interelectrode gap appear as round objects surrounded by the corn oil. (b,c) 1% (v/v) suspension in corn oil-silicone oil: A silicone oil column appears as a black domain on left-hand side in b and in the central region in c surrounded by the suspension; the ring of particles (white) has accumulated near the contact line of the silicone oil, the corn oil, and the bottom grounded electrode. The arrow in c indicates the boundary of the silicone oil column on the upper electrode. (d) 1% (v/v) suspension in corn oil-air: Air columns appear as round objects surrounded by the suspension; the rings of particles (white) have accumulated near the contact lines of the corn oil, air, and upper energized electrode.
3. Experimental Results We conducted three types of experiments. First, the cavity was filled partially with a horizontal layer of silicone oil, and a layer of lighter corn oil was subsequently spread on top of it to fill the interelectrode gap completely (Figure 1b). The force exerted by a strong electric field applied across the flat interface between two fluids having different electrical properties is known10-13 to destabilize this interface, resulting in the growth of disturbances with wavelengths sufficiently long for the electric force to overcome the capillary pressure generated by curvature. Under the conditions of our experiments, this electrohydrodynamic instability rearranged the initially horizontal layer of silicone oil into a set of columns spanning the interelectrode gap and surrounded by the corn oil. These columns appear as a set of round objects when viewed in the plane of the electrodes (i.e., along the direction of the applied field) in the photograph shown in Figure 2a. In another experiment, the corn oil was replaced by a cornoil-based 1% (v/v) suspension of polyalphaolefin spheres. The photographs presented in Figure 2b,c show the rearrangement
of the silicone oil and the particles in the plane of the electrodes following the application of an ac field, with the particles appearing as white spots and the particle-free domains being black. As was the case in the experiments with the pure fluids just described, the application of an ac field created conical columns of silicone oil bridging the electrodes and surrounded by the suspension. Such a silicone oil column appears as a black domain located on the left-hand side of the photograph in Figure 2b and in the center region of the photograph in Figure 2c. As can be seen clearly in Figure 2b,c, the field-driven pattern formation was accompanied by the migration of the particles toward the bottom of the columns where they built distinct twoto three-particle-wide rings (seen as white) surrounding the columns, with each ring being located near the three-phase contact line of the silicone oil, the corn oil, and the bottom grounded electrode (Figure 2c). We also observed a continuous circulation of particles that had not been trapped near the columns. Specifically, such particles traveled from the bulk region toward the column surface in the radial direction; then downward along the column to the three-phase contact line on
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the bottom; and then back to the bulk, again in the radial direction. This particle motion was caused most likely by the fluid circulation that is generated by the tangential electric force at the corn oil-silicone oil interface because both fluids are slightly conducting.14 We also performed experiments by partially filling the interelectrode gap with a horizontal layer of the corn-oil-based 1% (v/v) suspension. In this case, the application of an ac field to the interface between the suspension and the air (dielectric constant 1) caused the formation of air columns spanning the gap and surrounded by the suspension. These columns appear as a set of round objects when viewed in the plane of the electrodes in the photograph shown in Figure 2d, and just as in the photographs in Figure 2b,c, the particles are seen in Figure 2d as white spots and the particle-free domains as black. As can be seen in Figure 2d, the pattern formation was also accompanied by the appearance of distinct rings of particles (seen as white) around the columns, but now these rings were located near the three-phase contact line of the corn oil, the air, and the upper energized electrode. Notice that these rings are wider than those formed in the experiments with silicone oil (Figure 2c) because of the larger mismatch in the electric properties of the corn oil and air as contrasted to those of the corn oil and silicone oil. 4. Conclusions The experimental observations that we have presented demonstrate that the pattern formed in a multiphase fluid system by the growth of electrohydrodynamic interface instabilities following the application of a spatially uniform electric field can be used for the dielectrophoretic manipulation and separation of particles. This technique is straightforward and does not require the fabrication of complicated electric devices for technological applications. Further analysis is needed, however, to quantify the field-driven particle motions and aggregation associated with the growth of the field-induced electrohydrodynamic instabilities. Acknowledgment The work was supported in part by grants from NASA (NAG3-2698), NSF (CTS-0307099), and NSF/Sandia joint program (NIRT/NER-0330703) (B.K.).
Literature Cited (1) Pohl, H. A. Dielectrophoresis: The BehaVior of Neutral Matter in Nonuniform Electric Fields; Cambridge University Press: Cambridge, U.K., 1978. (2) Koch, M.; Evans, A.; Brunnschweiler, A. Microfluidic Technology and Applications; Research Studies Press: Baldock, Hertfordshire, U.K., 2000. (3) Vykoukal, J.; Gascoyne, P. R. C. Invited review: Particle separation by dielectrophoresis. Electrophoresis 2002, 23, 1973. (4) Jones, T. B. Electromechanics of Particles; Cambridge University Press: Cambridge, U.K., 1995. (5) Bennett, D. J.; Khusid, B.; James, C. D.; Galambos, P. G.; Okandan, M.; Jacqmin, D.; Acrivos, A. Combined field-induced dielectrophoresis and phase separation for manipulating particles in microfuidics. Appl. Phys. Lett. 2003, 83, 4866. (6) Kumar, A.; Qiu, Z.; Acrivos, A.; Khusid, B.; Jacqmin, D. Combined negative dielectrophoresis and phase separation in nondilute suspensions subject to a high-gradient ac electric field. Phys. ReV. E 2004, 69, 021402-1. (7) Hughes, M. P. Nanoelectromechanics in Engineering and Biology; CRC Press: Boca Raton, FL, 2003. (8) Chou, C.-F.; Tegenfeldt, J. O.; Bakajin, O.; Chan, S. S.; Cox, E. C.; Darnton, N.; Duke, Th.; Austin, R. H. Electrodeless dielectrophoresis of single- and double-stranded DNA. Biophys. J. 2002, 83, 2170. (9) Cummings, E. B.; Singh, A. K. Dielectrophoresis in microchips containing arrays of insulating posts: Theoretical and experimental results. Anal. Chem. 2003, 75, 4724. (10) Scha¨ffer, E.; Thurn-Albrecht, T.; Russell, T. P.; Steiner, U. Electrically induced structure formation and pattern transfer. Nature 2000, 403, 874. (11) Pease, L. F., III; Russel, W. B. Linear stability analysis of thin leaky dielectric films subjected to electric fields. J. Non-Newtonian Fluid Mech. 2002, 102, 233. (12) Pease, L. F., III; Russel, W. B. Electrostatically induced submicron patterning of thin perfect and leaky dielectric films: A generalized linear stability analysis. J. Chem. Phys. 2003, 118, 3790. (13) Lin, Z.; Kerle, T.; Baker, S. M.; Hoagland, D. A.; Scha¨ffer, E.; Steiner, U.; Russell, T. P. Electric field induced instabilities at liquid/liquid interfaces. J. Chem. Phys. 2001, 114, 2377. (14) Saville, D. A. Electrohydrodynamics: The Taylor-Melcher leaky dielectric model. Annu. ReV. Fluid Mech. 1997, 29, 27.
ReceiVed for reView October 15, 2005 ReVised manuscript receiVed February 2, 2006 Accepted February 3, 2006 IE051151J
