Anal. Chem. 1999, 71, 1923-1927
Articles
Imaging Microscopic Magnetohydrodynamic Flows Steven R. Ragsdale† and Henry S. White*
Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
Magnetohydrodynamic flows in nanoliter volumes of solution adjacent to the surface of a 25-µm-radius Pt disk electrode have been imaged with a scanning electrochemical microscope (SECM). Streamline and chaotic flows are imaged with submicrometer resolution. SECM images demonstrate that magnetic field-driven cyclotron flow within a ∼50-µm-radius torus results in spatial focusing of the electrogenerated molecules. SECM images also suggest that natural convective flow resulting from microscopic density gradients can be prevented by adjusting the external magnetic field strength such that magnetic and gravitational forces in the solution cancel one another.
Figure 1. Disk-shaped ultramicroelectrode shrouded in glass. The flux of current-carrying ions, J, is directed radially outward from the electrode surface, through the uniformly applied magnetic field, B. The force acting on the ions is given by Fm ) J × B. The drawing shows the field oriented parallel to the electrode surface. Experiments were performed in both parallel and orthogonal orientations.
Magnetohydrodynamic (MHD) flows occur over vastly differing length scales, ranging from the dimensions of galaxies to those of plasma-containment systems employed in fusion reactors.1-4 Irrespective of the length scale, the interaction of a conducting fluid with a magnetic field is described by magnetohydrodynamic theory, a synthesis of the laws and principles of classical electrodynamics and fluid dynamics.5,6 Recently, we observed MHD flows on micrometer length scales (l ∼10-6-10-5 m) that are associated with the electrochemical generation of a current in a magnetic field.7-10 MHD phenomena in electrochemical systems of macroscopic dimensions are well documented11 and are currently being
investigated in a number of different laboratories.12-16 The MHD flows that we report here, however, are unique and of fundamental interest in that they are constrained to nanoliter volumes. As demonstrated in this report, these flows may be used to spatially focus electrochemically generated molecules in ultrasmall regions of space. The ability to control the position and transport of small numbers of molecules using external fields is of general interest in nanotechnology and controlled-released drug delivery. Our experiments employ a disk-shaped Pt ultramicroelectrode (UME), Figure 1, to constrain the electrochemical generation of
* Corresponding author: (e-mail)
[email protected]; (phone) 801/ 585-6256; (fax) 801/585-3207. † Present address: Broadley-James Corp., 19 Thomas, Irvine, California 92618 (1) Brown, M. E.; Bouchez, A. H. Science 1997, 278, 268. (2) Shu, F. H.; Shang, H.; Glassgold, A. E.; Lee, T. Science 1997, 277, 1475. (3) Sarson, G. R.; Jones, C. A.; Zhang, K.; Schubert, G. Science 1997, 276, 1106. (4) Glanz, J. Science 1995, 270, 1569. (5) Freidberg, J. P. Ideal Magnetohydrodynamics; Plenum Press: New York, 1987. (6) Polovin, R. V.; Demutskii, V. P. Fundamentals of Magnetohydrodynamics; Plenum Press: New York, 1990. (7) Magnetic field-induced flow may also arise from the force exerted on an electrogenerated paramagnetic species in a nonuniform field (ref 8). This force may be neglected in the experiments reported herein which employ uniform fields. (8) Ragsdale, S. R.; Grant, K. M.; White, H. S. J. Am. Chem. Soc. 1998, 120, 13461.
(9) (a) Lee, J.; Gao, X.; Hardy, L. D. A.; White, H. S. J. Electrochem. Soc. 1995, 142, L90. (b) Ragsdale, S. R.; Lee, J.; Gao, X.; White, H. S. J. Phys. Chem. 1996, 100, 5913. (c) Lee, J.; Ragsdale, S. R.; Gao, X.; White, H. S. J. Electroanal. Chem. 1997 422, 169. (10) Ragsdale, S. R.; Lee, J.; White, H. S. Anal. Chem. 1997, 69, 2070. (11) Fahidy, T. J. Appl. Electrochem. 1983, 13, 553. Tacken, R. A.; Janssen, L. J. Appl. Electrochem. 1995, 25, 1. (12) Leventis, N.; Chen, M.; Gao, X.; Canalas, M.; Zhang, P. J. Phys. Chem. 1998, 102, 3512. (13) Yamamoto, I.; Yamaguchi, M.; Goto, T.; Mirura, S. Sci. Rep. 1996, A42, 309. (14) Takahashi, M.; Yamazaki, Y.; Inoue, A. Int. J. Multiphase Flow 1994, 20, 1095. (15) Mogi, I.; Watanabe, K. Bull. Chem. Soc. Jpn. 1997, 70, 2337. Mogi, I.; Kamiko, M. Sci. Rep. 1996, A42, 315. Mogi, I.; Kamiko, M.; Okubo, S. Physica B 1995, 211, 319. (16) O’Brien, R. N.; Santhanam, K. S. V. J. Appl. Electrochem. 1990, 20, 427. O’Brien, R. N.; Santhanam, K. S. V. J. Appl. Electrochem. 1997, 27, 573.
10.1021/ac981228w CCC: $18.00 Published on Web 04/09/1999
© 1999 American Chemical Society
Analytical Chemistry, Vol. 71, No. 10, May 15, 1999 1923
Faradaic current to essentially a point sourcesthe approximately radial-outward directed flow of current from the point-source electrode through a uniform magnetic field (B) results in a magnetic body force density, Fm, eq 1, that induces solution flow,
Fm ) J × B
(1)
but only in the immediate vicinity (within several radii) of the electrode surface where the current density (J) is large.17 The highly localized MHD flow, in turn, alters the rate of mass transport of the electrochemical reactants to the UME surface, resulting in a large enhancement or diminution of the electrochemical current. Because the force is localized at the tip of the UME, magnetic forces as small as 2 × 10-11 N result in a measurable perturbation of the Faradaic current.10 In this report, we describe imaging experiments using a scanning electrochemical microscope18 (SECM) that allow visualization of MHD flows in the nanoliter volume adjacent to the UME disk. The SECM images demonstrate that magnetic fielddriven cyclotron flow results in spatial focusing of the electrogenerated molecules. The flow visualization experiments also demonstrate that natural convection at the UME can be prevented by adjusting the external magnetic field strength such that magnetic and gravitational forces in the solution cancel one another. EXPERIMENTAL SECTION MHD flows at a disk-shaped UME were imaged using a homebuilt SECM.19 The SECM tip in these studies is a 4-µm-radius C fiber, insulated with a 1.5-µm-thick layer of polyphenylene.20 The C fiber was cut with a razor blade to expose a 4-µm-radius C disk (hereafter referred to as the SECM “tip”). The SECM images are recorded by rastering the SECM tip across the surface of the shrouded Pt UME at a height of ∼20 µm. The experimental arrangement for imaging MHD flows is shown in Figure 2. A glass electrochemical cell (5 mL volume) containing a 25-µm-radius Pt disk UME is centered between the poles of an electromagnet. The Pt UME is shrouded in a glass sheath, exposing a disk-shaped electrode to the electrolyte solution. The glass tube supporting the UME is bent at a 90° angle (Figure 2) such that the surface of the Pt disk is always parallel to the earth’s gravitational field; the electrode may be rotated within the cell to orient the Pt disk either parallel or orthogonal to the magnetic field. A GMW Associates model 5403 electromagnet was used to apply a uniform magnetic field, B, across the electrochemical cell. The magnet poles (7.6 cm diameter) were separated by ∼2 cm. The magnetic field strength, B ) |B|, was varied between 0 and (17) In the limit of d . a, the current density (J) at a distance d from the surface of a disk-shaped electrode of radius a decreases in proportion to d-2.21 Thus, the magnetic force, eq 1, decreases as d-2. (18) (a) Bard, A. J.; Fan, F.-R.; Kwak, J.; Lev, O. Anal. Chem. 1989, 61, 132. (b) Bard, A. J., Fan, F.-R. F.; Mirkin, M. V. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1994; Vol. 18, p 243. (c) Engstrom, R. C.; Weber, M.; Wunder, D. J.; Burgess, R.; Winquist, S. Anal. Chem. 1986, 58, 844. (d) Engstrom, R. C.; Meaney, T.; Tople, R.; Wightman, R. M. Anal. Chem. 1987, 59, 2005. (e) Engstrom R. C. Anal. Chem. 1984, 56, 890. (19) Scott, E. R.; White, H. S.; Phipps, J. B. Anal. Chem. 1993, 65, 1537. Scott, E. R.; Laplaza, A. I., White, H. S.; Phipps, J. B. J. Pharm. Res. 1993, 10, 1699. (20) Potje-Kamloth, K.; Janata, J.; Josowicz, M. Ber. Bunsen-Ges. Phys. Chem. 1989, 93, 1480.
1924 Analytical Chemistry, Vol. 71, No. 10, May 15, 1999
Figure 2. (A) Experimental arrangement for imaging magnetohydrodynamic flows in the solution volume element adjacent to the ultramicroelectrode surface. The UME is a 25-µm-radius Pt disk shrouded in glass and is positioned at the center of an electromagnet (0.01-0.5 T). The SECM tip, a 4-µm-radius carbon fiber, insulated except at the very end of the tip, is rastered across the UME surface at a height of ∼20 µm. (B) Enlargement of the UME/solution/SECM tip junction.
0.5 T by adjusting the current through the electromagnet. Field strength and uniformity were measured using a gauss meter (F. W. Bell, model 4048). The magnetic field varied by less than 0.01 T over a radial distance of 1 cm from the center of the poles; thus, a small error in positioning the cell has a negligible effect on the magnetic field applied across the surface of the microelectrode. Because the electrode surface areas are very small (
