Microfluidics without microfabrication

Abstract

Microfluidic devices create spatially defined, chemically controlled environments at microscopic dimensions. We demonstrate the formation and control of microscopic hydrodynamic and chemical environments by impinging a low-intensity acoustic oscillation on a cylindrical electrode. The interaction of small-amplitude (≤203 μm), low-frequency (≤515 Hz) fluid oscillations with a submillimeter cylinder creates four microscopic eddies that circulate adjacent to the cylinder. This steady flow is known as acoustic streaming. Because the steady circulation in the eddies has closed streamlines, reagent dosed from the electrode can escape the eddies only by slow molecular diffusion. As a result, reagent dosing rates of 10 nmol/s produce eddy concentrations as high as 8 mM, without a correspondingly large rise in bulk solution composition. Imaging Raman spectroscopy is used to visualize the eddy concentration distribution for various acoustic oscillation conditions, and point Raman spectra are used to quantify eddy compositions. These results, and corresponding numerical simulations, show that each eddy acts as a microchemical trap with size determined by acoustic frequency and the concentration tuned via reagent dosing rate and acoustic amplitude. Low-intensity acoustic streaming flows can serve as microfluidic elements without the need for microfabrication.

Microfluidics exploits the physics and chemistry of stable laminar flows to enable high-throughput experimentation and improved measurement science (1–3). Typical microfluidic devices consist of microfabricated channels possessing at least one characteristic dimension below a millimeter. At these dimensions, flows tend to be stable and laminar over a wide range of fluid velocities, fluid properties, and channel geometries. The stability, and thus predictability, of these flows arises from the important role of viscous forces at small dimensions, as reflected by a small to moderate Reynolds number, Re = VL/ν, where V is a characteristic velocity, L is a characteristic length, and ν is the kinematic viscosity.

Microfluidic devices often take advantage of these hydrodynamic traits to spatially organize fluid streams bearing chemical reagents, cells, proteins, and other items. Interaction between fluids of different composition occurs by diffusion across the “fluidic interface” defined by the streamline that divides the fluids. The organization of dividing streamlines and the creation of controlled microchemical environments has allowed measurement of chemical/biochemical transport and reaction rates (4–7), separations based on species diffusivity (8, 9), generation of custom concentration gradients (10), and in situ cell patterning (11) and microfabrication (12). Moreover, dividing streamlines can be organized in creative ways to promote rapid interdiffusion by using processes such as focusing (13, 14), laminating (15–18), and injecting (19).

Elementally, all of these microfluidic examples seek to control dividing streamlines and the resulting microchemical environments. We demonstrate an alternative strategy for creating and controlling microchemical environments without the use of microfabrication or continuous flow streams. Instead, a low-intensity acoustic oscillation is used to create microfluidic domains whose chemical composition can be controlled electrochemically. Here the acoustic oscillation impinges on a cylindrical object (an electrode), and the resulting time-averaged Reynolds stresses lead to a steady flow called acoustic streaming (20, 21). Low-intensity oscillations (i.e., low to moderate streaming Reynolds numbers) cause the formation of four microscopic eddies located symmetrically around the cylindrical electrode and separated from the bulk fluid by a stable dividing streamline (22–26). The cylinder electrochemically doses chemical reagents into the microscopic eddies, creating a steady-state well-mixed microchemical trap. Imaging Raman spectroscopy and numerical simulations show that the amplitude and frequency of the acoustic oscillation can be used to control the location of the dividing streamline and the reagent composition within the eddies.

Experimental Details and Data Analysis

Fig. 1 shows the experimental flow system. A horizontal cylindrical gold electrode (A in Fig. 1) with radius = 406 μm and length = 1.6 cm was rigidly affixed to an overhead optical micropositioning stage by electrically insulated vertical supports. The cylinder was positioned centrally in an electrolyte-filled custom-designed acrylic optical cuvette (B in Fig. 1) that was mounted to the coil of a 5.25-in audio woofer (C in Fig. 1). A function generator and audio amplifier drove the speaker, allowing vertical oscillations of the cuvette and electrolyte about the stationary cylindrical electrode. Free surface disturbances were limited to an “I-shaped” slot in the cuvette top that permitted insertion and positioning of the cylinder. A slotted baffle (D in Fig. 1) further suppressed flow disturbances in the lower compartment (1.5 × 1.5 × 2.5 cm³). The acoustic oscillations had frequencies in the range of 471 ≤ ω ≤ 3,234 rad/s and displacement amplitudes 32 ≤ s ≤ 203 μm. Values are reported as nondimensional frequency M² = a²ω/ν and amplitude ɛ = s/a, where a is the cylinder radius and ν is the electrolyte kinematic viscosity.

Figure 1.

Experimental system for flow generation. (Left) A horizontal gold cylindrical electrode (A) was suspended from a micropositioning stage by electrically insulated vertical uprights. An acrylic optical cuvette (B) filled with electrolyte was mounted to the coil of an audio speaker (C), and the cuvette and fluid were oscillated about the stationary cylinder. (Right) An I-shaped slot in the cuvette top limited the fluid free surface while allowing insertion and positioning of the cylinder. A baffle (D) partially isolated the lower compartment from free surface flow disturbances.

Flow visualization was achieved by using a pulsed SDL-8630 laser (SDL, San Jose, CA) (670 nm) synchronized to the acoustic frequency and focused as a sheet perpendicular to the electrode axis. A video microscope, imaging along the axis, captured scattered light from silica particles seeded in solution. Image sequences provided particle paths for the steady component of flow. Single-frame images taken with continuous laser illumination far from the electrode allowed accurate determination of the oscillation displacement amplitude.

Electrochemical experiments used platinum wire counter and reference electrodes, with the four counter electrodes mounted along each edge of the lower compartment parallel to the central cylinder (the working electrode). Well-supported electrolytes containing equimolar potassium ferricyanide and ferrocyanide in 1 M NaOH were used. A PAR 263A potentiostat/galvanostat (Princeton Applied Research, Oak Ridge, TN) controlled the rate of electrochemical dosing from the central cylinder.

A custom-built line-imaging Raman spectrometer [Spex 270M imaging spectrograph, Princeton Instruments (Trenton, NJ) LN/CCD 1024E detector] provided acquisition of up to 256 simultaneous, spatially resolved spectra along a thin vertical optical sampling volume (≈50 × 50 × 2,500 μm³). Principle component regression, a multivariate method, was used to quantify concentrations from each spectrum. Raman imaging (27) and multivariate analysis (28) were similar to those reported. By rastering the optical sampling volume horizontally through the flow cross section, two-dimensional concentration images were constructed. Two-dimensional images were derived from 17 line images recorded during mass-transfer-limited dosing of ferrocyanide in 25 mM solution. Charge-coupled device pixel binning gave a vertical resolution of 40 μm, and the raster motion gave a horizontal resolution of 50 μm. Raman images indicated the cylinder location and allowed sample volume positioning for quantification of “point” concentrations. Raman point measurements were derived from the average of 30 spectra recorded during galvanostatic dosing of ferricyanide in 50 mM solution.

The equations and boundary conditions used for the numerical simulations have been reported (26), although in this case numerical solutions were obtained by using FEMLAB 1.1 (Comsol, Los Angeles) with a far-field boundary condition that better accounted for the experimental arrangement. Flow field simulations took ≈2 h for each set of dimensionless parameters when using a 500-MHz computer. Concentration field simulations used previously solved flow fields and took ≈45 min more for each set of parameters. All simulations were for the maximum achievable chemical dosing rates into the microscopic eddies (i.e., the mass-transfer-limited current).

Results and Discussion

Fig. 2 shows that acoustic streaming flows near submillimeter cylinders possess two of the essential traits characteristic of microfluidic systems, namely, microscopic dimensions and the ability to predictably position the dividing streamline (or fluidic interface) that separates distinct fluid volumes. The particle path images in Fig. 2 show the steady flow structure next to the cylindrical electrode for three dimensionless frequencies (M² = 100, 200, and 500). In each of the images, only two of the four symmetric eddies are shown, owing to a laser shadow behind the cylinder. In each image, a white dashed curve highlights the fluidic interface that separates an eddy from the bulk fluid, and white arrows show the direction of fluid circulation. Increasing the frequency of the acoustic oscillation moves the fluidic interface toward the cylinder, as predicted by theory (22–26). Acoustic streaming flows are well known in the literature, but we present experimental characterization at microscopic length scales where diffusive transport allows the eddy to function as a microchemical trap. Because the electrode eddies are hydrodynamically isolated from the bulk fluid, chemicals added to the eddy can escape only by slow molecular diffusion. Thus, if a steady stream of reagent is dosed into the eddy, one expects to see it accumulate to an appreciable concentration. In short, the electrode eddies should serve as steady-state well-mixed microchemical traps.

Figure 2.

Cross-section particle path images of steady acoustic streaming near a cylindrical electrode for vertical oscillations. Three different dimensionless acoustic oscillation frequencies are shown (M² = 100, 200, and 500). An illumination shadow does not allow imaging of the symmetric flow behind the electrode. The electrode surface is revealed by a semicircular arc of very bright scattering in each cross-sectional image. The dashed curves indicate fluidic interfaces that separate electrode eddies from bulk fluid, whereas the straight dashed lines denote flow symmetry. Arrows denote the direction of fluid motion.

The ability of these eddies to trap reagents dosed from the cylinder surface is shown in Fig. 3 by using imaging Raman spectroscopy and numerical simulations. The results in Fig. 3 are for mass-transfer-limited ferrocyanide dosing (≈10 nmol/s) at three values of M². Because the experiments used equimolar ferricyanide/ferrocyanide solutions (to obtain a stable platinum reference potential), the image gray scale is based on the difference in ferrocyanide composition between the eddies and the bulk solution, that is,

with white denoting 100% and black 0%. The black semicircular region on the left center of each image indicates the half-cylinder cross section (again, only two eddies are shown, owing to a laser illumination shadow). The simulation results (Fig. 3 Upper) show that the electrochemically dosed ferrocyanide accumulates in the electrode eddies, with the most prominent features being well-mixed cores in each eddy. There is also some boundary-layer fine structure displayed. Signal-to-noise in the corresponding experimental Raman images (Fig. 3 Lower) does not allow one to discern fine structure, but chemical trapping behavior is clearly evident. Increasing the frequency (left to right) moves the dividing streamline toward the cylinder, with a corresponding shift in the size of the microchemical trap. In each of these experiments, the chemical dosing rate is ≈10 nmol/s, resulting in a steady-state eddy concentration of nearly 10 mM. Thus, small dose rates produced significant reagent accumulation within the eddies, but not in the bulk.

Figure 3.

Frequency dependence of predicted (Upper) and measured (Lower) reagent concentrations for mass-transfer-limited dosing from a cylindrical electrode. Experimental concentration images were acquired by using imaging Raman spectroscopy in 25 mM ferricyanide and ferrocyanide solution supported with 1 M NaOH. An illumination shadow does not allow imaging behind the electrode. The gray scale is defined in the text.

It is useful to consider the parameter space where the flow and transport traits seen in Figs. 2 and 3 are displayed. The nondimensional frequency, M², dictates eddy size when driven by small-amplitude oscillations (22–26). The size of the inner eddy increases dramatically as M² decreases below ≈50, so in confined flows, the inner eddy can displace much of the “bulk” solution (22, 25). Because it is desirable to have a microscopic eddy within a larger bulk fluid, it is necessary to operate at values of M² ≥ 50. However, in the limit ɛ²M² ≫ 1, a transition is made to a jetting flow regime that lacks useful eddies (29, 30). When a reagent is dosed from the cylinder surface, achieving a nearly uniform concentration within the eddy core requires convection to be fast compared with molecular diffusion; this constraint is satisfied when ɛ²ν/D ≫ 1 (ν/D ≈ 2,200 here), where D is the reagent diffusivity (26).

Raman point measurements of concentration within the well-mixed core of an eddy provide better signal-to-noise than is possible in images, allowing quantitative characterization of these microchemical traps. The dependence of the eddy core concentration is most easily predicted by using a steady-state mass-transfer model that integrates the flux across the dividing streamline to obtain a time and spatially averaged convective-diffusive mass-transfer coefficient, k_ds. At steady state, the electrochemical ferricyanide dosing rate, I/F, equals the integrated rate that mass leaves the eddy by diffusion across the dividing streamline,

where I is the applied current, F is Faraday's constant, A_c is the area of the cylinder, [Fe⁺³]_Eddy is the ferricyanide concentration in the well-mixed core of the eddy, and [Fe⁺³]_Bulk is the bulk ferricyanide concentration. For a given electrolyte, the dividing streamline mass transfer coefficient (k_ds) depends on ɛ and M (26). If ɛ and M are held constant, then the difference in composition between the eddy and the bulk electrolyte will linearly depend on the dosing rate. Fig. 4 shows families of curves at fixed frequency (M² = 100) for ferricyanide concentration difference as a function of electrochemical dosing rate and acoustic displacement amplitude. As expected, for any given amplitude, the concentration difference increases linearly with dosing rate. Increasing the acoustic amplitude (ɛ) leads to larger k_ds, (26), with reagent diffusing more readily across the dividing streamline, owing to its thinner convective-diffusive boundary layer. Thus, for any given dosing rate, an increase in k_ds reduces the eddy's ability to accumulate reagent. Overall, Fig. 4 shows that acoustic eddies can be used to spatially isolate appreciable concentrations of dosed species in a small volume; that is, millimolar concentrations are easily achieved at nmol/s dosing rates. Acoustic amplitude and dosing rate can be used to control the concentration over a wide range, for any given eddy size (set by M²).

Figure 4.

Experimental control of eddy concentration using reagent dosing rate and acoustic oscillation amplitude at fixed frequency (M² = 100). Ferricyanide concentration differences between the electrode eddy and bulk solution ([Fe⁺³]_Eddy − [Fe⁺³]_Bulk) were measured with Raman spectroscopy during galvanostatic dosing in 50 mM ferricyanide and ferrocyanide solutions supported by 1 M NaOH. Error bars represent one standard deviation for three replicate concentration measurements within the eddy.

The results in Fig. 4 suggest that very low amplitudes lead to the most concentrated microchemical traps. However, as the amplitude of the acoustic oscillation decreases, the strength of the acoustic streaming flow drops quadratically. Too low an amplitude results in flow instabilities because of buoyancy effects and also risks violating the constraint needed for a well-mixed eddy (ɛ²ν/D ≫ 1). For example, under the highest dosing rates in Fig. 4, buoyancy effects can be observed in particle imaging and concentration measurements when the amplitude is ɛ ≤ 0.1 (not shown).

Implications and Concluding Remarks

We have demonstrated that acoustic streaming provides a distinctly different approach to manipulating flow and chemical composition at a microscopic level, without microfabrication or continuous flow streams. The small eddies next to an electrode (or other dosing source) accumulate reagents and serve as microchemical traps. The recirculating flow leads to a steady-state reagent distribution different from a classic boundary layer in noncirculating flows, in that, a well-mixed region of nearly uniform composition can form within the eddy core (when the flow and transport constraints described above are met). Thus, the results presented here describe a well-mixed “container” of readily modified reagent concentration.

We are now exploring the use of these microchemical traps for carrying out small volume homogeneous reactions as well as chemical treatment of objects trapped in the eddy flow. For example, when one reagent needed for a homogeneous reaction is present in the bulk solution and the other is dosed from the cylinder, the eddy core is the only place where both reagents can coexist at significant concentrations. Measurement of the reagent or product concentrations in the eddy can be used to determine homogeneous reaction rate constants. Moreover, the control of reagent composition displayed in Fig. 4 permits systematic tuning of the eddy composition, with the possibility of rapid determination of reaction rate laws. We are currently using this approach to quantify the antioxidant properties of vitamin C. Further, the ability to hydrodynamically trap and hold small objects (e.g., 10-μm silica particles in Fig. 2) within an easily controlled local (and rather uniform) chemical environment suggests application of acoustic flows to catch, chemically treat, and release motile cells. In short, the integration of the methods described here with existing microfluidic systems offers flexibility to select and chemically treat small objects in individually tailored microchemical environments.