Visualization and Modeling of the Hydrodynamics of an Impinging

Jan 26, 2006 - The use of fluorescence confocal laser scanning micro- scopy (CLSM) for flow ... velocity but at moderate volume flow rates. For CLSM...
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Anal. Chem. 2006, 78, 1435-1443

Visualization and Modeling of the Hydrodynamics of an Impinging Microjet Eleni Bitziou, Nicola C. Rudd, Martin A. Edwards, and Patrick R. Unwin*

Department of Chemistry, University of Warwick, Coventry, CV4 7AL, UK

The use of fluorescence confocal laser scanning microscopy (CLSM) for flow visualization is described, with a focus on elucidating the pattern of flow in the microjet electrode (MJE). The MJE employs a nozzle, formed from a fine glass capillary, with an inner diameter of ∼100 µm, to direct solution at an electrode surface, using high velocity but at moderate volume flow rates. For CLSM visualization, the jetted solution contains a fluorescent probe, fluorescein at high pH, which flows into a solution buffered at low pH, where the fluorescence is extinguished, thereby highlighting the flow field of the impinging microjet. The morphology of the microjet and the hydrodynamic boundary layer are shown to be highly sensitive to the volume flow rate, with a collimated jet and thin boundary layer formed at the faster flow rates (∼1 cm3 min-1). In contrast, at lower flow rates and for relatively large substrates, an unusual recirculation zone is observed experimentally for the first time. This effect can be eliminated by employing small substrates. The experimental observations have been quantified through numerical solution of the Navier-Stokes equations of continuity and momentum balance. The new insights provided by CLSM imaging demonstrate that flow in the MJE, and impinging jets in general, are more complex than predicted by classical models but are well-defined and quantifiable. Impinging liquid jets have been used extensively in electroanalytical chemistry, for example, in flow-through electrochemical detectors1-5 for techniques such as high performance liquid chromatography6,7 and as a means of achieving well-defined and variable mass-transfer rates to electrode surfaces for investigations of electrode reaction mechanisms and kinetics.8-10 The usual configuration employs a submerged cylindrical jet of liquid impinging on a circular electrode surface positioned normal to the flow direction, although the effect of jet angle on the * To whom correspondence should be addressed. Phone: +44-24-7652-3264. Fax: +44-24-7652-4112. E-mail: [email protected]. (1) Brett, C. M. A.; Brett, A. M. O.; Mitoseriu, L. C. Electroanalysis 1995, 7, 225. (2) Elbicki, J. M.; Morgan, D. M.; Weber, S. G. Anal. Chem. 1984, 56, 978. (3) Soucaze-Guilous, B.; Kutner, W. Electroanalysis 1997, 9, 32. (4) Itagaki, M.; Tagaki, M.; Watanabe, K. J. Electroanal. Chem. 1997, 440, 139. (5) Simjee, N.; Unwin, P. R.; Macpherson, J. V. Electroanalysis 2003, 15, 1445. (6) Cannan, S.; Unwin, P. R. Electroanalysis 2004, 16, 712. (7) Swartzfager, D. G. Anal. Chem. 1976, 48, 2189. (8) Brett, C. M. A.; Brett, A. M. O.; Compton, R. G.; Fisher, A. C.; Tyler, G. P. Electroanalysis 1991, 3, 631. (9) Brett, C. M. A.; Brett, A. M. O.; Fisher, A. C.; Compton, R. G. J. Electroanal. Chem. 1992, 334, 57. (10) Compton, R. G.; Fisher, A. C.; Latham, M. H.; Brett, C. M. A.; Brett, A. M. O. J. Phys. Chem. 1992, 96, 8363. 10.1021/ac051692i CCC: $33.50 Published on Web 01/26/2006

© 2006 American Chemical Society

electrochemical response of such devices has recently been considered.11 Depending on the size of the disk electrode as compared to the nozzle, two limiting forms of impinging jet electrode geometry can be distinguished. The wall-tube electrode (WTE) is identified as a disk electrode with dimensions much smaller than the size of the nozzle outlet,12,13 and the wall-jet electrode has a disk electrode much larger than the nozzle.14,15 A miniaturized version of the WTE, the microjet electrode (MJE), has been developed in which solution flows at high speed from a nozzle of ∼100-µm diameter onto an ultramicroelectrode (UME) to achieve mass transport rates variable over a wide dynamic range. The MJE has found considerable kinetic and analytical applications.16-24 For kinetic studies, the MJE is capable of generating high mass transport rates, which has allowed the measurement of fast homogeneous17 and heterogeneous19 reactions. Impinging microjets have also recently been explored as a means of inducing and measuring the detachment of biomaterial from surfaces under well-defined shear.25 Extensions of the MJE include the radial flow microring electrode, which has also been used to measure fast heterogeneous electron transfer.26,27 The application of impinging jets for quantitative measurements in electroanalytical chemistry and in other areas requires that the underlying hydrodynamics is well-defined. The first analytical solutions to the impinging jet problem were those of Homann28 and Fro¨ssling,29 who solved the flow in the stagnation region in the vicinity of the substrate directly under the nozzle, termed the (11) Nowicka, A. M.; Donten, M.; Palys, M.; Stojek, Z. Anal. Chem. 2005, 77, 5174. (12) Chin, D.-T.; Tsang, C. H. J. Electrochem. Soc. 1978, 125, 1461. (13) Albery, W. J.; Bruckenstein, S. J. Electroanal. Chem. 1983, 144, 105. (14) Klymenko, O. V.; Gavaghan, D. J.; Harriman, K. E.; Compton, R. G. J. Electroanal. Chem. 2002, 531, 25. (15) Yamada, J.; Matsuda, H. J. Electroanal. Chem. 1973, 44, 189. (16) Macpherson, J. V.; Simjee, N.; Unwin, P. R. Electrochim. Acta 2001, 47, 29. (17) Martin, R. D.; Unwin, P. R. J. Electroanal. Chem. 1995, 397, 325. (18) Melville, J.; Coles, B. A.; Compton, R. G.; Simjee, N.; Macpherson, J. V.; Unwin, P. R. J. Phys. Chem. B 2003, 107, 379. (19) Macpherson, J. V.; Beeston, M. A.; Unwin, P. R. J. Chem. Soc., Faraday Trans. 1995, 91, 899. (20) Macpherson, J. V.; Marcar, S.; Unwin, P. R. Anal. Chem. 1994, 66, 2175. (21) Macpherson, J. V.; Unwin, P. R. Anal. Chem. 1997, 69, 5045. (22) Macpherson, J. V.; Unwin, P. R. Anal. Chem. 1999, 71, 2939. (23) Macpherson, J. V.; Unwin, P. R. Anal. Chem. 1999, 71, 4642. (24) Rees, N. V.; Klymenko, O. V.; Coles, B. A.; Compton, R. G. J. Electroanal. Chem. 2003, 557, 99. (25) Bayoudh, S.; Ponsonnet, L.; Ben Ouada, H.; Bakhrouf, A.; Othmane, A. Colloids Surf. A 2005, 266, 160. (26) Macpherson, J. V.; Jones, C. E.; Unwin, P. R. J. Phys. Chem. B 1998, 102, 9891. (27) Macpherson, J. V.; Unwin, P. R. Anal. Chem. 1998, 70, 2914.

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Figure 1. Schematic representation of the classical picture of flow in an impinging jet, in which flow is described in terms of four regions: (I) potential core region where the mean velocity is the same as in the nozzle exit; (II) well-developed velocity profile normal to the substrate; (III) stagnation region; and (IV) wall-jet region.12

wall-tube domain. The problem was first reduced to an ordinary differential equation, and solutions were in the form of a series expansion of the type introduced by Blasius.30 Later, Glauert31 solved the boundary layer equations for the full wall-jet region, originally derived by Prandtl32 using a similarity solution. The boundary conditions considered that the velocity dropped to zero as the distance from the axis of rotation tended to infinity, and it was assumed that flow was always directed away from the axis of rotation. The solution was in the form of an implicit equation, from which fluid velocity values could be readily and easily calculated. A modern review of the above methods is given by Schlichting.33 All of the analytical solutions are limited as follows: 1. The geometry of the substrate is taken to be an infinite plane. 2. The flow at the inlet is assumed to be plug flow, that is, a uniform velocity distribution applies across the entire jet at the exit of the nozzle. 3. The solutions apply only within certain limited spatial domains. 4. None of the solutions take the nozzle geometry into account. Consequently, none of the analytical approaches provide a universal solution to the flow profile problem. A semiempirical attempt to combine the limiting solutions was performed by Chin and Tsang,12 resulting in the classical flow picture shown in Figure 1, in which flow is considered in terms of four distinct regions. Numerical simulations of impinging jet flows have tended to focus on the challenging problem of turbulent flow.34 In the laminar regime, we draw attention to the work of Melville et al.,18,35,36 who recently treated the hydrodynamics of the MJE. One of the interesting results of these simulations was the evidence of vortex formation,35 especially when an infinitely thick nozzle wall was considered. This phenomenon, which was not evident (28) Homann Z. Angew. Math. Mech. 1936, 16, 153. (29) Fro ¨ssling, N. Lunds Universitets A° rsskrift N. F. avd. 2 1940, 36. (30) Blasius, H. Z. Math. Phys. 1908, 56. (31) Glauert, M. B. J. Fluid Mech. 1956, 1, 625. (32) Prandtl. Heidelberg, 1904; p 484. (33) Schlichting, H.; Gersten, K. Boundary Layer Theory, 8th ed.; Springer: New York, 2000. (34) Prakash, M.; Turan, O. F.; Li, Y.; Mahoney, J.; Thorpe, G. R. Chem. Eng. Sci. 2001, 56, 3855. (35) Melville, J.; Simjee, N.; Unwin, P. R.; Coles, B. A.; Compton, R. G. J. Phys. Chem. B 2002, 106, 2690. (36) Melville, J.; Simjee, N.; Unwin, P. R.; Coles, B. A.; Compton, R. G. J. Phys. Chem. B 2002, 106, 10424.

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in the analytical descriptions, was predicted to impact the local mass transfer rates in the region adjacent to the impinging jet. The simulation aspect of the present paper develops the hydrodynamic model further, toward conditions that closely mimic experiments: first, by considering a finite, rather than infinite, substrate and second, by applying a simulation domain that represents precisely the nozzle geometry employed in practice and the fluid exterior to it. Visualization of impinging jets on flat surfaces has been achieved using fluorescent dyes or particles to investigate heat and mass transfer distributions and the effect of various geometric and flow parameters.37-45 Many of these studies have dealt with high Reynolds numbers where flow is highly turbulent.37-39,46-48 Moreover, previous visualization studies in the field of engineering have examined large-scale fluid dynamics, which is unrelated to small-scale analytical applications.43,44 Flow visualization techniques applicable to microscale flow geometries have been developed recently.42 For example, particle streak velocimetry and particle imaging velocimetry have been used in flow characterization.49-52 However, these techniques have not been applied to microscale impinging jet systems. We have previously imaged local mass transport from an impinging microjet using a UME and a scanning electrochemical microscopy setup.19,36 This provided images of interfacial mass transfer rates but no information on the associated hydrodynamics in solution. CLSM allows direct, noninvasive, serial optical sectioning of objects and profiling of multilayer structures (three-dimensional imaging) on a rapid time scale (subsecond image acquisition rates). Furthermore, when compared to conventional fluorescence microscopy, CLSM reduces out-of-focus blur that would otherwise result from light’s being collected above and below the focal plane of an object.53-55 We show in this paper that these attributes are particularly valuable for flow visualization and the assessment of hydrodynamic models. We present experimental and theoretical (37) Ashforth-Frost, S.; Rudel, U. W. Int. J. Fluid Dynam. 2002, 7, 1. (38) Chung, Y. M.; Luo, K. H.; Sandham, N. D. Int. J. Heat Fluid Flow 2002, 23, 592. (39) Webster, D. R.; Rahman, S.; Dasi, L. P. J. Eng. Mech. 2003, 129, 11301137. (40) Kuricheti, K. K.; Buschmann, V.; Weston, K. D. Appl. Spectrosc. 2004, 58, 1180. (41) Hatch, A.; Kalmholz, A. E.; Hawkins, K. R.; Munson, M. S.; Schilling, E. A.; Weigl, B. H.; Yager, P. Nat. Biotechnol. 2001, 19, 461. (42) Yunus, K.; Rickson, S. A.; Fisher, A. C.; Henley, I. E.; Allsopp, D. W. E.; Ryan, T. Electrochem. Commun. 2001, 3, 455. (43) Scudder, K. M.; Pollemn, C. H.; Ruzicka, J. Anal. Chem. 1992, 54, 2657. (44) Simison, S.; Pellicano, A.; Brust, M.; Schiffrin, D. J. J. Electroanal. Chem. 1999, 470, 89. (45) Law, H.-S.; Masliyah, J. H. Int. J. Heat Mass Transfer 1984, 27, 529. (46) Chung, Y. M.; Luo, K. H. ASME J. Heat Transfer 2002, 124, 1039. (47) Jambunathan, K.; Lai, E.; Moss, M. A.; Button, B. L. Int. J. Heat Fluid Flow 1992, 13, 106. (48) Beitelman, A. H.; Saad, M. A.; Patel, C. D. Int. J. Heat Fluid Flow 2000, 6, 111. (49) Taylor, J. A.; Yeung, E. S. Anal. Chem. 1993, 65, 2928. (50) Krothapalli, A.; Rajkuperan, E.; Alvi, F.; Lourenco, L. J. Fluid Mech. 1999, 392, 155. (51) Meinhart, C. D.; Wereley, S. T.; Santiago, J. G. Exp. Fluids 1999, 27, 414. (52) Santiago, J. G.; Wereley, S. T.; Meinghart, C. D.; Beebee, D. J.; Adrian, R. J. Exp. Fluids 1998, 25, 316. (53) Sheppard, C. J. R.; Shotton, D. M. Confocal Laser Scanning Microscopy; BIOS Scientific Publishers Ltd: Abingdon, UK, 1997. (54) Cannan, S.; Macklam, I. D.; Unwin, P. R. Electrochem. Commun. 2002, 4, 886. (55) Rudd, N. C.; Cannan, S.; Bitziou, E.; Ciani, I.; Whitworth, A. L.; Unwin, P. R. Anal. Chem. 2005, 77, 6205.

Figure 2. Experimental setup showing the PTFE cell on the stage of the confocal microscope, together with the tubing connection to the nozzle and the substrate attached to a micropositioning translation stage.

evidence that the hydrodynamics of an impinging microjet is more complex than suggested hitherto but, nonetheless, that fluid flow can be readily characterized and is well-defined. The new insights reported in this paper thus provide a foundation for the further development of microscale impinging jets in electroanalytical chemistry and related fields. EXPERIMENTAL SECTION Apparatus and Instrumentation. The impinging microjet arrangement consisted of a rectangular PTFE cell (approximate volume 50 cm3) with an optical window and two holes on opposite sides to accommodate a nozzle and a substrate, as shown in Figure 2. A 2-mm-o.d. borosilicate glass capillary (Harvard Apparatus, UK) was drawn to a fine point with the aid of a PB7 Narishighe micropipet puller and then cut with a sharp scalpel, to produce a nozzle end (typically of internal diameter, d, ∼100 µm). To ensure a flat nozzle outlet, the pulled capillary end was polished using a home-built polishing wheel with a 0.05-µm diamond polishing pad (Buehler, Coventry, U.K.). The polished nozzle was fixed (using PTFE tape) in a 2-mm hole on one side of the cell. On the opposite side of the cell, the substrate was passed though a 12-mm diameter hole fitted with a latex finger cot, PTFE collar, and O-ring to prevent leakage of solution from the cell. The substrate was mounted on an x-y-z miniature positioner (Physik Instrumente, Germany) used to manually align the substrate. Two different circular substrates with diameters of 0.43 mm and 1.2 mm were employed to investigate the influence of substrate size. These are typical sizes of UME bodies employed in the MJE and were actually polished working electrodes56 consisting of a metal disk surrounded by glass insulation, but in these studies, they were used only to provide a flat circular surface of finite diameter. CLSM imaging employed a Zeiss LSM 510, Axioplan 2, microscope with a water immersion objective lens (Zeiss, Achroplan 20×/0.50W Ph2). An argon laser (λ ) 488 nm) was used for excitation in conjunction with a long-pass filter (λ ) 505 nm) to measure the fluorescence from fluorescein. All images in this paper were obtained at × 0.7 digital zoom so that an area of 650 × 650 µm in the x-y plane (through the center of the nozzle and the substrate) was imaged. Z-stack images were obtained by taking serial optical slices in this plane over a range of distances. (56) Wightman, R. F.; Wipf, D. O. Electroanalytical Chemistry; Marcel Dekker: New York, 1989.

Solution was delivered through the glass nozzle onto the substrate surface at a constant rate using a dual-syringe pump (U-74900-15, Cole Palmer Instruments Company) equipped with a 100-mL glass syringe (Hamilton). The system was capable of delivering flow rates in the range of 0.01-4.0 cm3 min-1. The PTFE cell contained a buffer solution (50 mM) of potassium biphthalate (Aldrich) at pH 3, whereas the solution jetted through the nozzle and onto the flat substrate consisted of 10 µM fluorescein (98%, Sigma) in a Borax (sodium tetraborate decahydrate, 35 mM, Aldrich) buffer of pH 8.5. All solutions were prepared using Milli-Q Reagent water (Millipore Corp.). Measurements were made in an air-conditioned laboratory at 22 ( 0.5 °C. Simulations. Modeling of the velocity profiles was carried out using a commercial finite element method modeling package (FEMLAB, version 3.1), used in conjunction with MATLAB (version 7.0, release 14). This was run on a Dell PC under Windows XP with an Intel Pentium 4 processor (2.50 GHz) and 1.5 GB of RAM. THEORY The finite element method57 was used to simulate the velocity profiles as a result of flow from a microcapillary nozzle impinging on a finite solid substrate in real space. The incompressible Navier-Stokes equations58 for momentum balance (eq 1) and continuity (eq 2) were solved in axisymmetric cylindrical coordinates (under steady-state conditions) for the domain shown in Figure 3.

FV‚∇V ) -∇p + η∇2V

(1)

∇‚V ) 0

(2)

In these equations, F is the density of water (1.00 g cm-3),59 V is the velocity vector (with components u and v in the r and z directions, respectively), p is pressure, and η is the dynamic (57) Burnett, D. S. Finite Element Analysis; Addison-Wesley: Reading, MA, 1987. (58) Josserand, J.; Lagger, G.; Jensen, H.; Ferrigno, R.; Girault, H. H. J. Electroanal. Chem. 2003, 546, 1-13. (59) CRC Handbook of Chemistry and Physics, 86th ed.; CRC Press: Boca Raton, FL, 2005.

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Figure 3. Simulation domain and coordinate system for the axisymmetric cylindrical geometry used to model the impinging jet system.

viscosity of water (1.002 mPa s).60 The boundary conditions used were

r ) 0, 0 < z < zmax n‚V ) 0

(3)

0 e r e rglass, z ) 0 u ) 0, v ) 0

(4)

0 e r e rin, z ) zmax u ) 0, v )

Vf πrin2

(5)

r ) rin, H < z < zmax u ) 0, v ) 0

(6)

rin e r e rout, z ) H u ) 0, v ) 0

(7)

r ) rout, H < z e zmax u ) 0, v ) 0

(8)

rout < r e rmax, z ) zmax n‚∇2V ) 0

(9)

r ) rglass, zmin < z < 0 u ) 0, v ) 0

(10)

rglass e r e rmax, z ) zmin n‚∇2V ) 0

(11)

r ) rmax, zmin < z < zmax u ) 0, v ) 0

(12)

where zmax, zmin and rmax indicate the extremes of the simulation domain (see Figure 3), n is the vector normal to the boundary, H is the vertical separation between the microcapillary nozzle exit and the substrate, Vf is the volume flow rate of solution introduced to the nozzle, rglass is the radius of the glass substrate, and rin and rout are the inner and outer radii of the microcapillary wall, respectively. Thus, solution was introduced to the system via a (60) CRC Handbook of Chemistry and Physics, 82th ed.; CRC Press: Boca Raton, FL, 2001.

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plug flow boundary condition at the inlet, but on traveling through the microcapillary flow, it became parabolic before exiting the nozzle. The value of rmax was chosen to be sufficiently large so that the no-slip boundary condition on the wall did not affect the outcome of the simulation in the region of interest. In practice, the domain extended 1 cm from the center of the substrate. In eqs 9 and 11, the condition is that no force is imposed at the boundary, and so the location of these boundaries did not alter the solution. The mesh was refined to the limit of the memory in the PC used, with a high concentration of points in the nozzle, between the nozzle and substrate and radially from the substrate edge. RESULTS AND DISCUSSION Flow Profile of an Impinging Microjet. Most experiments and simulations were carried out at a nozzle/substrate separation of ∼400 µm with a d of ∼100 µm, both of which are typical of MJE experiments.16-20,35,36 Typical CLSM images of the impinging jet are shown in Figure 4. In this case, the diameter of the circular substrate was 1.2 mm. Because the fluorescence of fluorescein is strongly pH-dependent, with the deprotonated form (pKa ∼ 5.5) fluorescing, the solution entering the cell through the nozzle (pH 8.5) appears bright in the CLSM images against the dark background of nonfluorescent solution in the cell (pH 3). As a consequence, the resulting images provide a sharp contrast of the pattern of flow as fluid exits from the nozzle onto the substrate. Figure 4 shows data for three different flow rates: (a)(i) 0.025 cm3 min-1 (Re ) 5), (b)(i) 0.25 cm3 min-1 (Re ) 53), and (c)(i) 1.0 cm3 min-1 (Re ) 212). The Reynolds number, Re, relates to the nozzle and is defined by

Re )

Fvjd η

(13)

where vj is the mean solution velocity in the microcapillary nozzle.

Figure 4. CLSM images (i) and simulated velocity field plots (ii) of a 10 µM fluorescein solution (pH ) 8.5) flowing toward a 1.2-mm-diameter substrate immersed in a buffered solution (pH ) 3). The CLSM images measure 651 × 651 µm, d ) 100 µm, and H ) 400 µm. The data are for flow rates of (a) 0.025 cm3 min-1 (Re ) 5), (b) 0.25 cm3 min-1 (Re ) 53), and (c) 1.0 cm3 min-1 (Re ) 212).

It should be noted that diffusion is expected to be minimal, as compared to convective flow, in these experiments, and in any case, any diffusional effects from fluorescein are eliminated by strong buffering of both solutions, fixed at values where fluorescein fluoresces either strongly or does not fluoresce at all. The three flow rates shown in Figure 4 exhibit distinctly different flow patterns. In Figure 4(a)(i), the fluorescent dye emerging from the nozzle outlet at 0.025 cm3 min-1 produces a very broad jet profile, where the hydrodynamic boundary layer adjacent to the substrate surface is thick, extending ∼200 µm in the direction normal to the substrate. The images in Figure 4(b)(i) and 4(c)(i) reveal more clearly the wall-jet region, where the thickness of the boundary layer adjacent to the substrate, beyond the position where the jet impinges, gradually increases in

thickness with radial distance. Furthermore, by comparing Figure 4(a)(i), (b)(i), and (c)(i), it can be seen that the overall thickness of the hydrodynamic boundary layer adjacent to the substrate decreases substantially with increasing flow rate. Another interesting effect, clearly evident, is that at low flow rates, the jet itself increases in thickness with distance from the nozzle (Figure 4(a)(i)), whereas at the faster flow rates, the jet thickness remains fairly constant, tending to the size of the nozzle exit (Figure 4(c)(i)). All of these observations are at least qualitatively consistent with the classical picture of impinging jet flow in Figure 1. The most striking feature of the flow pattern appears in Figure 4(b)(i), which shows an additional recirculation effect at a flow rate of 0.25 cm3 min-1. This effect is absent from classical models, but was predicted in recent simulations;35,36 however, the latter Analytical Chemistry, Vol. 78, No. 5, March 1, 2006

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Figure 5. CLSM images (i) and simulated velocity field plots (ii) of a 10 µM fluorescein solution (pH ) 8.5) flowing toward a 1.2-mm-diameter substrate immersed in a buffered solution (pH ) 3). The CLSM images measure 651 × 651 µm, d ) 100 µm, and H ) 400 µm. The data are for flow rates of (a) 0.1 cm3 min-1 (Re ) 21), (b) 0.15 cm3 min-1 (Re ) 32), and (c) 0.4 cm3 min-1 (Re ) 85).

simulations employed a nozzle with a much thicker wall than was used in this study. As outlined in the theory section, we have further developed these simulations to represent experimental conditions as closely as possible (in terms of nozzle and substrate geometry) so as to identify the correlation between theory and experiment. For comparison with experiment, Figure 4 shows the velocity field (i.e. the magnitude of the velocity) and predicted flow profiles from the numerical simulations for the conditions of each of the three CLSM images. Note that these profiles are in the axisymmetric cylindrical geometry (Figure 3) and show flow up to r ) 600 µm, which is about twice the distance of the experiments. This applies to all the simulation results which follow. The flow 1440 Analytical Chemistry, Vol. 78, No. 5, March 1, 2006

profile is indicated by the streamline shown in the figure, which originated at the end of the nozzle immediately adjacent to the glass wall. This highlights the movement of solution at the extreme of the jet, thus representing the hydrodynamic boundary layer. For Figure 4(b), where recirculation is visible, additional streamlines have been plotted. These were calculated by selecting a start point that corresponded to the edge of the fluorescent zone seen in experimental images and then tracking the entire streamline. It is, thus, evident that the recirculation phenomenon is also predicted by simulations, since the calculated streamlines map well to all of the edges of the experimental fluorescent region(s). The theoretical studies therefore confirm all experimental observations, including the recirculation effect. For each of the

Figure 6. CLSM images (i) and simulated velocity field plots (ii) of a 10 µM fluorescein solution (pH ) 8.5) flowing toward a 0.43-mm-diameter substrate immersed in a buffered solution (pH ) 3). The CLSM images measure 651 × 651 µm, d ) 107 µm, and H ) 380 µm. The data are for flow rates of (a) 0.075 cm3 min-1 (Re ) 15), (b) 0.5 cm3 min-1 (Re ) 99) and (c) 2.0 cm3 min-1 (Re ) 397).

flow rates, which cover a wide range, it can be seen that agreement between experiment and simulation is excellent. Figure 5 considers the nature of the recirculation effect in more detail, showing experimental data (i) alongside the corresponding simulations (ii), focusing on a narrower range of flow rates where the recirculation effect is significant. The images represent flow rates of (a) 0.1 cm3 min-1 (Re ) 21), (b) 0.15 cm3 min-1 (Re ) 32), and (c) 0.4 cm3 min-1 (Re ) 85). The streamlines were calculated as described previously, and there is again excellent agreement between the simulated velocity boundary streamlines and the visual observations obtained by CLSM. Even for this relatively narrow range of flow rates, it is clear that the morphology of the recirculation zone is sensitive to the volume flow rate.

Notably, as the flow rate increases, the contribution of axial flow in the recirculation zone becomes more significant. Flow to a Small Substrate. Some experiments with impinging microjets have been carried out with UMEs that have a substrate size which is smaller than considered hitherto in this paper.21,23 Thus, the effect of decreasing the substrate diameter to 0.43 mm (which is comparable to a 50-µm-diameter disk UME with an insulating sheath ∼10 times larger) was studied to observe its influence on the impinging jet hydrodynamics. The results which follow correspond to a nozzle (d ) 107 µm) placed at a height of 380 µm above the substrate. Figure 6 shows the CLSM images for flow rates of (a) 0.075 cm3 min-1 (Re ) 15), (b) 0.5 cm3 min-1 (Re ) 99), and (c) 2.0 cm3 min-1 (Re ) 397). As expected, on the Analytical Chemistry, Vol. 78, No. 5, March 1, 2006

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basis of the results presented hitherto, an increase in the flow rate leads to a diminution in the size of the hydrodynamic boundary layer; however, significantly, the recirculation effect seen previously is no longer evident. Rather, solution flows axially onto the substrate and then radially away to the substrate edge. Thus, it appears that the substrate surface must be sufficiently large for recirculation to occur. The velocity field plots obtained by simulation are again highly consistent with the experimental observations, and the boundary layer streamlines are comparable with the CLSM images. These results suggest that recirculation can be eliminated by appropriate tuning of the substrate size. An interesting effect with the smaller substrate is the nature of the flow at the substrate edge. At the highest flow rate of 2.0 cm3 min-1 (Re ) 397) the fluid runs parallel to the substrate surface, and the flow stream only deviates slightly at the edge of the substrate and beyond as the fluid moves radially into the bulk (see Figure 6(c)(i)). In contrast, at the lowest flow rate (Figure 6(a)(i)), the profiles show that flow occurs around the side of the substrate with the development of a significant axial component. The simulations confirm these observations, illustrating once again the excellent agreement between the experimental system and the theoretical model. Quantitative Analysis of Streamlines. To highlight the quantitative nature of the CLSM measurements with the two different substrate surfaces employed, Figure 7 shows the experimental and theoretical streamline plots for (a) 1.2-mm- and (b) 0.43-mm-diameter substrates at a wide range of volume flow rates, taken from images such as those shown in Figures 4-6. The plots focus on the edge of the fluorescent zone from the capillary edge, as measured experimentally and predicted by the theoretical streamlines. The distances are measured from the center of the substrate, where the z ) 0 plane represents the location of the substrate surface and the z ) 400 or 380 µm (for the 1.2- and 0.43-mm-diameter substrates, respectively) plane is the end of the glass nozzle. The theoretical model is represented by the solid lines and reveals the streamlines emerging from the inner wall of the nozzle, as shown on the original velocity plots. The points show the edge of the fluorescent zone observed (in z, r coordinates) in the experiments. An excellent fit of the experimental data with the theoretical model is generally evident. Note, however, that for the 0.43-mm-diameter substrate, at the lowest flow rates, the experimental points lie below the theoretical profiles. At such low flow rates, stepping effects from the syringe pump are evident (see, for example, Figure 6(a)(i)) which not only introduce uncertainty into the measurement of the hydrodynamic boundary layer but also disturb the smooth, steady flow on which the model is based. These effects appear to be more significant for the smaller substrate. Three-Dimensional Flow Imaging. A significant feature of CLSM is the possibility of obtaining three-dimensional images by serial optical sectioning of the object under investigation. Although the images presented hitherto were taken as a cross section through the center of the jet, which could be compared to theory due to the axisymmetric cylindrical geometry of the jet system, it is also useful to provide a full three-dimensional image of the flow system. Such an image is shown in Figure 8 for a flow rate of 0.25 cm3 min-1.The projection is shown at an angle of 25° with respect to the (z, r) plane and illustrates the recirculation effect 1442 Analytical Chemistry, Vol. 78, No. 5, March 1, 2006

Figure 7. Streamline plots displaying experimental (b) and simulated (;) results for (a) 1.2- and (b) 0.43-mm substrates. The flow rates in both plots are 0.025 (black), 0.05 (red), 0.075 (green), 0.1 (dark blue), 0.25 (cyan) and 0.5 cm3 min-1 (pink). In (a), the yellow line is 1.0 cm3 min-1; in (b), 2.0 cm3 min-1.

as a three-dimensional object. It is evident that the dipping lens slightly disrupts part of the recirculation effect but that overall, CLSM is relatively noninvasive for these measurements. CONCLUSIONS Fluorescence CLSM has been shown to be a powerful method for visualizing flow from an impinging microjet. The methodology is simple and involves the flow of a solution containing a fluorescent probe (fluorescein at pH > 8) into a buffered solution where fluorescein does not fluoresce. The resulting images thus map out, with high precision, the path of solution flow from the nozzle as it impinges onto the substrate. This study has highlighted how the volume flow rate and substrate size affect the hydrodynamics of an impinging microjet for typical nozzle-substrate separations employed in the MJE. Notably, with a circular substrate of diameter 1.2 mm (as compared to a nozzle diameter of 100 µm), flow recirculation has been found at intermediate flow rates. This novel phenomenon, which is not predicted by earlier analytical treatments of the impinging microjet, is also evident from the numerical solution

a significant radial distance beyond the nozzle edge. An approach to eliminating the recirculation effect is to shrink the size of the substrate, as evident from the studies with the 0.43-mm-diameter substrate. In general, the investigations in this paper have demonstrated that rather complex electrode geometries and flow phenomena can readily be treated quantitavely with finite element modeling. The studies presented provide a foundation for the further development of the MJE and related small-scale impinging microjet techniques in electrochemistry and interfacial science. In particular, the new experimental understanding of flow presented in this paper should facilitate the use of ring electrodes in the MJE configuration, and this will be the subject of a future paper. Figure 8. Three-dimensional projection image (551 × 651µm), at a 25° angle to the (z, r) plane, of an impinging jet flowing at a flow rate of 0.25 cm3 min-1 with d ) 93 µm and H ) 400 µm.

of the flow problem, with a geometry that matches the experimental conditions closely. Although this recirculation effect would not be expected to impact significantly mass transport to a disk electrode co-aligned with the nozzle in the MJE configuration, it would be important for formats employing ring electrodes or discring electrodes, in which an electrode is offset radially from the axis of the nozzle. Moreover, such effects are also likely to be important for the wall-jet electrode, in which the electrode extends

ACKNOWLEDGMENT This research was funded by the EPSRC (E.B.), University of Warwick Postgraduate Research Fellowship Scheme (N.C.R.), and the EPSRC through the MOAC doctoral training center (M.A.E.). We thank Dr. Yongmann Chung (Department of Engineering, University of Warwick) and Dr. Julie Macpherson (Department of Chemistry, University of Warwick) for helpful discussions.

Received for review September 21, 2005. Accepted December 22, 2005. AC051692I

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