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Electrokinetic Vortices and Traveling Waves in Nondilute Colloidal Dispersions Carlos L. Perez and Jonathan D. Posner* Mechanical Engineering, Chemical Engineering, Arizona State University, Tempe, Arizona 85287 Received January 11, 2010. Revised Manuscript Received March 16, 2010 We report a diverse set of coherent fluid flow instabilities, particle patterns, and traveling waves that develop when an ac electric field is applied to nondilute colloidal dispersions with volume fractions that span 3 orders of magnitude. Novel observed phenomena include the following: vortices with steady and unsteady axes of rotation, unsteady time evolution of vortices formation and vortex merging, as well as traveling waves that propagate through the dispersion. Vortical flows are influenced by strong interactions between particle electrical dipoles as well as electric body forces due to electric fields coupled with gradients in particle volume fraction. We use a 1D Burgers equation to predict the existence of traveling waves in colloidal dispersions.
Introduction Colloidal dispersions of insulating microparticles can exhibit a variety of static and flow patterns when exposed to ac electric fields. Particles can form chains,1-4 crystalline aggregates,1,5,6 and rotating bands.2,7-11 An understanding of the conditions necessary for pattern formation in the nondilute volume fraction regime can be leveraged for applications such as the electrophoretic deposition of colloidal crystals,1,5,12 field induced pattern formation,13 electrorheological devices,14 and electrophoretic separations.15 Many of these phenomena are due to particle polarization induced by the externally applied electric field. The application of an ac electric field to an aqueous colloid induces a dipole moment on each particle due to particle polarization and the migration and redistribution of mobile charges in the surrounding medium. Interfacial polarization redistributes charges due to the disparity in electrical conductivity and dielectric permittivity between the particle and the medium.3 In an electrolyte, the applied electric field also causes a redistribution of ions in the enveloping electric double layer (EDL).16,17 Several studies have investigated the conditions under which particle chains and aggregates are formed and their dependence *Corresponding author. E-mail:
[email protected]. (1) Lumsdon, S. O.; Kaler, E. W.; Velev, O. D. Langmuir 2004, 20, 2108–2116. (2) Lele, P. P.; Mittal, M.; Furst, E. M. Langmuir 2008, 24, 12842–12848. (3) Jones, T. B. Electromechanics of Particles; Cambridge University Press: Cambridge, U.K., 1995. (4) Fraden, S.; Hurd, A. J.; Meyer, R. B. Phys. Rev. Lett. 1989, 63, 2373. (5) Trau, M.; Saville, D. A.; Aksay, I. A. Langmuir 1997, 13, 6375–6381. (6) Martin, J. E.; Anderson, R. A.; Tigges, C. P. J. Chem. Phys. 1998, 108, 3765– 3787. (7) Murtsovkin, V. A.; Gamayunov, N. I. Kolloidn. Zh. 1983, 45, 760–763. (8) Jennings, B. R.; Stankiewicz, M. Proc. R. Soc. London, Ser. A, Math. Phys. Sci. 1990, 427, 321–330. (9) Hu, Y.; Glass, J. L.; Griffith, A. E.; Fraden, S. J. Chem. Phys. 1994, 100, 4674–4682. (10) Isambert, H.; Ajdari, A.; Viovy, J.; Prost, J. Phys. Rev. Lett. 1997, 78, 971. (11) Isambert, H.; Ajdari, A.; Viovy, J.; Prost, J. Phys. Rev. E 1997, 56, 5688. (12) Moran, J. L.; Wheat, P. M.; Posner, J. D. Langmuir 2008, 24, 10532–10536. (13) Trau, M.; Sankaran, S.; Saville, D. A.; Aksay, I. A. Nature 1995, 374, 437– 439. (14) Zukoski, C. F. Annu. Rev. Mater. Sci. 1993, 23, 45–78. (15) Noble, R. P. J. Lipid Res. 1968, 9, 693–700. (16) Shilov, V. N.; Delgado, A. V.; Gonzalez-Caballero, F.; Horno, J.; LopezGarcia, J. J.; Grosse, C. J. Colloid Interface Sci. 2000, 232, 141–148. (17) Lyklema, J. Fundamentals of Interface and Colloid Science; Academic Press: London, 1991.
Langmuir 2010, 26(12), 9261–9268
on various controlling parameters such as field intensity,1-4 ac frequency1-3 and background electrolyte’s properties.1 Experimental investigations on chains, aggregates and rotating bands have primarily focused on Hele-Shaw cells with electrode deposited on the cell’s bottom surface. Fraden et al. reported that the application of an ac electric field causes the average chain length to increase with time.4 It has been shown that the electric field intensity required to form chains2 and aggregates1 increases with excitation frequencies and decreasing particle diameters. Lumsdon et al. suggested that the increase in viscosity and decrease in static dielectric permittivity of the background electrolyte results in higher values of electric field intensity required to form chains and aggregates.1 Rotating bands are regions of high particle concentration in which particles and chains circulate continuously without permanently aggregating. Gamayunov and Murtosovkin first demonstrated that rotating bands are highly dependent on the electric field intensity and frequency.7 Isherwood et al. showed that rotating bands can occur in aqueous dispersions of quartz particles and emulsions of kerosene in water.18 They briefly reported that their systems displayed an optimal frequency and electric field intensity for rapid band formation. Jennings’ results confirmed this and showed that bands form more rapidly with higher electric field intensities.8 Lele et al. showed that the electric field threshold to form bands increases with frequency (in the range 6-30 kHz) and for any given frequency, low field intensities lead to chains and higher intensities lead to bands.2 They theorized that band formation is the results of induced flows generated by individual particle rotations. These investigations provide information on the roles of the electric field intensity, ac frequency, and solution properties in the formation and evolution of bands and chains. They collectively show that higher electric field intensities lead to faster band formation and particle chain growth and higher frequencies increase the electric field required to form bands and chains. Here, we report on rotating bands, particle patterns, and traveling waves that develop when an ac electric field is applied to nondilute colloidal dispersions of insulating particles in electrolyte solutions with nondilute volume fractions spanning three-orders (18) Isherwood, R.; Jennings, B. R.; Stankiewicz, M. M. Chem. Eng. Sci 1987, 913–914.
Published on Web 04/01/2010
DOI: 10.1021/la100132w
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of magnitude (0.025-10%). Specifically, we report the experimental observation of three novel flows: (1) rotating bands with unsteady axes of rotation, (2) unsteady time evolution of vortices formation and merging, and (3) traveling waves that propagate through the dispersion. We present an experimental phase map of these phenomena as a function of the applied field and the particle volume fraction. The dependence of the flow behavior on the volume fraction is one of the unique aspects of the present work. Perhaps the most novel of the reported phenomena is the existence of traveling waves. For the first time, we report the observation of periodic local high volume fraction regions that, like sound waves, propagate through the dispersion by locally compressing and rarefying their propagation medium. We end the paper with theoretical discussion of the observed phenomena. We describe the importance of the electric double layer surface conductance on the induced dipole forces of insulating particles in an electrolyte solution. We discuss the role of electrical fluid body forces in the formation and evolution of rotating bands and present a compact Burgers equation model that describes the existence of traveling waves in colloidal dispersions driven by electric fields.
Experimental Methodology We use dispersions of fluorescent 1.9 μm polystyrene microspheres (Thermo Scientific) in 0.1 mM phosphate buffer with pH 8 and conductivity 2.4 10-3 S/m. Sucrose was added to the dispersion in a concentration of 409 mM to achieve neutral particle buoyancy. In this work we examine volume fractions of 0.025, 0.05, 0.1, 0.25, 0.5, 1, 2.5, 5, and 10%. Poly(dimethylsiloxane) (PDMS) microchannels were used that were 7 mm long with a rectangular cross-section of 200 μm wide by 360 μm deep (along the optical axis). The straight microchannels were fabricated using softlithography of PDMS. SU-8 (negative photoresist) patterned on a 400 silicon wafer served as the master for soft lithography.19 The surface of the master was silanized with trichloro methyl silane (TCMS) vapor for about 30 min. PDMS (Dow Corning Corporation, Midland, MI) in a 10:1 polymer:fixing agent ratio was poured over the master, degassed at low pressure in a desiccator, and baked at 80 C in a convection oven for 60 min. The resultant structures were then exposed to oxygen plasma (TegalPlasmaline Asher, Rocklin, CA) at a power of 200 W and 400 mTorr pressure for 60 s. Alternating current electric fields were applied by a function generator (Agilent, 33220A) and amplifier (Trek, 601C) through platinum wires submerged in the channel-end reservoirs, resulting in field lines parallel to the length of the channel. AC fields of 40 Hz and E0 values of 20 V cm-1 and between 100 and 700 V cm-1 in 100 V cm-1 intervals were used. The field required to form chains and bands depends on frequency,2,18 but a fixed low frequency of 40 Hz was chosen because it reduced the number of experimental parameters and resulted in the rapid formation on bands. All experiments were conducted for 15 min, when the observed phenomena had approached steady state. We did not observe electrolysis bubble formation during experiments due to low Faradaic currents and the use of ac electric fields. We used epifluorescence microscopy (Nikon TE2000-U) and a cooled CCD camera (Photometrics, Coolsnap HQ) to record images. Images were recorded at 4 Hz with a 40 ms exposure time. The measurement window was centered in the channel and was 3.9 mm long in the direction of the electric field lines and 50 μm wide.
Results and Discussion Figure 1 shows sample micrograph images of (a) chains (φ= 0.1% and E0= 200 V cm-1), (b) aggregates (φ=2.5% and E0 = 400 V cm-1), (c) a stable vortex (φ = 1% and E0=500 V cm-1), and (d) two unstable vortices (φ = 0.5% and E0 = 700 V cm-1). (19) Duffy, D. C.; McDonald, J. C.; Schueller, O. J. A.; Whitesides, G. M. Anal. Chem. 1998, 70, 4974–4984.
9262 DOI: 10.1021/la100132w
Figure 1. Sample micrographs of (a) chains, (b) particle aggregates, (c) a stable vortex, and (d) two unstable vortices. Arrows in parts c and d represent the direction of particle rotation. Electric field lines are aligned horizontally. Movies of chains, aggregates, stable and unstable vortices are available on the web as Supporting Information. The scale bar represents 25 μm.
Chains are linear ensembles of particles aligned with electric fields lines and form due to the interaction of dipole forces induced by the external electric field. Chains lengths increase with electric field intensity, particle volume fraction, and time. Aggregates also form due to induced dipole forces and are a natural extension of chains when either the volume fraction or the electric field becomes large. Aggregates often exhibit 2- and 3-dimensional crystalline structure. Chains and aggregates were also observed when direct current was used at representative electric field intensities. We use the terms stable and unstable vortices for rotating regions of high volume fraction that exhibit and steady and an unsteady axis of rotation, respectively. Several equally spaced vortices typically form in a single channel. When observed Langmuir 2010, 26(12), 9261–9268
P erez and Posner
Figure 2. Phase map diagram of observed colloidal and flow patterns as a function of the applied field and volume fraction. Motions are classified into Brownian motion, chains (cf. Figure 1a), aggregates (cf. Figure 1b), stable vortices (cf. Figure 1c), unstable vortices (cf. Figure 1d), waves, as well as combinations of behaviors such as unstable plus stable vortices, and aggregates plus stable vortices. Movies of each condition are available as Supporting Information.
in the far field, these vortices with periodic spacing resemble a striped pattern and are often called bands. In Figure 1c, the stable vortex’s axis of rotation is perpendicular to the electric field lines and aligned with the smallest channel dimension (vertical direction in Figure 1c) such that particles circulate from left to right. Movies of chain and aggregate formation as well as stable and unstable vortices are available on the web as Supporting Information. Figure 2 shows a phase map of the colloidal patterns and unstable flow behavior observed as a function of the applied electric field and the colloidal volume fraction. The behavior denoted in the phase map is the steady state behavior observed after 15 min. At low electric fields (
