Patent Publication Number: US-2004047767-A1

Title: Microfluidic channel for band broadening compensation

Description:
BACKGROUND OF THE INVENTION  
       [0001] 1. Field of the Invention  
       [0002] The present invention relates generally to the field of microfluidic devices, and more particularly to a microchannel configuration for redirecting the paths of samples in a manner that compensates for sample dispersion.  
       [0003] While the present invention is subject to a wide range of applications, it is particularly well suited for analyte plug band broadening compensation in electrophoretic separation applications.  
       [0004] 2. Technical Background  
       [0005] Microchannel devices are finding increased use in the separation, identification and synthesis of a wide range of chemical and biological species. Such devices, which incorporate microfluidic channel dimensions in the range from a few microns to about 1 millimeter may permit the miniaturization and large-scale integration of many chemical processes in a manner analogous to that already achieved in microelectronics. Applications incorporating such microchannel devices include such diverse processes as DNA sequencing, immunochromatography, the identification of explosives, the identification of chemical and biological warfare agents, and the synthesis of chemicals and drugs.  
       [0006] A promising approach to microscale chemical analysis is electrophoretic separation. In electrophoretic separation, the carrier fluid may be either moving or nearly stationary, and an applied electric field is used to drive ionic species through a gel or liquid. Separation occurs because the ion speeds depend on the unique charge and mobility of each species. Provided the applied field is uniform across the channel cross-section, the ions of the same charge and mobility move at the same speed and so progress along the column without any induced dispersion. Such motion is analogous to the flat velocity profile of an electroosmotic flow, and the various species thus again exhibit unique arrival times at the channel exit. Electrophoretic separations may, however, be severely degraded by diffusion or dispersion. Dispersion may arise not only from non-uniformity of the carrier fluid speed, but may also arise directly from non-uniformity of the electric field across the cross-column section.  
       [0007] Despite these shortcomings, numerous studies have demonstrated the potential benefits of miniaturizing capillary electrophoresis on microfabricated devices. The benefits include, for example, portability, reduced reagent use, and increased opportunities for parallel analysis. Since the separation efficiency of capillary electrophoresis increases with the length of the separation channel, longer channels are generally desirable. Generally speaking, confining such channels to a small area for use in microfluidic devices typically requires configurations with multiple channel turns (e.g., serpentine channels). Unfortunately, such turns generally add dispersion to analyte bands and therefore often reduce the benefits of channel length.  
       [0008] The bends or turns briefly mentioned above typically introduce a phenomenon, which is often referred to as the “race track effect,” in microfluidic channels utilized in high-resolution electrophoretic separations. In essence, the race trace effect results in band broadening in an analyte plug as a result of the plug traversing the bends or turns. More specifically, when an electrophoretic band is migrating through a linear channel, the molecules making up the band, which are all migrating at roughly the same speed, tend to migrate as a tight band. When migrating through a turn in a serpentine pathway, however, the same molecules will tend to migrate through the shorter inner side of the channel faster than the longer outside of the channel, which leads to band spreading and non-uniformity across the width of the channel. Generally speaking, at each turn in the pathway, more band resolution is lost. Accordingly, an initially flat interface will be severely skewed when passing through one or more turns.  
       [0009] Despite these and other shortcomings and given the small size of microfluidic devices, there will likely continue to be a need for microfluidic devices incorporating both multiple channels and/or long lengths of micron-sized channels in order to utilize the maximum amount of space, while possibly reducing the microfluidic device size. What is needed therefore, are improved microfluidic channels having increased length and which include turns or bends that are constructed and arranged to substantially compensate for the analyte plug band skewing (the race track effect) generally experienced by analyte plugs traversing a bend or turn. It is to the provision of such a microchannel that the present invention is primarily directed.  
       SUMMARY OF THE INVENTION  
       [0010] One aspect of the present invention relates to a microchannel for analyte band broadening compensation. A microchannel includes a bend having an inside radius of curvature, an outside radius of curvature and a width. The bend is constructed such that the width and either the inside radius of curvature, the outside radius of curvature or both change simultaneously.  
       [0011] Another aspect of the invention relates to a microchannel for analyte band broadening compensation. The microchannel includes a first working section, a second working section, remote from the first working section, and a redirecting section connecting the first working section to the second working section. The redirecting section includes a bend having a width that changes simultaneously with an inside radius of curvature, an outside radius of curvature, or inside and outside radii of curvature, and a counter bend.  
       [0012] In yet another aspect the present invention is directed to a microchannel for analyte band broadening compensation. The microchannel includes a first working section, a second working section remote from the first working section and a redirecting section connecting the first and second working sections. The redirecting section, the first working section and the second working section define a pathway and the redirecting section is constructed and arranged to define a total angular displacement along the pathway of greater than about 340°.  
       [0013] The microchannel of the present invention results in a number of advantages over other microchannels and microfluidic devices known in the art. For example, the microfluidic channel, including the bends or turns, of the present invention may be fabricated utilizing conventional molding, embossing, and etching techniques, such as, but not limited to, reactive-ion etching (RIE). Moreover, because of the turns or bends and junctions, such as tapered sections, are constricted over relatively short distances, they do not lead to excessive increases in electrical resistance and Joule heating.  
       [0014] An additional advantage of the microfluidic channel of the present invention relates to the bend or curved portion of the microfluidic channel. Several known channel designs require either two opposite bend sections that must be followed almost immediately by one another to avoid translational diffusion, or wide microchannel widths in order to compensate for the race track effect. In accordance with the present invention, a single bend section may be utilized, which reduces space and offers the option of significantly longer linear sections or working sections rather than serpentine channels, if desired. In addition, and in accordance with the present invention, the redirecting section or bend section width need not be widened above the normal working channel width in order to compensate for substantially all of the analyte plug skewing as a result of the analyte plug traversing the bend or turn.  
       [0015] Additional features and advantages of the invention will be set forth in the detailed description which follows and in part will be readily apparent to those skilled in the art from a description or recognized by practicing the invention as described herein.  
       [0016] It is to be understood that both the foregoing general description and the following detailed description are merely exemplary of the invention, and are intended to provide an overview or framework for understanding the nature and character of the invention as it is claimed. The accompanying drawings are included to provide further understanding of the invention, illustrate various embodiments of the invention, and together with the description serve to explain the principles and operation of the invention. 
     
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
     [0017] The invention can be better understood with reference to the following drawings.  
     [0018]FIG. 1 depicts a simulation showing the effect that a conventional microchannel having a 90° bend has on an analyte band plug traversing the bend.  
     [0019]FIG. 2 is a perspective view of a conventional microfabricated device having an open electrophoresis channel and liquid reservoirs formed on a substrate.  
     [0020]FIG. 3 depicts a first preferred embodiment of the microchannel in accordance with the present invention.  
     [0021]FIG. 4 depicts a second preferred embodiment of a microchannel in accordance with the present invention.  
     [0022]FIG. 5 schematically depicts a simulation showing the plug shape after an analyte band plug has traversed the redirecting section of the microchannel depicted in FIG. 3.  
     [0023]FIG. 6 schematically depicts a simulation showing the plug shape after an analyte band plug has traversed the redirecting section of the microchannel depicted in FIG. 4.  
     [0024]FIG. 7 graphically depicts an XY plot of the leading concentration edge of an analyte band plug after a simulation has allowed the plug to completely traverse the redirecting section in accordance with the present invention.  
     [0025]FIG. 8 depicts a third preferred embodiment of a microchannel in accordance with the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
     [0026] As discussed briefly above, the “race track effect” in microchannels, particularly microfluidic channels, used in performing high-resolution electrophoretic separations is a known problem induced by bends or turns in the microchannels. Generally speaking, the race track effect results in band broadening of an analyte plug traversing the bend or turn. The simulation depicted in FIG. 1 shows the dispersion or “race track effect” experienced by an analyte plug at various locations through a 90° turn. Simulation  2  depicts representations of analyte plug  4  passing through microchannel  6  having a 90° bend as analyte plug  4  traverses the bend. Before entering the bend, analyte plug  4  has a leading edge  8  and a lagging edge  9  that are substantially aligned with each other along the anlyte plug  4  axis which is oriented substantially normal to the microchannel  6  wall preceding the bend. As analyte plug  4  approaches and traverses the turn in microchannel  6 , the molecules making up the band plug  4  will migrate through the shorter inner side of the bend portion of microchannel  6 , then through the longer outer side of the bend portion of microchannel  6 , leading to band spreading and non-uniformity across the width of the channel. As a result, analyte plug  4  exhibits a skewed profile where the leading edge  8  of plug  4  is ahead of the lagging edge  9  of plug  4  within microchannel  6  after plug  4  has cleared the bend portion of microchannel  6 . Generally speaking, two different phenomena are responsible for this effect. One is simply the distance traveled by the two outside band edges  8 ,  9  around the curve or bend. The second is the electric field strength which exacerbates the first. Generally speaking, the electric field strength present around the bend is at a maximum on the interior surface of the curve and decreases as the distance away from the radius of the inner channel wall is increased. Accordingly, the amount by which the leading edge  8  leads lagging edge  9  is a function of the angle, width and radius of the curve of the microchannel.  
     [0027] A conventional microfabricated device  10  utilized to compensate for the “race track effect” in electrophoretic separations is shown in FIG. 2. Device  10  generally includes a planar substrate  12  having formed in its upper surface  14  open reservoir  16 ,  18 ,  19 , and  20 , and a serpentine electrophoresis channel  22  connecting the reservoirs  18  and  16 , which are intended to contain electrophoresis buffer and sample fluid, respectively, are connected in fluid communication with each other and with channel  22  through a fork-like connector  24 . Reservoirs  19 ,  20  are intended to maintain electrical continuity for the separation. The four reservoirs are connected to electrodes  26 ,  28 , and  21 , and  30 , as shown, which are in turn connected to suitable voltage leads during operation of the device, for (i) loading sample from reservoir  16  into channel  22 , by applying a voltage across electrodes  26 ,  28 , and (ii) electrophoretically separating charged sample components, by applying a voltage difference across opposite ends of the channel, i.e,. across electrodes  21 ,  30 .  
     [0028] With continued reference to FIG. 2, channel  22  further includes a plurality of parallel linear channel segments, such as segments  32 ,  34 , and  36 , and curved channel regions connecting the adjacent ends of the adjacent linear segments, such as curved channel region  38  connecting adjacent ends of segments  32 ,  34 . In a typical embodiment, the substrate or chip has side dimensions of about 1 to 15 cm, and the linear segments are each about 0.5 to 10 cm in length. Thus, for example, a channel having 30 linear segments each about 8 mm in length has a column length, ignoring the lengths of the connecting regions of about 250 mm. With the added lengths of the connecting regions, the total length may be in the 30 cm range on a chip whose side dimensions may be as little as 1 cm. A cover slip  23  placed over the portion of the substrate having the serpentine channel serves to enclose the channel, although an open serpentine channel may alternatively be employed.  
     [0029] In the device  10  depicted in FIG. 2, the particular design of curved region  38  is intended to compensate for the “race track effect” in electrophoretic separations conducted within channel  22  of device  10 . Generally speaking, curved region  38  is formed by two turn segments which result in a net 180° turn in curved region  38 . Further details relating to the particular microchannel design depicted in FIG. 2 can be found in U.S. Pat. No. 6,176,991, which issued on Jan. 23, 2001. While the device  10  depicted in FIG. 2 may minimize the “race track effect” or band skewing, it is not optimized and therefore does not adequately compensate for band skewing when the microchannel dimensions are other than those disclosed in U.S. Pat. No. 6,176,991.  
     [0030] Reference will now be made in detail to the present preferred embodiments of the invention, examples of which are illustrated in the accompanying drawing figures. Wherever possible, the same reference numerals will be used throughout the drawing figures to refer to the same or like parts. An exemplary embodiment of the microchannel of the present invention is depicted in FIG. 3 and is designated generally throughout by reference numeral  40 .  
     [0031] Generally speaking, exemplary microchannel  40  depicted in FIG. 3 preferably includes a first working section  42 , a second working section  44 , both of which are preferably straight or linear sections, and a redirecting section  46  connecting the first and second working sections. In accordance with the present invention, redirecting section  46  provides a pathway for the redirection of a sample fluid, in particularly one or more analytes in a sample mixture during electrophoretic separation. Redirecting section  46  preferably includes a bend  48  depending from first working section  42 , followed by a counterbend  50 , which turns redirecting section  46  in a direction opposite bend  48 , preferably followed by a tapered section  52  that communicates with second working section  44 .  
     [0032] More specifically, a preferred exemplary microchannel  40  may include a first working section  42  having a width of between about 50.0 microns to about 200.0 microns. The bend  48  in fluid communication with first working section  42  may preferably define a 90° turn having a varying average radius of curvature or centerline radius of curvature R c1  that preferably increases from first working section  42  to second bend  50 . Accordingly, first bend  48  may preferably be tapered from a width equal to the width of first working section  42  to a width equal to between about 15% and about 50% of the first working section  42  width. Thus, in the preferred embodiment of microchannel  40  depicted in FIG. 3, where the first working section  42  width is 100.0 microns, first bend  48  may be optimized to include an inlet width W 1  of approximately 100.0 microns, an outlet width W o  of approximately 40.0 microns, and an R c1  value increasing from about 100.0 microns to about 130.0 microns in the direction of fluid flow.  
     [0033] First bend  48  may preferably be immediately followed by counterbend  50  defining a 270° counterturn having a constant centerine radius of curvature R c2  and a constant width. Thus, for the optimized microchannel  40  depicted in FIG. 3, counterbend  50  has an R c2  of approximately 263.0 microns and a constant width W t  of approximately 40.0 microns.  
     [0034] Tapered section  52 , preferably in fluid communication with the end of counterbend  50  remote from bend  48 , is preferably a straight section that is gradually tapered to return microchannel  40  to the working section width (in this case 100.0 μm). In a case of preferred microchannel  40  depicted in FIG. 3, tapered section  52  preferably increases in width from the counterbend width W t  (in this case 40 μm) to second working section width W ws  (in this case 100 μm). In a preferred embodiment, tapered section  52  preferably defines a length of approximately 125.0 microns having a width that increases linearly along its length. In a preferred embodiment, second working section  44  preferably has a width W ws  that is equal to or substantially equal to the width of first working section  42 . Accordingly, the width of second working section  44  may be between about 50.0 microns to 200.0 microns. In accordance with the optimized microchannel depicted in FIG. 3, W ws  of second working section  44  is preferably 100.0 microns.  
     [0035] A second exemplary microchannel  54  is depicted in FIG. 4. Generally speaking, microchannel  54  includes a first working section  56 , a second working section  58 , both of which are preferably straight or linear sections, and a redirecting section  60  connecting the first and second working sections. In accordance with the present invention, redirecting section  60  provides a pathway for the redirection of a sample fluid, in particular one or more analytes in a sample mixture during electrophoretic separation. Redirecting section  60  preferably includes a bend  62  depending from first working section  56 , followed by a counterbend  64  which turns redirecting section  60  in a direction opposite bend  62 , preferably followed by a tapered section  66  that communicates with second working section  58 . In a preferred embodiment, counterbend  64  of microchannel  54  may preferably include a plurality of distinct sections. As depicted in FIG. 4, second bend  64  may preferably include a first counterturn  68  following and communicating with bend  62 , followed by a second counterturn  70 , followed by straight portion  72 , followed by a third counterturn  74 , which communicates with tapered section  66 . Although other configurations may be employed in accordance with the present invention, the one or more counterturns embodied by counterbend  64  preferably results in a 270° turn in a direction opposite of the direction of first bend  62 .  
     [0036] In the second preferred embodiment of microchannel  54  depicted in FIG. 4, first working section  56  may also have a width of about 50.0 microns to about 200.0 microns. First bend  62  in fluid communication with first working section  56  may preferably define a 90° turn having a varying average radius of curvature or centerline radius of curvature R c3  that preferably increases from first working section  56  to first counterturn  68 . Accordingly, bend  62  may preferably be tapered from a width equal to the width of first working section  56  to a width equal to between about 15% to about 50% of the first working section  56  width. Thus, for the second preferred embodiment of microchannel  54  depicted in FIG. 4, wherein first working section  56  has a first working section  56  width of 100 microns, bend  62  has been optimized to include an inlet width W i2  of approximately 100.0 microns, an outlet width W o2  of approximately 25.0 microns, and an R c3  value increasing from 100.0 microns to 137.5. microns in the direction of fluid flow.  
     [0037] In addition, first counterturn  68  preferably follows and communicates with bend  62  and defines a 90° turn opposite the direction of the turn defined by bend  62 . The width of first counterturn  68  preferably increases from 25.0 microns at the beginning of first counterturn  68  to 31.0 microns at the end of first counterturn  68  and has an centerline radius of curvature R c4  that decreases from 132.50 microns to 129.50 microns. Second counterturn  70  also defines a 90° turn in the same direction as first counterturn  68  and also has a width that is constantly increasing from 31.0 microns at the beginning of the turn to 38.0 microns at the end of the turn. The centerline radius of curvature R c5  of second counterturn  70  also decreases from 129.50 microns at the beginning of the turn to 126.0 microns at the end of the turn. Straight portion  72  communicating with second counterturn  70  preferably has a constant width of approximately 38.0 microns and preferably extends a length of about 150.0 microns between second counterturn  70  and third counterturn  74 .  
     [0038] Third counterturn  74  preferably defines a 90° turn in the same direction as first counterturn  68  and second counterturn  70 , and preferably has a width that continuously increases from 38.0 microns at the beginning of the turn to 44.0 microns at the end of the turn. Again, the average radius of curvature R c6  continuously decreases from 126.0 microns at the beginning of the turn to 123.0 microns at the end of the turn. Third counterturn  74  preferably communicates with straight portion  72  that is tapered to return redirecting section  60  to the working channel width. Thus, for the optimized microchannel  54  depicted in FIG. 4, tapered section  66  preferably has a channel width that is constantly increasing from 44.0 microns to 100.0 microns over a length of approximately 125.0 microns. Although second working section  58  may also have a width of between about 50.0 microns to about 200.0 microns, the second working section  58  width W ws2  is 100.0 microns.  
     [0039] The microchannels of the present invention are preferably manufactured on a glass substrate using conventional etching techniques such as, but not limited to, reactive-ion etching (RIE). Generally speaking, the specific design criteria for the microchannels of the present invention such as the optimized microchannels  40  and  54  depicted in FIGS. 3 and 4, respectively, may be determined using commercially available software packages such as, “Gambit,” compiled by Fluent, Inc. and “Fluent,” compiled by Fluent, Inc. Two-dimensional microchannel designs may first be constructed in Gambit and then imported into the Fluent fluid modeling package in order to simulate an analyte plug flow through the microchannel with respect to the electrophoretic field applied across the inlet and outlet of the designed microchannels of the present invention. Knowing the steady-state voltage field and electric field at various locations along the microchannel, the flow under electrophoretic conditions may be analyzed. In both the microchannel  40  depicted in FIG. 3 and microchannel  54  depicted in FIG. 4, bend  48  and  62 , respectively, create the skew to be corrected for in counterbend  50  and  64 , respectively. A specific example of operable dimensions for microchannel  54  depicted in FIG. 4 are presented in Table 1 which follows below. Determining the proper amount of taper for the various portions of redirecting section  62  depends upon all of the parameters of each turn including the average (or centerline) radius of curvature, average width and angle of the turn, and has been previously described by the following equation: 
     α 1   R   1   w   1   2 =α 2   R   2   w   2   2   
     [0040] Further details relating to the application of the above-mentioned equation may be found in Mulho, J. I., Herr, A. E., Mosier, B. B., Santiago, J. G., Kenny, T. W., Brennen, R. A., Gordon, G. G., and Mohammadi, V.,  Anal. Chem . 73 (2000), which is hereby incorporated herein by reference.  
                                           TABLE 1                                      Centerline               Avg.   Avg. Radius of           Radius (μm)       Width (μm)       Width   Entire Turn                                                 End 1   End 2   End 1   End 2   Angle   (μm)   (μm)                                                         Turn 1   100   137.5   100   25     90°   62.5   118.8       Turn 2   132.5   129.5   25   31   −90°   28.2   130.9       Turn 3   129.5   126   31   38   −90°   34.5   127.8       Turn 4   126   123   38   44   −90°   40.8   124.6                  
 
     [0041] Generally speaking, the radius of curvature (R c ) may preferably be determined as the average or centerline radius of curvature between the radius of the inside and outside channel walls. The design for microchannel  54  of the present invention was determined by describing the geometry of bend  62  and then choosing general desires for the geometry of counterbend  64  and included the step of varying the radius of curvature for the outside channel wall until a solution was found to coincide with the electric fields compensating one another.  
     [0042] An alternative solution to solving the equation set forth above is solved by microchannel  40  depicted in FIG. 3. The design may preferably be arrived at by holding the radius of curvature of the outside wall of counterbend  50  of microchannel  40  constant and solving for the necessary width to taper down to around bend  48  so that the width of the channel may be held constant around counterbend  50 . The preferred embodiment depicted in FIG. 3 thus included a bend  48  tapering down to a width of 40.0 microns and the radius of curvature for the outside wall of counterbend  50  may then be maintained at a constant 263.0 microns  
     [0043] Simulation results demonstrating the analyte band skew compensation provided by microchannels  40  and  54  depicted in FIGS. 3 and 4, respectively, are shown in FIGS. 5 and 6, respectively. Each of FIGS. 5 and 6 depict the analyte plug  4  shape after analyte plug  4  has traversed microchannels  40  and  54 , respectively. In both cases, analyte plug  4  returned to a plug profile having a plug profile axis that is perpendicular to the microchannel walls. Essentially, after traversing redirecting sections  46  and  60 , analyte plug  4  has neither a leading edge  8 , nor a lagging edge  9 .  
     [0044] The amount of analyte plug band skew remaining after band skew compensation in accordance with the present invention may also be characterized with reference to the plot depicted in FIG. 7. FIG. 7 depicts a plot of the leading edge of an analyte plug in XY coordinates. The values of the slopes of the skew for different microchannel geometries including those depicted in FIGS. 3 and 4 are set out in the following table.  
                           TABLE 2                                   Channel Design   Slope                                                    20 μm constant width design (FIG. 3)   −0.505           25 μm constant width design (FIG. 3)   −0.344           40 μm constant width design (FIG. 3)   +0.095           144 μm outside radius of curvature design   +0.060           (FIG. 4)           Known skew minimizing design   +0.135           180° turn with 150 μm R c     +6.64                      
 
     [0045] Given that the objective is for the analyte plug front to be perpendicular to the second working section walls after the analyte plug has traversed the redirecting section of the microchannel, a slope of 0.0 is the target. Referring now to Table 2, one of skill in the art will readily recognize that microchannel  54  depicted in FIG. 4 has a slope closest to 0.0, and is thus the most preferred embodiment for anlayte band plug compensation of the embodiments listed in Table 2. A close second is microchannel  40  depicted in FIG. 3 as it has a slope of +0.095, only 0.035 greater than the slope of an analyte band plug passed through microchannel  54  depicted in FIG. 4. As the analyte plug front shape deviates more from perpendicular with respect to the working section walls, the slope becomes larger and the sign of the slope indicates whether or not the leading edge is the inner (+) or outer (−) side of the plug. In general, the slopes provided in Table 2 indicate a significant improvement over known analyte plug compensation microchannel designs which have slopes as high as, and in some instances higher than, +0.135x.  
     [0046] While the specific details of two optimized microchannels  40  and  54  have been described above with reference to FIGS. 3 and 4, one of ordinary skill in the art will readily recognize that numerous other designs may be equally operative in accordance with the present invention. One such microchannel  80  is depicted in FIG. 8. As depicted clearly in the drawing figure, microchannel  80  has a substantially spiral configuration. In accordance with the present invention, one of ordinary skill in the art may readily employ the, “Gambit,” and “Fluent” software packages and the equation (α 1 R 1 w 1   2 =α 2 R 2 w 2   2 ) described above to arrive at the specific design criteria for microchannel  80 .  
     [0047] As may be recognized from the wide variety of embodiments disclosed and depicted herein, any number of microchannel designs/configurations may be operable in accordance with the present invention. Preferably, each such design/configuration share certain common elements or features. More specifically, a given microchannel for analyte band broadening compensation in accordance with the present invention may preferably include a bend  82  having an inside radius of curvature R c1 , an outside radius of curvature R co , and a width that continuously varies between an inlet width Win  and an outlet width W out . Bend  82  is preferably constructed such that the width and either the inside radius of curvature, R ci , the outside radius of curvature, R co , or both R ci  and R co  change simultaneously. In the preferred embodiments depicted in FIG. 3, 4 and  8 , that width preferably decreases and thus bend  82  is a reducing taper. In addition, bend  82  and bends  48  and  62  depicted in FIG. 3 and  4 , respectively, effect a 90° turn in each of the preferred embodiments. One of skill in the art will recognize, however, that bend  82 ,  48  and  62  are in no way limited to a 90° turn. Smaller and greater angles may also be utilized to facilitate analyte band broadening compensation in accordance with the present invention, but such angles may significantly affect the other aspects and features of the microchannel of the present invention.  
     [0048] Referring again to FIG. 8, the centerline radius of curvature, R cc  is indicated to depict the location of the average radius curvature of bend  82 . As discussed briefly above, one of ordinary skill in the art may utilize the centerline radius of curvature R c C rather than the inside radius of curvature R c I and the outside radius of curvature R c O to optimize the design elements of microchannel  80 . For the embodiment depicted in FIG. 8, one of skill in the art will further understand that the counterbend  84  of microchannel  80  preferably includes that portion of microchannel  80  extending from outlet  86  of bend  82  to the inlet  88  of a tapered section  90  connecting counterbend  84  with a working section  92 . Moreover, it may be readily recognized that bend  82  and counterbend  84  depicted in FIG. 8 represent a redirecting section capable of redirecting the flow of an analyte band plug through a pathway that undergoes a total angular displacement measuring approximately 1080°. The first 90° angular displacement is preferably in a counterclockwise direction, while the second angular displacement follows in a clockwise direction covering an angular displacement of about 990°. In each of the embodiments, the initial bend (such as bend  48 ,  62 , or  82 ) actually creates an analyte band plug skew, while the counterbend (such as counterbend  46 ,  64 , or  84 ) returns the analyte band plug to its substantially original shape, thus compensating for the racetrack effect.  
     [0049] While the invention has been described in detail, it is to be expressly understood that it will be apparent to persons skilled in the relevant art that the invention may be modified without departing from the spirit of the invention. Various changes of form, design or arrangement may be made to the invention without departing from the spirit and scope of the invention. Therefore, the above mentioned description is to be considered exemplary, rather than limiting, and the true scope of the invention is that defined in the following claims.