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Electrokinetic generation of temporally and spatially stable concentration gradients in microchannels
Journal of Colloid and Interface Science 288 (2005) 606–615 www.elsevier.com/locate/jcis
Electrokinetic generation of temporally and spatially stable concentration gradients in microchannels Elaine Biddiss, Dongqing Li ∗ Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON, Canada M5S 3G8 Received 4 January 2005; accepted 10 March 2005 Available online 12 April 2005
Abstract Generating stable microscale concentration gradients is key to numerous biological and chemical analyses. Microfluidic systems offer the ability to maintain laminar fluid diffusion interfaces ideal for the production of temporally stable concentration gradients. Previous efforts have focused on pressure driven flows and have relied on networks of branching channels to create streams of varying concentrations which can subsequently be combined to form the desired gradients. In this study, we numerically and experimentally demonstrate a novel electrokinetic technique which utilizes applied voltages and surface charge heterogeneity in simpler channel geometries to control and manipulate microscale concentration gradients without the need for parallel lamination. Flow rates ranged from 30 to 460 nl min−1 for Péclet numbers between 70 and 1100. Spatial stability of 0.6 mm or greater was obtained for a wide range of gradient shapes and magnitudes over lateral dimensions of 400–450 µm. Sensitivity analysis determined that this technique is largely independent of channel depth and species electrophoretic mobility, however channel width and the diffusion coefficient of the analyte are critical. It was concluded that by adjusting applied voltages and/or channel width, this approach to concentration gradient generation can be adapted to a wide range of applications. 2005 Elsevier Inc. All rights reserved. Keywords: Electrokinetics; Microfluidics; Concentration gradient
1. Introduction En route to the development of a functional set of miniaturized tools to succeed their lab-sized counterparts, is the challenge of creating temporally and spatially stable concentration gradients suitable for chemical and biological analyses on lab-on-a-chip devices. Generation of manageable concentration gradients, both substrate bound and in solution, is necessary for the exploration of numerous biological processes such as chemotaxis [1–4], neuron growth and axon specification [5,6], not to mention various chemical processes such as directional crystal growth [7]. The inherently laminar nature of microfluidics renders it particularly suited to the task of generating stable gradients, while offering additional benefits such as reduced analysis time, * Corresponding author. Fax: +1 416 978 7753.
E-mail addresses: [email protected] (E. Biddiss), [email protected] (D. Li). 0021-9797/$ – see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2005.03.037
consumption of reagents and production of possibly harmful byproducts, together with improvements in resolution, portability, not to mention decreased cost of manufacture, operation and disposal. Early efforts to microscopically observe the effects of naturally formed concentration gradients, as in in vivo cellular responses, were challenged by the inability to control gradients and specimens effectively, in conjunction with the difficulty of distinguishing between concentration induced effects and those of alternate stimulants such as convection, contact guidance or random motion [3]. This led to the development of a variety of techniques for the generation of isolated concentration gradients in vitro including, most notably, filter membrane chambers such as the Boyden [8], the Dunn [9], and the Ebrahimzadeh et al. [1], as well as a multitude of gel and assay techniques [10–12]. Common amongst the majority of these techniques is the application of diffusive mechanisms through a medium, emanating from a concentrated and static solid or liquid source. The
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ability to maintain spatially and temporally stable concentration profiles by these techniques, however, is plagued by the presence of strong convection currents which accompany the diffusive mechanisms. In addition, control of gradient shapes and magnitudes often proves insufficient and difficult to quantify. Microfluidic-based devices capitalize on their inherently laminar flow characteristics in order to maintain spatially and temporally stable gradients. One such device proposed by Dertinger et al. [13,14] consists of a branching network of serpentine channels used to create streams of varying concentrations which are subsequently used to form gradients of assorted shapes. Spatial stability over 800 µm with minimal diffusional blurring was realized for lateral dimensions of 900 to 2200 µm for pressure driven flows with velocities from 0.8 to 1.2 mm s−1 [14]. This device has since been used in studies of neutrophil chemotaxis [15] and axonal specification of neurons [16]. Holden et al. [17,18] presented an alternative microfluidic diffusion diluter (µDD) based on a Y-shaped channel, which similarly to the above-described device, also creates streams of varying concentrations. This technique, however, employed a less complex geometry and minimized the amount of sample required in comparison to the Dertinger et al. method, which is characterized by high flowrates, long channel lengths and significant dead volumes [17]. The pressure-driven flows through the µDD ranged between 50 and 500 nl min−1 . The concentrations of the resulting diluted streams were effectively controlled by varying the flow rate. The ability to construct complex and stable gradients from these streams, however, was not demonstrated, and overall the Dertinger approach enables greater flexibility in the creation of gradients. Both the above-described devices incorporate parallel lamination to create streams of varied concentrations from which gradients can be formed. This technique introduces a significant flow resistance which, although surmountable in pressure-driven flows, may not be conducive to electrokinetically driven flows [19]. For lab-on-a-chip applications where electrokinetically driven flow is preferable, either for ease of implementation and flow control or for elimination of large, external piping and pumping devices, an alternate method of generating concentration gradients is required. Control of electrokinetic flows has been well demonstrated by management of key factors including channel geometry, applied voltages, and surface charge properties through which filtration [20], directional control [21,22] and enhanced mixing [23–31] have been realized. This study proposes to incorporate these tools in a novel microfluidic approach for the creation of stable electrokinetic concentration gradients in microchannels. Specifically, simple channel geometries will be exploited to generate both linear and parabolic gradients in T-shaped (2 inlets) and fork-shaped (3 inlets) microchannels, respectively. Furthermore, it will be demonstrated that the magnitude of these concentration gradients can be controlled conveniently by altering the ap-
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plied voltages and downstream distances. Lastly, a method for selectively patterning positively charged molecules onto the negatively charged channel wall in order to promote flow disruption caused by potential differences between oppositely charged regions, is presented as an additional means by which to control concentration gradients. The following will demonstrate the ability to manipulate electrokinetically generated concentration gradients and will characterize their spatial stability using both numerical and experimental analysis. Sensitivity of the generated concentration gradients to parameters such as channel width and depth, together with analyte properties, such as the diffusion coefficient, will also be explored.
2. Experimental 2.1. Chemicals and materials Positive masters were constructed by exposing SU-8 25 negative photoresist (MicroChem, Newton, MA) and developing in 4-hydroxy-4-methyl-2-pentanone (Fluka Chemie, Messerschmittstr). Microchannels were fabricated from polydimethylsiloxane (PDMS) using a Sylgard 184 silicone elastomer kit (Dow Corning, Midland, MI) with an elastomer to curing agent ratio of 20:1 to obtain improved sealing of the PDMS with glass. All solutions were prepared using de-ionized filtered water (Fischer Scientific, ON, Canada). Surface charge heterogeneities were selectively patterned using a positively charged polymer solution of 5% (by mass) polybrene (1,5dimethyl-1, 5-diazaundecamethylene polymethobromide, hexadimethrine bromide) dissolved in water. Glass surfaces were prepared by flushing with 0.1 M sodium hydroxide prior to polybrene coating and rinsed with de-ionized water subsequently. Sodium bicarbonate, 1 M, and sodium carbonate, 1 M, were combined in equal ratio to form a sodium carbonate/bicarbonate buffer with an ionic strength, I = 0.05 and pH = 9.0. The buffer was diluted with water to 25 mM. For fluorescent imaging, fluorescein was dissolved with 25 mM buffer to a concentration of 100 µM. Solutions were filtered with 0.2 µm pore size syringe filters prior to use. 2.2. Microchannel fabrication Microchannels were fabricated using a rapid prototyping/ soft-lithography technique [32]. Specifically, photomasks were designed in AutoCAD, exported as PDF files, and printed on a 3500 dpi image setter (UTPress, Toronto, ON). Fig. 1 indicates the microchannel geometry for (a) a Tshaped channel, 450 µm in width and (b) a fork-shaped channel, 400 µm in width. Glass slides were soaked overnight in acetone, dried on a hot plate at 200 ◦ C, exposed to oxygen plasma (Harrick Plasma Cleaner model PDC-32G) for 5 min and again heated to 200 ◦ C subsequently, in order to
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Fig. 1. Microchannel geometry for (a) a T-shaped channel, 450 µm in width and (b) a fork-shaped channel, 400 µm in width. Inlet channels are approximately 7.5 mm in length and mixing channels, 30 mm in length. Channel depths are approximately 8 µm.
prepare the surface for coating. 1.5 ml of SU-8 25 photoresist was then distributed onto each slide and degassed in a high vacuum. The photoresist was spin-coated at 1800 rpm for 10 s, and at 4000 rpm for 40 s with a ramping phase of 5 s between stages in order to obtain a smooth film with a thickness of 8 µm (Special Coating System Spin Coat model G3P-8). Films were baked at 65 ◦ C for 3 min and at 95 ◦ C for 7 min to harden. The photomasks were positioned on the photoresist films and exposed to UV light for 1 min. A twostage post-exposure bake at 65 ◦ C for 1 min and 95 ◦ C for 2 min was then conducted. Masters were developed in 4hydroxy-4-methyl-2-pentanone for approximately 2 min or until the photoresist rinsed cleanly off. Subsequent to developing, masters were placed under a heat lamp for several hours. To form the microchannels, PDMS was poured over the masters and cured at 65 ◦ C for approximately 2 h at a pressure of −34 kPa (gauge). Silanization of the masters was not necessary as the PDMS casts did not adhere to the hardened photoresist. 2.3. Surface charge patterning The rapid prototyping/soft lithography technique as described in the previous section allowed for control of and flexibility in surface charge patterning configurations, examples of which are detailed in Fig. 2. To selectively pattern the surface charge heterogeneity, the following procedure was followed as presented previously [23]. The PDMS master, featuring a channel configuration corresponding with the pattern of heterogeneities to be examined, was reversibly sealed to a glass slide. Using a plastic syringe to induce
Fig. 2. Examples of surface charge patterning configurations in the heterogeneous T-channel with patch width w, for (a) a single centered stripe, (b) an off-centered stripe, (c) two stripes aligned with the channel wall, (f) two stripes positioned symmetrically within the channel, and (e) three stripes asymmetrically positioned within the channel. The dark regions indicate the polybrene coated surface.
suction with an approximate flow rate of 2.5 ml min−1 , the PDMS master was flushed sequentially with 0.1 M sodium hydroxide for 2 min, de-ionized water for 4 min, and 5% polybrene solution for 2 min, resulting in selective regions of positive surface charge while leaving the majority of the glass slide with its native negative charge. This polyelectrolyte coating procedure is based on that developed by Liu et al. [33] for capillary electrophoresis microchips. All fluid was then removed from the channel and the system was left undisturbed for 40 min before flushing again with water for 20 min. The slide was aged in air for 24 h prior to use. Before removing the PDMS master, the location of the heterogeneities was landmarked. The appropriate microchannel was then permanently sealed to the glass slide such that the patterned surface heterogeneities were appropriately positioned within the mixing channel. 2.4. Electroosmotic mobility measurements Using the well-established current monitoring technique [34], the zeta potentials of the native-oxidized PDMS and the polybrene-coated surface were determined using a sodium carbonate/bicarbonate buffer of pH 9.0. Briefly, a dilute buffer was introduced into a uniaxial PDMS channel with the surface treatment of interest. The current was monitored and allowed to stabilize under a constant applied voltage. A concentrated buffer was then introduced through one reservoir and the time required for the current to reach a new plateau corresponding to the higher concentration of buffer was recorded. The electroosmotic mobility of the native-oxidized PDMS was determined to be −5.9 × 10−4 cm2 V−1 s−1 (zeta-potential of −83 mV) compared with 2.3 × 10−4 cm2 V−1 s−1 (zeta-potential of 33 mV) for the polybrene-coated surface, results that compared well with previous findings [33]. Electroosmotic mobilities were measured over a period of 8 h. Following an initial decay within the first 3 to 4 h subsequent to coating, the electroosmotic mobilities and therefore the surface charge acquired by the PDMS channel remained virtually constant. 2.5. Image acquisition and processing The concentration gradients, formed perpendicular to the flow direction by the interaction of fluorescein and buffer streams introduced through different inlet channels, were then examined in the T-shaped and fork-shaped microfluidic chips with and without surface charge patterning. To generate the gradients, 25 mM sodium carbonate/bicarbonate buffer and 100 µM fluorescein were introduced through different inlet channels and a voltage potential was created by means of platinum electrodes inserted into the centre of each reservoir. The system was illuminated by a mercury arc lamp equipped with a fluorescein filter set. The steady state transport of the dye was observed using a Leica DM LM fluorescence microscope with a 5× objective, and captured using a Retiga 12-bit cooled CCD camera. Digital images
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were obtained by QCapture 1394 and OpenLab 3.1.5 imaging software at an exposure time of 1 s. The acquired images were of resolution 1280 × 1024 pixels with each pixel representing a 2.5 µm2 in the object plane. Images were exported in TIF format to MATLAB for digital processing. Dark field subtraction and bright field normalization were performed to eliminate anomalies introduced by the image acquisition system. Following image processing, concentration profiles were developed directly from values of pixel intensities for varying downstream distances. Profiles were smoothed using a convolution filter and linearly scaled to range between 0 and 1.
3. Results and discussion The goal of this study was to develop a novel method of producing and controlling stable, microscale concentration gradients for electrokinetic applications. PDMS microfluidic systems as developed herein enable experimental flexibility at a low cost both in terms of time and money. A trade-off in long-term durability of the system is encountered due to the tendency of plasma-treated PDMS to return to its native state when exposed to air and solvents. In certain applications in which long-term durability is of importance, different manufacturing processes from those presented in this paper may be required. Conceptually however, the ability to manipulate concentration gradients using surface charge heterogeneity is transferable regardless of fabrication techniques. To experimentally demonstrate the potential of surface charge heterogeneity in gradient creation, gradients were created in simple channel geometries and controlled by varying applied voltages and surface charge patterning. The BLOCS (BioLab-On-a-Chip Simulation) finite element code [24,35,36] was adapted to simulate the experimental conditions and sur-
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face charge heterogeneity. Specifically, channel dimensions for the T- and fork-shaped channels were modeled along with the physiochemical properties of fluorescein, namely a diffusion coefficient D = 4.37 × 10−10 m2 s−1 , and an electrophoretic mobility µep = 3.3 × 10−8 m2 V−1 s−1 . Numerical models were validated experimentally and used to support further analyses of gradient variability and stability. 3.1. Control of developed gradients An essential feature of an efficient gradient generator is the ability to vary shapes and magnitudes effectively. One means of accomplishing this is through channel geometry. Cliff gradients were developed perpendicular to the flow direction within the T-shaped channel while hill gradients were created within the fork-shaped channel (Figs. 3 and 4). Gradient shapes could be mirrored by introducing the buffer and fluorescein solutions through opposite channel inlets. Therefore in the case of the fork-shaped channel, a hill gradient was obtained when fluorescein was introduced through the central inlet, whereas a valley gradient was generated when the fluorescein entered by way of the peripheral inlets. Velocities varied between 0.1 and 2.4 mm s−1 for potentials between 27 and 405 V cm−1 resulting in flow rates of 30 to 460 nl min−1 with Péclet numbers between 70 and 1100 and Reynolds numbers between 0.03 and 0.5. For a given channel geometry and in the absence of surface charge heterogeneity, the magnitudes of generated gradients could be controlled by two parameters: (a) downstream distance and (b) applied voltage. Diffusion over distances on the order of millimeters in a 400 µm microchannel will significantly alter the concentration profile. Therefore, for a given microchannel and applied voltage, significantly different concentration gradients may be generated at dif-
Fig. 3. Experimental and numerical analysis of concentration gradients formed in a 450 µm T-channel for varying potentials. Experimentally (dotted lines) and numerically (solid lines) derived concentration profiles were plotted in (a) for an applied potential of 27 V cm−1 at (A) 400 µm downstream and (B) 4000 µm downstream, and for a potential of 68 V cm−1 at downstream distances of (C) 400 and (D) 4000 µm, and lastly for a potential of 405 V cm−1 at (E) 400 µm downstream. Fluorescence images are presented in (b) for an applied voltage of 27 V cm−1 between 3800 and 4600 µm downstream and in (c) for an applied voltage of 405 V cm−1 between 200 and 1000 µm downstream with labeled dotted lines corresponding to the gradients as plotted in (a).
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Fig. 4. Experimental and numerical analysis of concentration gradients formed in a 400 µm fork-shaped channel for varying potentials. Experimentally (dotted lines) and numerically (solid lines) derived concentration profiles were plotted in (a) for an applied potential of 27 V cm−1 at (A) 400 and (B) 4000 µm downstream and for an applied potential of 405 V cm−1 at (C) 400 and (D) 4000 µm downstream. Fluorescence images are presented in (b) for an applied voltage of 27 V cm−1 and in (c) for an applied voltage of 405 V cm−1 between 200 and 1000 µm downstream with labeled dotted lines corresponding to the gradients as plotted in (a).
Fig. 5. Numerical concentration profiles across the channel width for a homogeneous fork-shaped channel of 400 µm in width for (a) a center inlet voltage of Vapp and peripheral inlet voltages of 95% Vapp at (A) 600, (B) 2000, and (C) 4000 µm, and for (b) a center inlet voltage of 95% Vapp and outside peripheral inlet voltages of Vapp (D) 300, (E) 600, and (F) 2000 µm. In both cases, Vapp = 405 V cm−1 .
ferent downstream distances that are suitable for analyses provided that spatial stability on the order of a millimeter is sufficient and downstream channel length is not the defining constraint. The second method of controlling gradients shapes and magnitudes is through the applied voltages. Increasing potentials will render steeper gradients while decreasing voltages will produce more gradual gradients due to increased diffusion. Figs. 3 and 4 illustrate the variety of gradients that can be obtained by varying downstream distance and/or voltages for the T-shaped channel and for the fork-shaped channel respectively. In the preceding cases, the voltage at each of the channel inlets was maintained equal. However, by varying the inlet voltages, the gradient shapes and magnitudes may be further manipulated and the element of asymmetry introduced. Fig. 5 depicts the distinct profiles obtained by applying dif-
ferent voltages at different inlets of the fork-shaped channel. Evidently, a higher voltage applied to the central inlet containing the fluorescein will result in a hill gradient of higher concentration with a flattened top as the potential pumping fluorescein into the channel is proportionally larger. Conversely, a lower voltage applied to the central inlet will result in more peaked gradients of smaller magnitudes as the buffer is the predominant solution present in the channel. Pursuing this tactic further will enable the generation of asymmetric gradients in both the fork- and T-shaped channels. Fig. 6 illustrates this for a T-shaped channel with the fluorescein driving potential at 95% of that of the buffer. Fig. 7 illustrates asymmetry in a fork-shaped channel where the right peripheral buffer containing inlet voltage is 95% of remaining two inlets. Evidently, the symmetry of the developed concentration gradients can be directly controlled by varying
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the individual driving potentials of the buffer and fluorescein streams within the microchannel. Furthermore, by varying applied voltages and/or downstream distances, it is possible to customize the concentration gradient’s shape, magnitude and symmetry as generated within the microchannel. An additional method for customizing concentration gradients is by the introduction of charge heterogeneity on the microchannel’s surface. By selectively patterning regions of charge which oppose the bulk flow and cause local flow circulation and “bending” of flow streams, additional profiles above and beyond those of the cliff- and hill-shaped, can be obtained. For example, by selectively patterning a stripe of positive charge down the centre of the predominantly negatively charged channel surface, a more linear gradient than that observed in the homogeneously charged T-channel can be obtained and again varied by voltage. A slight flattening
Fig. 6. Numerical concentration profiles across the channel width for a homogeneous T-channel, 450 µm in width, with a potential of Vapp applied to the left inlet and a potential of 95% of Vapp applied to the right inlet for Vapp = 68 V cm−1 at (A) 400 and (B) 6000 µm and for Vapp = 405 V cm−1 (C) 400 and (D) 6000 µm. The adjoining fluorescent image is for Vapp = 68 V cm−1 .
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of this gradient is observed in the proximity of the channel walls. This non-linearity however is contained typically within 25 µm of the wall in a 450 µm channel. Fig. 8 depicts the experimental and numerical results for a 200 µm wide strip in a 450 µm T-channel. Experimentally, small deviations from linearity were observed particularly at higher voltage potentials. These deviations are believed to result from limitations of manufacturing processes as opposed to the overall technique which was numerically demonstrated. Surface patterning was conducted by hand in lieu of precise, automated equipment operating in a clean room environment. With improved manufacturing processes, it may be possible to achieve greater experimental linearity if that demonstrated is not adequate. By incorporating multiple strips, both in symmetrical and asymmetrical configurations, a large variety of shapes can be obtained as illustrated in Fig. 9. By these means concen-
Fig. 7. Numerical concentration profiles across the channel width for a homogeneous fork-shaped channel, 400 µm in width, with a potential of Vapp applied to the right inlet and center inlet and a potential of 95% of Vapp applied to the left inlet for Vapp = 405 V cm−1 at (A) 400, (B) 2000, and (C) 7000 µm presented along with the corresponding fluorescent image.
Fig. 8. Experimental (dotted lines) and numerical (solid lines) concentration gradients formed in a 450 µm T-shaped channel with a 200 µm wide stripe of positive charge down the centre of the predominantly negatively charged channel bottom surface plotted in (a) at a downstream distance of 4000 µm for (A) 27, (B) 68, and (C) 405 V cm−1 . Fluorescence images are presented in (b) for an applied potential of 27 V cm−1 between 200 and 1000 µm downstream and in (c) for an applied voltage of 405 V cm−1 between 200 and 1000 µm downstream with labeled dotted lines corresponding to the gradients as plotted in (a).
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Fig. 9. Numerical concentration gradients developed by introducing varying surface charge patterning configuration into a 400 µm T-shaped channel with an applied potential of 810 V cm−1 at a downstream distance of 2400 µm for (A) a single centered stripe (Fig. 2a), 300 µm in width, (B) a single asymmetrical stripe (Fig. 2b), 50 µm wide and offset 125 µm left of the center of the channel, (C) two stripes (Fig. 2c), 80 µm in width situated along the channel walls, (D) two stripes (Fig. 2d), 80 µm in width, situated 120 µm to either side of the channel center, and (E) three asymmetrical stripes (Fig. 2e), each 50 µm in width. The fluorescent images corresponding to (A)–(E) are also presented.
tration gradients can be shifted to create asymmetry while maintaining constant applied voltages (Fig. 9B). Secondly, the extremities of gradients at the channel walls may be flattened and extended (Fig. 9C). Lastly, local maximums and minimums can be introduced (Fig. 9D), leading to the creation of increasingly complex and customized gradients (Fig. 9E). Magnitudes of gradients formed using surface charge heterogeneity are directly linked to the relative surface area patterned by the opposite charge. Specifically, a large ratio of positive to negative surface charge will result in slower fluid velocities, increased mixing, and hence, more uniform gradients, whereas a smaller ratio will maintain higher levels of concentrated fluids. One limitation to the use of surface charge patterning its incompatibility for applications where surface bound gradients are required as the polyelectrolyte coating may interfere with bonding reactions. However, for applications where gradients are required in solution such as chemotaxis [1–4], neuron growth and axon specification [5,6], not to mention various chemical processes such as directional crystal growth [7], this technique offers additional flexibility and control of concentration gradients. Overall, effective control of electrokinetic concentration gradients’ shapes and magnitudes is achievable using simple microchannel configurations. Altering voltages and/or downstream distances yields a large variety of cliff- and hill-shaped gradients. Through further application of surface charge patterning, more linear and customized gradients may also be obtained while maintaining the simplicity and reliability of the microfluidic system. 3.2. Stability of developed gradients The generation of microscale concentration gradients requires both temporal and spatial stability in order to be pertinent for biological and chemical analyses. As the flow sys-
tem operates at steady state, temporal stability is ensured and gradients can be sustained indefinitely provided that the fluid supply is maintained and the voltage source is steady. Joule heating was not observed to be problematic for the range of voltages applied (27–405 V cm−1 ). This is because the high thermal conductivity of the glass channel base allowed for adequate heat transfer from the system, as discussed in previous studies of joule heating conducted by Erickson et al. [9]. The spatial stability (i.e. the downstream distance for which the gradient remains approximately constant) of generated gradients was analyzed numerically for a variety of downstream distances and applied voltages. As expected, greater spatial stability was obtained firstly, at higher voltages and secondly, at increasing downstream distances, due to lowered diffusive flux. In the first case, greater fluid velocities induced by higher potentials reduced the time available for diffusive mechanisms, thereby extending the downstream distance for which the gradient remained approximately constant. In the latter case at increasing downstream distances, local concentration gradients were increasingly more uniform and thus, the driving flux induced diffusion was weaker, which again resulted in greater spatial stability for the developed gradients. For low potentials (<30 V cm−1 ), spatial stability is limited at downstream distances very close to the intersection (<1000 µm). This obstacle can be overcome simply by avoiding excessively low potentials and using a higher voltage at a greater downstream channel length to obtain more uniform gradients. This is illustrated in Fig. 10 for the fork-shaped channel in which a range of gradients are obtained with good spatial stability over a distance of 600 µm while maintaining applied voltages greater than 135 V cm−1 . Spatial stability of gradients generated in the homogeneous and heterogeneous T-channels was comparable or greater than that of the homogeneous fork-shaped channels and exhibited the same trends
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Fig. 10. Numerical profiles depicting concentration gradient stability over a distance of 600 µm in a homogeneous fork-shaped channel, 400 µm in width for an applied potential of 405 V cm−1 at (A) 400, (B) 4000, and (C) 7000 µm and for an applied potential of 135 V cm−1 at (D) 4000 µm, and (E) 7000 µm. Dotted lines indicate the corresponding concentration gradients developed 600 µm downstream from gradients (A)–(E).
with regard to applied voltages and downstream distances. An additional method by which increased spatial stability may be obtained without sacrificing the performance of the gradient generator is by increasing the channel width. This will be discussed further in the following section. 3.3. Sensitivity of developed gradients To assess the suitability of this technique of generating concentration gradients for a wide range of chemical and biological applications, numerical analysis was conducted to determine its sensitivity to species characteristics such as the diffusion coefficient and electrophoretic mobility. In addition, the dependence of gradient shapes and magnitudes on microchannel geometry, specifically channel depth and width, was also investigated.
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3.3.1. Channel geometry Numerical analysis was conducted to ascertain the sensitivity of the developed concentration gradient generator on channel depth and width. It was found that a 10-fold increase in channel depth resulted in negligible changes in gradient shape and magnitudes for varying voltages and downstream distances (Fig. 11a). Previous studies of flows in the presence of heterogeneous surface charge also indicated that channel depth was not a predominant factor affecting flow characteristics and concentrations [23]. Therefore, it was concluded that this technique is not sensitive to channel depth in microchannels with or without surface charge heterogeneity. Channel width affected the developed concentration gradients to a greater respect. Larger channel width decreases the efficiency of diffusive mechanisms, therefore gradients, especially those formed at increasing downstream distances and lower potentials, were less uniform than those formed in a channel of smaller width at an equivalent potential. In order to obtain the same range of gradients in a wider channel as in the narrower channel, lower voltages were applied. Fig. 11b illustrates that gradients of identical magnitudes over a greater channel width are obtainable for a 900 µm channel width as in a 450 µm channel width. Spatial stability was comparable even at lower potentials as the channel width and the length over which diffusion must occur was larger. At higher potentials, spatial stability was improved to over 1 mm. 3.3.2. Physiochemical properties Through numerical analysis, it was determined that the developed gradient generator was not sensitive to the electrophoretic mobility of the analyte over a range of 4 magnitudes of order. Typically, in biological and chemical analysis, analytes are negatively charged in aqueous solutions with electrophoretic mobilities within the range of those
Fig. 11. Numerical concentration gradients developed for (a) a channel depth of 8 µm (solid lines) and 80 µm (dotted lines) for varying voltages for a homogeneous T-shaped channel, 450 µm in width at a downstream distance of 1000 µm and for (b) a channel width of 450 µm (dotted lines) and 900 µm (solid lines) for varying potentials at a downstream distance of 1000 µm for a 8 µm channel depth.
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addressed in this study. For example, ssDNA has an electrophoretic mobility of 2.0 × 10−8 m2 V−1 s−1 [37], viruses such as HRV serotypes typically range from 9.6 × 10−9 to 2.27 × 10−8 m2 V−1 s−1 , while typical values for bacteria range between 2 × 10−4 and 3 × 10−8 m2 V−1 s−1 [38]. In terms of ionic strengths, this method is applicable to the typical range as used in electrokinetic applications from 10−6 to 10−2 M. Performance was however influenced by the diffusion coefficient of the analyte. Diffusion coefficients are widely variable among common biological and chemical analytes, ranging from small cells and proteins with coefficients on the order of 1 × 10−10 m2 s−1 to large DNA molecules with coefficients on the order of 1 × 10−12 m2 s−1 . Larger diffusion coefficients will lead to more uniform gradients while smaller diffusion coefficients will result in gradients of greater magnitudes. Numerical analysis determined that the developed gradient generator was easily adapted to diffusion coefficients within the biological range by altering channel width and applied voltages accordingly. This technique is not conducive to applications where the diffusion coefficient is higher than ∼1 × 10−8 m2 s−1 or lower than ∼1 × 10−13 m2 s−1 as the necessary potentials and channel widths become unreasonable for electrokinetic, microscale applications.
4. Conclusions This study aimed to develop an effective and flexible method of producing stable concentration gradients for electrokinetic lab-on-a-chip applications. By manipulating applied voltages, downstream distances and by selectively patterning an arrangement of surface charge heterogeneities, control and variability of concentration gradients was experimentally and numerically demonstrated in simple channel geometries. Cliff, hill and linear shaped gradients were developed of varying magnitudes. Asymmetrical gradients were obtained by applying unbalanced potentials. Alternatively, selective surface charge patterning could also be used to shift gradients, to create local minimums and maximums and more complex gradient shapes. Spatial stability of 600 µm or greater was achieved for lateral widths as low as 400 µm and flow rates ranging between 30 and 460 nl min−1 which corresponded to Péclet numbers between 70 and 1100 and Reynolds numbers between 0.03 and 0.5. Gradient generation was not sensitive to channel depth or electrophoretic mobility, but did depend on channel width and most significantly on the diffusion coefficient. By adjusting applied voltages and/or channel width accordingly, our numerical models, validated herein, indicate that this technique for generating concentration gradients is adaptable to a range of potential analytes typical of biological and chemical analyses.
Acknowledgments The authors gratefully acknowledge the financial support of the National Sciences and Engineering Research Council through scholarships to E. Biddiss and through a research grant to D. Li. Additionally, the authors are thankful for the financial support of the Province of Ontario and Dupont Canada for a scholarship granted to E. Biddiss.
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Electrokinetic generation of temporally and spatially stable concentration gradients in microchannels Elaine Biddiss, Dongqing Li ∗ Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON, Canada M5S 3G8 Received 4 January 2005; accepted 10 March 2005 Available online 12 April 2005
Abstract Generating stable microscale concentration gradients is key to numerous biological and chemical analyses. Microfluidic systems offer the ability to maintain laminar fluid diffusion interfaces ideal for the production of temporally stable concentration gradients. Previous efforts have focused on pressure driven flows and have relied on networks of branching channels to create streams of varying concentrations which can subsequently be combined to form the desired gradients. In this study, we numerically and experimentally demonstrate a novel electrokinetic technique which utilizes applied voltages and surface charge heterogeneity in simpler channel geometries to control and manipulate microscale concentration gradients without the need for parallel lamination. Flow rates ranged from 30 to 460 nl min−1 for Péclet numbers between 70 and 1100. Spatial stability of 0.6 mm or greater was obtained for a wide range of gradient shapes and magnitudes over lateral dimensions of 400–450 µm. Sensitivity analysis determined that this technique is largely independent of channel depth and species electrophoretic mobility, however channel width and the diffusion coefficient of the analyte are critical. It was concluded that by adjusting applied voltages and/or channel width, this approach to concentration gradient generation can be adapted to a wide range of applications. 2005 Elsevier Inc. All rights reserved. Keywords: Electrokinetics; Microfluidics; Concentration gradient
1. Introduction En route to the development of a functional set of miniaturized tools to succeed their lab-sized counterparts, is the challenge of creating temporally and spatially stable concentration gradients suitable for chemical and biological analyses on lab-on-a-chip devices. Generation of manageable concentration gradients, both substrate bound and in solution, is necessary for the exploration of numerous biological processes such as chemotaxis [1–4], neuron growth and axon specification [5,6], not to mention various chemical processes such as directional crystal growth [7]. The inherently laminar nature of microfluidics renders it particularly suited to the task of generating stable gradients, while offering additional benefits such as reduced analysis time, * Corresponding author. Fax: +1 416 978 7753.
E-mail addresses: [email protected] (E. Biddiss), [email protected] (D. Li). 0021-9797/$ – see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2005.03.037
consumption of reagents and production of possibly harmful byproducts, together with improvements in resolution, portability, not to mention decreased cost of manufacture, operation and disposal. Early efforts to microscopically observe the effects of naturally formed concentration gradients, as in in vivo cellular responses, were challenged by the inability to control gradients and specimens effectively, in conjunction with the difficulty of distinguishing between concentration induced effects and those of alternate stimulants such as convection, contact guidance or random motion [3]. This led to the development of a variety of techniques for the generation of isolated concentration gradients in vitro including, most notably, filter membrane chambers such as the Boyden [8], the Dunn [9], and the Ebrahimzadeh et al. [1], as well as a multitude of gel and assay techniques [10–12]. Common amongst the majority of these techniques is the application of diffusive mechanisms through a medium, emanating from a concentrated and static solid or liquid source. The
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ability to maintain spatially and temporally stable concentration profiles by these techniques, however, is plagued by the presence of strong convection currents which accompany the diffusive mechanisms. In addition, control of gradient shapes and magnitudes often proves insufficient and difficult to quantify. Microfluidic-based devices capitalize on their inherently laminar flow characteristics in order to maintain spatially and temporally stable gradients. One such device proposed by Dertinger et al. [13,14] consists of a branching network of serpentine channels used to create streams of varying concentrations which are subsequently used to form gradients of assorted shapes. Spatial stability over 800 µm with minimal diffusional blurring was realized for lateral dimensions of 900 to 2200 µm for pressure driven flows with velocities from 0.8 to 1.2 mm s−1 [14]. This device has since been used in studies of neutrophil chemotaxis [15] and axonal specification of neurons [16]. Holden et al. [17,18] presented an alternative microfluidic diffusion diluter (µDD) based on a Y-shaped channel, which similarly to the above-described device, also creates streams of varying concentrations. This technique, however, employed a less complex geometry and minimized the amount of sample required in comparison to the Dertinger et al. method, which is characterized by high flowrates, long channel lengths and significant dead volumes [17]. The pressure-driven flows through the µDD ranged between 50 and 500 nl min−1 . The concentrations of the resulting diluted streams were effectively controlled by varying the flow rate. The ability to construct complex and stable gradients from these streams, however, was not demonstrated, and overall the Dertinger approach enables greater flexibility in the creation of gradients. Both the above-described devices incorporate parallel lamination to create streams of varied concentrations from which gradients can be formed. This technique introduces a significant flow resistance which, although surmountable in pressure-driven flows, may not be conducive to electrokinetically driven flows [19]. For lab-on-a-chip applications where electrokinetically driven flow is preferable, either for ease of implementation and flow control or for elimination of large, external piping and pumping devices, an alternate method of generating concentration gradients is required. Control of electrokinetic flows has been well demonstrated by management of key factors including channel geometry, applied voltages, and surface charge properties through which filtration [20], directional control [21,22] and enhanced mixing [23–31] have been realized. This study proposes to incorporate these tools in a novel microfluidic approach for the creation of stable electrokinetic concentration gradients in microchannels. Specifically, simple channel geometries will be exploited to generate both linear and parabolic gradients in T-shaped (2 inlets) and fork-shaped (3 inlets) microchannels, respectively. Furthermore, it will be demonstrated that the magnitude of these concentration gradients can be controlled conveniently by altering the ap-
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plied voltages and downstream distances. Lastly, a method for selectively patterning positively charged molecules onto the negatively charged channel wall in order to promote flow disruption caused by potential differences between oppositely charged regions, is presented as an additional means by which to control concentration gradients. The following will demonstrate the ability to manipulate electrokinetically generated concentration gradients and will characterize their spatial stability using both numerical and experimental analysis. Sensitivity of the generated concentration gradients to parameters such as channel width and depth, together with analyte properties, such as the diffusion coefficient, will also be explored.
2. Experimental 2.1. Chemicals and materials Positive masters were constructed by exposing SU-8 25 negative photoresist (MicroChem, Newton, MA) and developing in 4-hydroxy-4-methyl-2-pentanone (Fluka Chemie, Messerschmittstr). Microchannels were fabricated from polydimethylsiloxane (PDMS) using a Sylgard 184 silicone elastomer kit (Dow Corning, Midland, MI) with an elastomer to curing agent ratio of 20:1 to obtain improved sealing of the PDMS with glass. All solutions were prepared using de-ionized filtered water (Fischer Scientific, ON, Canada). Surface charge heterogeneities were selectively patterned using a positively charged polymer solution of 5% (by mass) polybrene (1,5dimethyl-1, 5-diazaundecamethylene polymethobromide, hexadimethrine bromide) dissolved in water. Glass surfaces were prepared by flushing with 0.1 M sodium hydroxide prior to polybrene coating and rinsed with de-ionized water subsequently. Sodium bicarbonate, 1 M, and sodium carbonate, 1 M, were combined in equal ratio to form a sodium carbonate/bicarbonate buffer with an ionic strength, I = 0.05 and pH = 9.0. The buffer was diluted with water to 25 mM. For fluorescent imaging, fluorescein was dissolved with 25 mM buffer to a concentration of 100 µM. Solutions were filtered with 0.2 µm pore size syringe filters prior to use. 2.2. Microchannel fabrication Microchannels were fabricated using a rapid prototyping/ soft-lithography technique [32]. Specifically, photomasks were designed in AutoCAD, exported as PDF files, and printed on a 3500 dpi image setter (UTPress, Toronto, ON). Fig. 1 indicates the microchannel geometry for (a) a Tshaped channel, 450 µm in width and (b) a fork-shaped channel, 400 µm in width. Glass slides were soaked overnight in acetone, dried on a hot plate at 200 ◦ C, exposed to oxygen plasma (Harrick Plasma Cleaner model PDC-32G) for 5 min and again heated to 200 ◦ C subsequently, in order to
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Fig. 1. Microchannel geometry for (a) a T-shaped channel, 450 µm in width and (b) a fork-shaped channel, 400 µm in width. Inlet channels are approximately 7.5 mm in length and mixing channels, 30 mm in length. Channel depths are approximately 8 µm.
prepare the surface for coating. 1.5 ml of SU-8 25 photoresist was then distributed onto each slide and degassed in a high vacuum. The photoresist was spin-coated at 1800 rpm for 10 s, and at 4000 rpm for 40 s with a ramping phase of 5 s between stages in order to obtain a smooth film with a thickness of 8 µm (Special Coating System Spin Coat model G3P-8). Films were baked at 65 ◦ C for 3 min and at 95 ◦ C for 7 min to harden. The photomasks were positioned on the photoresist films and exposed to UV light for 1 min. A twostage post-exposure bake at 65 ◦ C for 1 min and 95 ◦ C for 2 min was then conducted. Masters were developed in 4hydroxy-4-methyl-2-pentanone for approximately 2 min or until the photoresist rinsed cleanly off. Subsequent to developing, masters were placed under a heat lamp for several hours. To form the microchannels, PDMS was poured over the masters and cured at 65 ◦ C for approximately 2 h at a pressure of −34 kPa (gauge). Silanization of the masters was not necessary as the PDMS casts did not adhere to the hardened photoresist. 2.3. Surface charge patterning The rapid prototyping/soft lithography technique as described in the previous section allowed for control of and flexibility in surface charge patterning configurations, examples of which are detailed in Fig. 2. To selectively pattern the surface charge heterogeneity, the following procedure was followed as presented previously [23]. The PDMS master, featuring a channel configuration corresponding with the pattern of heterogeneities to be examined, was reversibly sealed to a glass slide. Using a plastic syringe to induce
Fig. 2. Examples of surface charge patterning configurations in the heterogeneous T-channel with patch width w, for (a) a single centered stripe, (b) an off-centered stripe, (c) two stripes aligned with the channel wall, (f) two stripes positioned symmetrically within the channel, and (e) three stripes asymmetrically positioned within the channel. The dark regions indicate the polybrene coated surface.
suction with an approximate flow rate of 2.5 ml min−1 , the PDMS master was flushed sequentially with 0.1 M sodium hydroxide for 2 min, de-ionized water for 4 min, and 5% polybrene solution for 2 min, resulting in selective regions of positive surface charge while leaving the majority of the glass slide with its native negative charge. This polyelectrolyte coating procedure is based on that developed by Liu et al. [33] for capillary electrophoresis microchips. All fluid was then removed from the channel and the system was left undisturbed for 40 min before flushing again with water for 20 min. The slide was aged in air for 24 h prior to use. Before removing the PDMS master, the location of the heterogeneities was landmarked. The appropriate microchannel was then permanently sealed to the glass slide such that the patterned surface heterogeneities were appropriately positioned within the mixing channel. 2.4. Electroosmotic mobility measurements Using the well-established current monitoring technique [34], the zeta potentials of the native-oxidized PDMS and the polybrene-coated surface were determined using a sodium carbonate/bicarbonate buffer of pH 9.0. Briefly, a dilute buffer was introduced into a uniaxial PDMS channel with the surface treatment of interest. The current was monitored and allowed to stabilize under a constant applied voltage. A concentrated buffer was then introduced through one reservoir and the time required for the current to reach a new plateau corresponding to the higher concentration of buffer was recorded. The electroosmotic mobility of the native-oxidized PDMS was determined to be −5.9 × 10−4 cm2 V−1 s−1 (zeta-potential of −83 mV) compared with 2.3 × 10−4 cm2 V−1 s−1 (zeta-potential of 33 mV) for the polybrene-coated surface, results that compared well with previous findings [33]. Electroosmotic mobilities were measured over a period of 8 h. Following an initial decay within the first 3 to 4 h subsequent to coating, the electroosmotic mobilities and therefore the surface charge acquired by the PDMS channel remained virtually constant. 2.5. Image acquisition and processing The concentration gradients, formed perpendicular to the flow direction by the interaction of fluorescein and buffer streams introduced through different inlet channels, were then examined in the T-shaped and fork-shaped microfluidic chips with and without surface charge patterning. To generate the gradients, 25 mM sodium carbonate/bicarbonate buffer and 100 µM fluorescein were introduced through different inlet channels and a voltage potential was created by means of platinum electrodes inserted into the centre of each reservoir. The system was illuminated by a mercury arc lamp equipped with a fluorescein filter set. The steady state transport of the dye was observed using a Leica DM LM fluorescence microscope with a 5× objective, and captured using a Retiga 12-bit cooled CCD camera. Digital images
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were obtained by QCapture 1394 and OpenLab 3.1.5 imaging software at an exposure time of 1 s. The acquired images were of resolution 1280 × 1024 pixels with each pixel representing a 2.5 µm2 in the object plane. Images were exported in TIF format to MATLAB for digital processing. Dark field subtraction and bright field normalization were performed to eliminate anomalies introduced by the image acquisition system. Following image processing, concentration profiles were developed directly from values of pixel intensities for varying downstream distances. Profiles were smoothed using a convolution filter and linearly scaled to range between 0 and 1.
3. Results and discussion The goal of this study was to develop a novel method of producing and controlling stable, microscale concentration gradients for electrokinetic applications. PDMS microfluidic systems as developed herein enable experimental flexibility at a low cost both in terms of time and money. A trade-off in long-term durability of the system is encountered due to the tendency of plasma-treated PDMS to return to its native state when exposed to air and solvents. In certain applications in which long-term durability is of importance, different manufacturing processes from those presented in this paper may be required. Conceptually however, the ability to manipulate concentration gradients using surface charge heterogeneity is transferable regardless of fabrication techniques. To experimentally demonstrate the potential of surface charge heterogeneity in gradient creation, gradients were created in simple channel geometries and controlled by varying applied voltages and surface charge patterning. The BLOCS (BioLab-On-a-Chip Simulation) finite element code [24,35,36] was adapted to simulate the experimental conditions and sur-
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face charge heterogeneity. Specifically, channel dimensions for the T- and fork-shaped channels were modeled along with the physiochemical properties of fluorescein, namely a diffusion coefficient D = 4.37 × 10−10 m2 s−1 , and an electrophoretic mobility µep = 3.3 × 10−8 m2 V−1 s−1 . Numerical models were validated experimentally and used to support further analyses of gradient variability and stability. 3.1. Control of developed gradients An essential feature of an efficient gradient generator is the ability to vary shapes and magnitudes effectively. One means of accomplishing this is through channel geometry. Cliff gradients were developed perpendicular to the flow direction within the T-shaped channel while hill gradients were created within the fork-shaped channel (Figs. 3 and 4). Gradient shapes could be mirrored by introducing the buffer and fluorescein solutions through opposite channel inlets. Therefore in the case of the fork-shaped channel, a hill gradient was obtained when fluorescein was introduced through the central inlet, whereas a valley gradient was generated when the fluorescein entered by way of the peripheral inlets. Velocities varied between 0.1 and 2.4 mm s−1 for potentials between 27 and 405 V cm−1 resulting in flow rates of 30 to 460 nl min−1 with Péclet numbers between 70 and 1100 and Reynolds numbers between 0.03 and 0.5. For a given channel geometry and in the absence of surface charge heterogeneity, the magnitudes of generated gradients could be controlled by two parameters: (a) downstream distance and (b) applied voltage. Diffusion over distances on the order of millimeters in a 400 µm microchannel will significantly alter the concentration profile. Therefore, for a given microchannel and applied voltage, significantly different concentration gradients may be generated at dif-
Fig. 3. Experimental and numerical analysis of concentration gradients formed in a 450 µm T-channel for varying potentials. Experimentally (dotted lines) and numerically (solid lines) derived concentration profiles were plotted in (a) for an applied potential of 27 V cm−1 at (A) 400 µm downstream and (B) 4000 µm downstream, and for a potential of 68 V cm−1 at downstream distances of (C) 400 and (D) 4000 µm, and lastly for a potential of 405 V cm−1 at (E) 400 µm downstream. Fluorescence images are presented in (b) for an applied voltage of 27 V cm−1 between 3800 and 4600 µm downstream and in (c) for an applied voltage of 405 V cm−1 between 200 and 1000 µm downstream with labeled dotted lines corresponding to the gradients as plotted in (a).
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Fig. 4. Experimental and numerical analysis of concentration gradients formed in a 400 µm fork-shaped channel for varying potentials. Experimentally (dotted lines) and numerically (solid lines) derived concentration profiles were plotted in (a) for an applied potential of 27 V cm−1 at (A) 400 and (B) 4000 µm downstream and for an applied potential of 405 V cm−1 at (C) 400 and (D) 4000 µm downstream. Fluorescence images are presented in (b) for an applied voltage of 27 V cm−1 and in (c) for an applied voltage of 405 V cm−1 between 200 and 1000 µm downstream with labeled dotted lines corresponding to the gradients as plotted in (a).
Fig. 5. Numerical concentration profiles across the channel width for a homogeneous fork-shaped channel of 400 µm in width for (a) a center inlet voltage of Vapp and peripheral inlet voltages of 95% Vapp at (A) 600, (B) 2000, and (C) 4000 µm, and for (b) a center inlet voltage of 95% Vapp and outside peripheral inlet voltages of Vapp (D) 300, (E) 600, and (F) 2000 µm. In both cases, Vapp = 405 V cm−1 .
ferent downstream distances that are suitable for analyses provided that spatial stability on the order of a millimeter is sufficient and downstream channel length is not the defining constraint. The second method of controlling gradients shapes and magnitudes is through the applied voltages. Increasing potentials will render steeper gradients while decreasing voltages will produce more gradual gradients due to increased diffusion. Figs. 3 and 4 illustrate the variety of gradients that can be obtained by varying downstream distance and/or voltages for the T-shaped channel and for the fork-shaped channel respectively. In the preceding cases, the voltage at each of the channel inlets was maintained equal. However, by varying the inlet voltages, the gradient shapes and magnitudes may be further manipulated and the element of asymmetry introduced. Fig. 5 depicts the distinct profiles obtained by applying dif-
ferent voltages at different inlets of the fork-shaped channel. Evidently, a higher voltage applied to the central inlet containing the fluorescein will result in a hill gradient of higher concentration with a flattened top as the potential pumping fluorescein into the channel is proportionally larger. Conversely, a lower voltage applied to the central inlet will result in more peaked gradients of smaller magnitudes as the buffer is the predominant solution present in the channel. Pursuing this tactic further will enable the generation of asymmetric gradients in both the fork- and T-shaped channels. Fig. 6 illustrates this for a T-shaped channel with the fluorescein driving potential at 95% of that of the buffer. Fig. 7 illustrates asymmetry in a fork-shaped channel where the right peripheral buffer containing inlet voltage is 95% of remaining two inlets. Evidently, the symmetry of the developed concentration gradients can be directly controlled by varying
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the individual driving potentials of the buffer and fluorescein streams within the microchannel. Furthermore, by varying applied voltages and/or downstream distances, it is possible to customize the concentration gradient’s shape, magnitude and symmetry as generated within the microchannel. An additional method for customizing concentration gradients is by the introduction of charge heterogeneity on the microchannel’s surface. By selectively patterning regions of charge which oppose the bulk flow and cause local flow circulation and “bending” of flow streams, additional profiles above and beyond those of the cliff- and hill-shaped, can be obtained. For example, by selectively patterning a stripe of positive charge down the centre of the predominantly negatively charged channel surface, a more linear gradient than that observed in the homogeneously charged T-channel can be obtained and again varied by voltage. A slight flattening
Fig. 6. Numerical concentration profiles across the channel width for a homogeneous T-channel, 450 µm in width, with a potential of Vapp applied to the left inlet and a potential of 95% of Vapp applied to the right inlet for Vapp = 68 V cm−1 at (A) 400 and (B) 6000 µm and for Vapp = 405 V cm−1 (C) 400 and (D) 6000 µm. The adjoining fluorescent image is for Vapp = 68 V cm−1 .
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of this gradient is observed in the proximity of the channel walls. This non-linearity however is contained typically within 25 µm of the wall in a 450 µm channel. Fig. 8 depicts the experimental and numerical results for a 200 µm wide strip in a 450 µm T-channel. Experimentally, small deviations from linearity were observed particularly at higher voltage potentials. These deviations are believed to result from limitations of manufacturing processes as opposed to the overall technique which was numerically demonstrated. Surface patterning was conducted by hand in lieu of precise, automated equipment operating in a clean room environment. With improved manufacturing processes, it may be possible to achieve greater experimental linearity if that demonstrated is not adequate. By incorporating multiple strips, both in symmetrical and asymmetrical configurations, a large variety of shapes can be obtained as illustrated in Fig. 9. By these means concen-
Fig. 7. Numerical concentration profiles across the channel width for a homogeneous fork-shaped channel, 400 µm in width, with a potential of Vapp applied to the right inlet and center inlet and a potential of 95% of Vapp applied to the left inlet for Vapp = 405 V cm−1 at (A) 400, (B) 2000, and (C) 7000 µm presented along with the corresponding fluorescent image.
Fig. 8. Experimental (dotted lines) and numerical (solid lines) concentration gradients formed in a 450 µm T-shaped channel with a 200 µm wide stripe of positive charge down the centre of the predominantly negatively charged channel bottom surface plotted in (a) at a downstream distance of 4000 µm for (A) 27, (B) 68, and (C) 405 V cm−1 . Fluorescence images are presented in (b) for an applied potential of 27 V cm−1 between 200 and 1000 µm downstream and in (c) for an applied voltage of 405 V cm−1 between 200 and 1000 µm downstream with labeled dotted lines corresponding to the gradients as plotted in (a).
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Fig. 9. Numerical concentration gradients developed by introducing varying surface charge patterning configuration into a 400 µm T-shaped channel with an applied potential of 810 V cm−1 at a downstream distance of 2400 µm for (A) a single centered stripe (Fig. 2a), 300 µm in width, (B) a single asymmetrical stripe (Fig. 2b), 50 µm wide and offset 125 µm left of the center of the channel, (C) two stripes (Fig. 2c), 80 µm in width situated along the channel walls, (D) two stripes (Fig. 2d), 80 µm in width, situated 120 µm to either side of the channel center, and (E) three asymmetrical stripes (Fig. 2e), each 50 µm in width. The fluorescent images corresponding to (A)–(E) are also presented.
tration gradients can be shifted to create asymmetry while maintaining constant applied voltages (Fig. 9B). Secondly, the extremities of gradients at the channel walls may be flattened and extended (Fig. 9C). Lastly, local maximums and minimums can be introduced (Fig. 9D), leading to the creation of increasingly complex and customized gradients (Fig. 9E). Magnitudes of gradients formed using surface charge heterogeneity are directly linked to the relative surface area patterned by the opposite charge. Specifically, a large ratio of positive to negative surface charge will result in slower fluid velocities, increased mixing, and hence, more uniform gradients, whereas a smaller ratio will maintain higher levels of concentrated fluids. One limitation to the use of surface charge patterning its incompatibility for applications where surface bound gradients are required as the polyelectrolyte coating may interfere with bonding reactions. However, for applications where gradients are required in solution such as chemotaxis [1–4], neuron growth and axon specification [5,6], not to mention various chemical processes such as directional crystal growth [7], this technique offers additional flexibility and control of concentration gradients. Overall, effective control of electrokinetic concentration gradients’ shapes and magnitudes is achievable using simple microchannel configurations. Altering voltages and/or downstream distances yields a large variety of cliff- and hill-shaped gradients. Through further application of surface charge patterning, more linear and customized gradients may also be obtained while maintaining the simplicity and reliability of the microfluidic system. 3.2. Stability of developed gradients The generation of microscale concentration gradients requires both temporal and spatial stability in order to be pertinent for biological and chemical analyses. As the flow sys-
tem operates at steady state, temporal stability is ensured and gradients can be sustained indefinitely provided that the fluid supply is maintained and the voltage source is steady. Joule heating was not observed to be problematic for the range of voltages applied (27–405 V cm−1 ). This is because the high thermal conductivity of the glass channel base allowed for adequate heat transfer from the system, as discussed in previous studies of joule heating conducted by Erickson et al. [9]. The spatial stability (i.e. the downstream distance for which the gradient remains approximately constant) of generated gradients was analyzed numerically for a variety of downstream distances and applied voltages. As expected, greater spatial stability was obtained firstly, at higher voltages and secondly, at increasing downstream distances, due to lowered diffusive flux. In the first case, greater fluid velocities induced by higher potentials reduced the time available for diffusive mechanisms, thereby extending the downstream distance for which the gradient remained approximately constant. In the latter case at increasing downstream distances, local concentration gradients were increasingly more uniform and thus, the driving flux induced diffusion was weaker, which again resulted in greater spatial stability for the developed gradients. For low potentials (<30 V cm−1 ), spatial stability is limited at downstream distances very close to the intersection (<1000 µm). This obstacle can be overcome simply by avoiding excessively low potentials and using a higher voltage at a greater downstream channel length to obtain more uniform gradients. This is illustrated in Fig. 10 for the fork-shaped channel in which a range of gradients are obtained with good spatial stability over a distance of 600 µm while maintaining applied voltages greater than 135 V cm−1 . Spatial stability of gradients generated in the homogeneous and heterogeneous T-channels was comparable or greater than that of the homogeneous fork-shaped channels and exhibited the same trends
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Fig. 10. Numerical profiles depicting concentration gradient stability over a distance of 600 µm in a homogeneous fork-shaped channel, 400 µm in width for an applied potential of 405 V cm−1 at (A) 400, (B) 4000, and (C) 7000 µm and for an applied potential of 135 V cm−1 at (D) 4000 µm, and (E) 7000 µm. Dotted lines indicate the corresponding concentration gradients developed 600 µm downstream from gradients (A)–(E).
with regard to applied voltages and downstream distances. An additional method by which increased spatial stability may be obtained without sacrificing the performance of the gradient generator is by increasing the channel width. This will be discussed further in the following section. 3.3. Sensitivity of developed gradients To assess the suitability of this technique of generating concentration gradients for a wide range of chemical and biological applications, numerical analysis was conducted to determine its sensitivity to species characteristics such as the diffusion coefficient and electrophoretic mobility. In addition, the dependence of gradient shapes and magnitudes on microchannel geometry, specifically channel depth and width, was also investigated.
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3.3.1. Channel geometry Numerical analysis was conducted to ascertain the sensitivity of the developed concentration gradient generator on channel depth and width. It was found that a 10-fold increase in channel depth resulted in negligible changes in gradient shape and magnitudes for varying voltages and downstream distances (Fig. 11a). Previous studies of flows in the presence of heterogeneous surface charge also indicated that channel depth was not a predominant factor affecting flow characteristics and concentrations [23]. Therefore, it was concluded that this technique is not sensitive to channel depth in microchannels with or without surface charge heterogeneity. Channel width affected the developed concentration gradients to a greater respect. Larger channel width decreases the efficiency of diffusive mechanisms, therefore gradients, especially those formed at increasing downstream distances and lower potentials, were less uniform than those formed in a channel of smaller width at an equivalent potential. In order to obtain the same range of gradients in a wider channel as in the narrower channel, lower voltages were applied. Fig. 11b illustrates that gradients of identical magnitudes over a greater channel width are obtainable for a 900 µm channel width as in a 450 µm channel width. Spatial stability was comparable even at lower potentials as the channel width and the length over which diffusion must occur was larger. At higher potentials, spatial stability was improved to over 1 mm. 3.3.2. Physiochemical properties Through numerical analysis, it was determined that the developed gradient generator was not sensitive to the electrophoretic mobility of the analyte over a range of 4 magnitudes of order. Typically, in biological and chemical analysis, analytes are negatively charged in aqueous solutions with electrophoretic mobilities within the range of those
Fig. 11. Numerical concentration gradients developed for (a) a channel depth of 8 µm (solid lines) and 80 µm (dotted lines) for varying voltages for a homogeneous T-shaped channel, 450 µm in width at a downstream distance of 1000 µm and for (b) a channel width of 450 µm (dotted lines) and 900 µm (solid lines) for varying potentials at a downstream distance of 1000 µm for a 8 µm channel depth.
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addressed in this study. For example, ssDNA has an electrophoretic mobility of 2.0 × 10−8 m2 V−1 s−1 [37], viruses such as HRV serotypes typically range from 9.6 × 10−9 to 2.27 × 10−8 m2 V−1 s−1 , while typical values for bacteria range between 2 × 10−4 and 3 × 10−8 m2 V−1 s−1 [38]. In terms of ionic strengths, this method is applicable to the typical range as used in electrokinetic applications from 10−6 to 10−2 M. Performance was however influenced by the diffusion coefficient of the analyte. Diffusion coefficients are widely variable among common biological and chemical analytes, ranging from small cells and proteins with coefficients on the order of 1 × 10−10 m2 s−1 to large DNA molecules with coefficients on the order of 1 × 10−12 m2 s−1 . Larger diffusion coefficients will lead to more uniform gradients while smaller diffusion coefficients will result in gradients of greater magnitudes. Numerical analysis determined that the developed gradient generator was easily adapted to diffusion coefficients within the biological range by altering channel width and applied voltages accordingly. This technique is not conducive to applications where the diffusion coefficient is higher than ∼1 × 10−8 m2 s−1 or lower than ∼1 × 10−13 m2 s−1 as the necessary potentials and channel widths become unreasonable for electrokinetic, microscale applications.
4. Conclusions This study aimed to develop an effective and flexible method of producing stable concentration gradients for electrokinetic lab-on-a-chip applications. By manipulating applied voltages, downstream distances and by selectively patterning an arrangement of surface charge heterogeneities, control and variability of concentration gradients was experimentally and numerically demonstrated in simple channel geometries. Cliff, hill and linear shaped gradients were developed of varying magnitudes. Asymmetrical gradients were obtained by applying unbalanced potentials. Alternatively, selective surface charge patterning could also be used to shift gradients, to create local minimums and maximums and more complex gradient shapes. Spatial stability of 600 µm or greater was achieved for lateral widths as low as 400 µm and flow rates ranging between 30 and 460 nl min−1 which corresponded to Péclet numbers between 70 and 1100 and Reynolds numbers between 0.03 and 0.5. Gradient generation was not sensitive to channel depth or electrophoretic mobility, but did depend on channel width and most significantly on the diffusion coefficient. By adjusting applied voltages and/or channel width accordingly, our numerical models, validated herein, indicate that this technique for generating concentration gradients is adaptable to a range of potential analytes typical of biological and chemical analyses.
Acknowledgments The authors gratefully acknowledge the financial support of the National Sciences and Engineering Research Council through scholarships to E. Biddiss and through a research grant to D. Li. Additionally, the authors are thankful for the financial support of the Province of Ontario and Dupont Canada for a scholarship granted to E. Biddiss.
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