Experimental Optimization of Flow Distributors for Pressure-Driven

We report on the results of an experimental study established to optimize the design of microfabricated flow distributors for use in pressure-driven s...
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Anal. Chem. 2011, 83, 467–477

Experimental Optimization of Flow Distributors for Pressure-Driven Separations and Reactions in Flat-Rectangular Microchannels Joris Vangelooven,† Stefan Schlautman,‡ Frederik Detobel,† Han Gardeniers,‡ and Gert Desmet*,† Department of Chemical Engineering (Transport Modelling & Analytical Separation Science-group), Vrije Universiteit Brussel, Brussels, Belgium, and MESA+ Research Institute, University of Twente, Enschede, The Netherlands We report on the results of an experimental study established to optimize the design of microfabricated flow distributors for use in pressure-driven separations and reactions in flat-rectangular channels. For this purpose, the performance of a wide variety of possible flow distributor designs etched in glass/silicon wafers was compared, using CCD camera detection to study the shape and variance of the bands eluting from them. The best performance was obtained with radially interconnected distributors with a diverging inlet section and filled with diamond-shaped pillars, oriented perpendicular to the main flow direction and with a high transversal over axial aspect ratio. It was found that the best distributor designs start with a diverging section containing some 10-12 subsequent rows of high aspect ratio pillars (with a transversal width making up 10-15% of the final channel width) and with a divergence angle selected such that the sloped side-walls run parallel with the sides of the diamond-shaped pillars. After this zone, one or more regions with pillars with a smaller aspect ratio should be provided to increase the number of exit points. To prevent the formation of dead zones in these subsequent zones, so-called distributor wedges can be used to prevent the formation of any dead zones in the wake of the large aspect ratio pillars of the preceding section. One of the drawbacks of chip-based separation and reaction devices is their limited volumetric capacity. The obvious solution to this problem consists of providing channels with a flatrectangular cross-section, using the large channel width to compensate for the fact that most microfabrication techniques only allow one to produce shallow channels.1-5 This solution, however, raises the problem of homogeneously distributing a fluid flow * To whom correspondence should be addressed. Phone: (+)32.(0)2.629.32.51. Fax: (+)32.(0)2.629.32.48. E-mail: [email protected]. † Vrije Universiteit Brussel. ‡ University of Twente. (1) De Pra, M.; Kok, W.; Gardeniers, J.; Desmet, G.; Eeltink, S.; van Nieuwkasteele, J.; Schoenmakers, P. J. Anal. Chem. 2006, 78, 6519–6525. (2) Fonverne, A.; Ricoul, F.; Demesmay, C.; Delattre, C.; Fournier, A.; Dijon, J.; Vinet, F. Sens. Actuators, B 2008, 129, 510–517. (3) Eghbali, H.; De Malsche, W.; Clicq, D.; Gardeniers, H.; Desmet, G. LC GC Eur. 2007, 20, 208. (4) Lavrik, N. V.; Taylor, L. C.; Sepaniak, M. J. Lab Chip 2010, 10, 1086– 1094. 10.1021/ac101304p  2011 American Chemical Society Published on Web 12/22/2010

across the full width of a flat-rectangular channel and recollecting the flow at the column outlet. This problem has already been investigated by numerous authors for applications such as field flow fractionation (FFF),6 capillary electro chromatography (CEC),7 and hydrodynamic chromatography (HDC),8 proposing solutions such as a repeatedly bifurcating network of inlet channels9,10 or a gradually diverging channel section (with optimal divergence angle 60° < R < 90°), either fully open6 or filled with microstructures.11,12 One of the applications where the need for a good distributor is most pressing is the field of liquid chromatography, as this is a separation process whose performance depends very strongly on the degree of band broadening or axial dispersion that is created inside the separation device, and it is a well-known fact that a poor radial liquid distribution can completely ruin liquid chromatography separations.13-16 Good flow distributors can also decrease axial dispersion caused by gradually tapering side-walls in the especially designed geometries of bends that can be incorporated in flat-rectangular channels to obtain longer channels on a chip.17 The present study builds further upon a previous experimental study,18 showing that distributors consisting of an ordered bed of transversally oriented diamond-shaped micropillars with a large aspect-ratio (so-called “radially interconnected” (RI) distributors, see Figure 1a,b) offer a better distributor performance than the so-called repeatedly bifurcating distributors (Figure 1c), wherein the flow is spread over the entire width of the channel by a series (5) Mery, E.; Ricoul, F.; Sarrut, N.; Constantin, O.; Delapierre, G.; Garin, J.; Vinet, F. Sens. Actuators, B 2008, 134, 438–446. (6) Giddings, J.; Schure, M.; Myers, M.; Velez, G. Anal. Chem. 1984, 56, 2099– 2104. (7) He, B.; Regnier, F. J. Pharm. Biomed. Anal. 1998, 17, 925–932. (8) Blom, M. T.; Chmela, E.; Oosterbroek, R. E.; Tijssen, R.; van den Berg, A. Anal. Chem. 2003, 75, 6761–6768. (9) He, B.; Tait, N.; Regnier, F. Anal. Chem. 1998, 70, 3790–3797. (10) Regnier, F. E. J. High Resolut. Chromatogr. 2003, 23, 19–26. (11) Sant, H.; Kim, J.; Gale, B. Anal. Chem. 2006, 78, 7978–7985. (12) Chmela, E.; Blom, M. T.; Gardeniers, J. G. E.; van den Berg, A.; Tijssen, R. Lab Chip 2002, 2, 235–241. (13) Abia, J. A.; Mriziq, K. S.; Guiochon, G. A. J. Chromatogr., A 2009, 1216, 3185–3191. (14) Broeckhoven, K.; Desmet, G. J. Chromatogr., A 2009, 1216, 1325–1337. (15) Broyles, B. S.; Shalliker, R. A.; Guiochon, G. J. Chromatogr., A 1999, 855, 367–382. (16) Wu, Y.; Ching, C. Chromatographia 2003, 57, 329–337. (17) Aoyama, C.; Saeki, A.; Noguchi, M.; Shirisaki, Y.; Shoji, S.; Funatsu, T.; Mizuno, J.; Tsunoda, M. Anal. Chem. 2010, 82, 1420–1426. (18) Vangelooven, J.; De Malsche, W.; Op De Beeck, J.; Gardeniers, H.; Desmet, G. Lab Chip 2010, 10, 349–356.

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Figure 1. An overview of the three main investigated distributors types (top views): (a) radially interconnected distributors with a uniform width (R ) 180°) with a rectangular distributor zone filled with elongated pillars (see also zooms in Figure 3); (b) radially interconnected distributors with diverging side-walls and a triangular distributor zone filled with elongated pillars (R ) 157°-175°, depending on the AR of the distributor); and (c) a continuously bifurcating channel distributor.

of bifurcations, doubling the number of channels at each step and meanwhile halving the channel diameter to maintain a constant flow velocity. Other examples of radially interconnected flow distributors can be found in the work of Gale et al.,11 using distributors filled with pillars of different shapes, but always with an aspect ratio (AR) of 1 (AR ) ratio of transversal width over axial length). In our previous study,18 it was found that radially interconnected distributors filled with pillars with an AR of 10 performed better than those filled with an AR of 5. It was also found that, although distributors with a gradually diverging cross section (Figure 1b) perform best,19 good results can also be obtained with distributors having a uniform cross section (Figure 1a, divergence angle R ) 180°), provided a short open region is placed just in front of the first row of pillars to provide a preferential flow path in the transversal direction. The present study also builds further upon a recent theoretical computational fluid dynamics (CFD) study,20 systematically surveying a comprehensive set of possible radially interconnected flow distributors. This latter study showed that the shape of the bands eluting from a radially interconnected distributor improves with increasing AR of the pillars, in terms of both global warp and local axial dispersion. Considering pillars with an axial width of 5 µm, and looking at the length needed to bring the maximal transversal velocity difference below 5%, increasing the AR from 5 to 25 reduced the required distributor length from 170 to 20 µm. The obtained results, however, also revealed an important drawback of high AR pillar distributors, that is, the fact that they only have a limited number of exit points and therefore produce strongly undulating bands. The amplitude of this wavy pattern is still very small at AR ) 10, but rapidly becomes unacceptably large when considering AR’s in the range of 20-25. The obvious solution for this exit point problem is to construct mixed size flow distributors, that is, distributors that first consist of a zone filled with several rows of distributor pillars with a very high AR to produce a sufficiently uniform velocity profile as (19) Williams, P.; Giddings, S.; Giddings, J. Anal. Chem. 1986, 58, 2397. (20) Vangelooven, J.; Desmet, G. J. Chromatogr., A 2010, 1217, 6724-6732.

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quickly as possible, followed by one or more zones consisting of pillars with a much smaller AR to increase the number of exit points and bring it sufficiently close to the number of parallel through-pores in the actual separation bed. As was also demonstrated in this theoretical study,20 the best possible way to design such a mixed size distributor is by providing so-called “distributor wedges”, which prevent the formation of poorly permeated zones in the wake of the pillars of the last row of high AR pillars (see also (3) in Figure 2d). To experimentally verify the insights obtained in our theoretical study, the present study has been set up by producing siliconglass wafers chips containing a multitude of different micropillar array separation channels, all filled with the same type of hexagonally shaped pillars (see Figure 2), but preceded by a variety of different flow distributors. The wafer contained about 20 different distributor designs, allowing one to make a comprehensive study of the effect of the pillar AR as well as of the distributor angle, and with some built-in redundancy to anticipate the accidental occurrence of etching errors. Because our theoretical simulation work was exclusively limited to distributors with a uniform cross section (i.e., with divergence angle R ) 180°), it was deemed very important to verify whether the mixed pillarsize distributors proposed during this work would also work as well when the distributor has a diverging cross section.20 The experimental setup also allowed us to measure the distributor performance for a wide range of flow rates in a relatively short time frame, anyhow much faster than possible with the numerical simulation approach. The experimental study is also needed to assess the frequency and the effect of the inevitably occurring etching errors, for example, leading to a deviation between the side-wall distance designed on the mask and that obtained on the finally etched wafer. CONSIDERED DESIGNS AND EXPERIMENTAL PROCEDURES Considered Designs. Figure 2 shows some of the pillar arrangements in the tested distributors. A special case is the

Figure 2. (a) Schematic of the colum, injection volume definition, and supply channels. (b-d) Top views of the central zones of three of the different considered distributors, filled with (b) single-size pillars with AR 5, (c) single-size pillars with AR 25, and (d) two regions of differently sized pillars, with, respectively, an AR of 25 and 5. Each picture shows the distributor zone (1) as well as the actual separation bed (2). The red dots represent the so-called exit points of the distributor. Panel (c) also shows how the transition between the two distributor zones (1 and 1′) can be optimized by adding “distributor wedges” (3).

Figure 3. Zooms of the side-wall regions of four of the different considered distributors for (a-c) radially interconnected distributors with (a) a uniform width (and pillars with AR 25) and a predistributor gap (width ) 5 µm), and with (b,c) diverging sidewalls, parallel to the sides of the diamonds in the distributor zone (and pillars with (b) AR 25 and (c) AR 5), and (d) the repeatedly bifurcating distributor.

mixed-size distributor shown in Figure 2d. Besides the represented designs, distributors filled with pillars with other AR’s (AR ) 2, 10, 15, 20, 25) and with a constant instead of a diverging width have been considered as well. Figure 3 shows some details of the side-wall design and the transition to the actual bed.

A constant in the design was the axial width of the pillars (lp), which was always taken as equal to 5 µm (see Figure 2b). This value was selected because this leads in combination with the target porosity of the distributor (porosity ε ) ratio of open space volume over total distributor volume) to an interpillar distance of Analytical Chemistry, Vol. 83, No. 2, January 15, 2011

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in which β ) tan-1(AR), δ is the minimal interpillar distance, and lp is the axial width of a distributor pillar. In all diverging distributor cases, the divergence angle R was selected such that the sloped side-walls of the distributor run parallel with the sides of the diamond-shaped pillars. Hence, the divergence angle R was different for each considered AR (see Figure 2), ranging from R ) 127° for AR ) 2 to R ) 175° for AR ) 25. The main motivation to use parallel running side-walls is that any other conceivable solution would lead to the formation of local deadzones. All designs proposed by Sant et al.,11 for example, also only included designs where the diverging side-wall runs parallel with the sides of the distributor pillars. Especially for high AR pillars, another advantage of the use of parallel side-walls is that it leads to distributors with large divergence angles, which in turn allows one to keep the distributors as short as possible because less axial distance is needed to reach a given column width. This is an advantage, because our simulations showed that very short distributor lengths suffice to obtain a homogeneous velocity field when high AR pillars are being used (down to 35 µm for the AR ) 25 pillars).20 Given that with its divergence angle of R ) 110°, the AR ) 2 pillar distributor needs a minimal distributor length of 200 µm to reach the full width of the 1 mm wide separation channel, and given that we wanted to compare all distributor types on the same foot (i.e., for the same total length), the majority of the diverging distributor designs with high AR pillars tested in the present study were proceeded by a uniform-width part after the diverging section to reach a total length of 200 µm. However, a few shorter variants were included as well to assess the importance of the distributor length. In the mixed-size distributor, so-called “distributor wedges” (see (3) in Figure 2d) were added to prevent the formation of a poorly permeated region in the wake of the last row of high AR pillars.20 The side-walls of these wedges are designed in the same way as the sloped side-wall in the diverging section of the diverging width distributors (see discussion immediately below). On the basis of our earlier experimental experiences,18 as well as on the seminal work of the Regnier group (see Figure 5 of ref 21), it was deemed critical to carefully design the side-walls of

the distributors. For the constant-width distributors (Figure 3a) and the constant part of the diverging distributors, we simply used the semiembedded side-wall designs we have developed in a sister study.22 In this approach, the side-wall is composed of semiembedded pillars identical to those in the channel. The entire ensemble of side-wall and semiembedded pillars was then shifted away from the first row of pillars to obtain the same fluid velocities in the side-wall region as in the central part of the channel. The optimal shift distance was determined via numerical flow simulations and varied between 0.3 and 0.35 µm, depending on the shape of the pillars. This shift is necessary to compensate for the difference in flow resistance between the side-wall region and the central region caused by the excess wall surface per volume in the side-wall region. To find the optimal through-pore size for which the higher liquid velocity in the side-wall zone would compensate for the extra distance sample molecules in this zone have to travel to the sidewall region, a number of different diverging distributor designs were considered. In these designs, the distance between the last pillar and the side-wall was gradually varied (with steps of 0.25 µm), going from the interpillar distance (2.5 µm) prevailing in the bulk of the distribution zone up to some 4.5 µm. Rather than using a fully straight-running side-wall, we opted for a stepwise profiled side-wall, with a periodicity equaling that of the pillar rows (see Figure 3b,c). In this way, the side-wall can run perfectly parallel with the sides of the distributor pillars over the longest possible distance. In addition, the small steps that are needed to pass on to the next row of pillars contribute to forcing the liquid through the through-pores running to the next row of pillars (see white arrows added to Figure 3c and d). Obviously, a number of other possible side-wall designs exist, out of which a straight line is the most obvious option. However, as can be verified by studying the mask designs shown in Figure 3, the best-fitting straight line through the stepped profiles would nowhere run perfectly parallel with the pillar side-walls. This would inevitably result in a more inhomogeneous side-wall region but would most probably still give good results. However, because this design parameter was not deemed important enough to be included in this study, and to allow for a fair comparison, the stepped profile was used in all investigated diverging distributor types. The stepped side-wall approach was also used for the bifurcating distributors (see Figure 3a). Each distributor was followed by the same separation bed, consisting of elongated hexagonal pillars (dlat ) 5 µm and dax ) 12.5 µm), positioned in a such a way that the distance between neighboring pillars is equal to 2.5 µm, with an external porosity ε ) 0.46. Fabrication Methods. To fabricate the microfluidic chip, a (100) silicon wafer (p-type, 5-10 Ω cm, thickness 525 µm, diameter 100 mm) was processed via three ultraviolet (UV) contact-photolithography and deep reactive ion etching (DRIE) steps. The first step defines the supply channels, the second step defines the separation channel with the pillar array, and the final lithography and etching step creates access holes (Figure 2a). Because the separation channel (pillar array) and the supply channels need to be etched to different depths, a “buried mask” method was applied for the first two etching steps. First, the silicon

(21) Regnier, F. E.; He, B. U.S. patent 6,596,144, 2003.

(22) Vangelooven, J.; Desmet, G. J. Chromatogr., A 2010, 1217, 8121-8126.

about 2.5 µm, which was considered to be just at the lower limit of the etching resolution of the available lithography and etching processes (obviously the nominal etching resolution was considered as being the lower limit at which the risks for unresolved pillars were negligible on the full wafer scale). The target porosity was more or less arbitrarily set around ε ) 50%, similar to that of the subsequent separation bed. For the perpendicular distance between neighboring diamond shaped pillars to be exactly δ ) 2.5 µm, they are positioned in a grid of unity cells with a transversal width ddom and axial length ldom as indicated in Figure 2b:

ddom )

ldom )

470

AR*lp + δ 2

(1)

lp cos β δ + δ sin β + 2 AR 2*AR

(

)

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(2)

wafer was oxidized by dry oxidation (Amtech tempress omega junior, 1100 °C, 1 h 40 min) to obtain a silicon oxide layer of 200 nm thickness. Photolithography (EVG 501) was carried out with the mask containing the separation channel (pillar array) geometry (Olin 907/12, spun for 20 s @ 6000 rpm, vacuum contact, exposure time 2.5 s). Subsequently, the geometry is transferred into the silicon oxide layer by reactive ion etching (Adixen AMS100DE). The photoresist layer was then removed in an oxygen plasma (Tepla 300E), and a new photoresist layer was applied (Olin 908/ 35, spun for 20 s @ 4000 rpm, hard contact, exposure time 8 s). This second lithography step defined the supply channels geometry, which was etched into the silicon oxide layer by wet chemical etching in BHF. At this point, the silicon surface was only exposed in the areas of the supply channels, while the separation channel geometry was still covered with (“buried under”) the photoresist layer. By DRIE (Adixen AMS100DE), the supply channels were etched to a depth of 25 µm. Next, the photoresist was removed in an oxygen plasma to expose the separation channel pattern in the silicon oxide layer. The second DRIE step etched the separation channel to a depth of 25 µm, while the supply channels continue etching to a final depth of 50 µm. To create the access holes, a photolithography step was performed on the backside of the wafer with the mask containing the access hole pattern. The silicon oxide layer was pattered in BHF, and the final DRIE step is then performed to etch 500 µm through the wafer. Removing the photoresist layer as well as the silicon oxide layer finishes the processing steps of the silicon wafer. To finalize the device, a glass wafer (Schott Borofloat BF-33, 100 mm diameter, 500 µm thickness) was attached to the patterned silicon wafer by anodic bonding (T ) 400 °C, Umax ) 1200 V), and the wafer stack was diced into individual chips. Chemicals, Setup, and Measurement Methods. The experimental setup employed in this study was made in-house and has already extensively been described elsewhere.23,3 Briefly, the connection between the chip and the external sample and mobile phase reservoirs was made by fixing the chips in an in-house fabricated PMMA holder with threaded through-holes designed to be compatible with commercially available Nanoport (Achrom, Belgium) fluidic connectors. Both the sample and the mobile phase were forced into the chip using gas-pressurized stainless steel vessels, wherein the pressure in both containers could be regulated independently through two different pressure controllers (EL-Press, Bronkhorst, The Netherlands), fed by nitrogen gas. A maximum pressure of 30 bar was used during the experiments. An in-line filter (dpor ) 2 µm) was integrated in the fluid circuit between these vessels and the chip to reduce the risk of blockages within these microfluidic channels. The distribution of the fluorescent tracer bands (Coumarine 440, 5.10-3M, Fluka, Belgium) across the channel inlet was recorded by an inverted microscope ((IX71, Olympus, Belgium), equipped with a UV-1 filter cube set allowing for excitation at 350 nm and for emission above 450 nm and an air-cooled charged coupled device (CCD) fluorescence camera (ORCA-ERC4742, Hamamatsu Photonics, Belgium). The microscope was mounted on a breadboard (MIG 23-2, Newport, The Netherlands), together with a linear displacement stage (M-TS100DC.5, Newport) and a speed control-

ler (MM, 4006 Newport). The displacement stage was used to translate the chip during the flow experiments at the same but opposite speed as the migrating bands. This allowed keeping the migrating tracer bands (moving at speeds up to 6.5 mm/ s) continuously in the field of view of the CCD camera while being able to use a sufficiently high magnification. As in our previous study,18 an off-chip injection was mimicked on the chip using an “injection box” in front of the actual column. The actual injection consists of two steps: in the first step, the fluorescent dye is pumped into an “injection box” by opening the sample supply channels and closing the mobile phase inlet and outlet. In the second step, the off-chip valves (Rheodyne MX, Germany) are switched, closing the sample inlet and outlet channels and opening the mobile phase channel (HPLC grade Methanol, Fluka, Belgium). Subsequently, the sample is pumped into the head of the 1 mm wide column, where it is distributed by one of the studied distributor designs. The two injection steps were automated using two externally connected six-port nanovalves (RheodyneMX, Germany) controlled via an in-house written C++ program. The performance of the different tested distributors is evaluated on the basis of the variance (σx2) of the sample bands eluting from the distributors. The injection box has identical volumes in all columns, and monitoring the M0’s of the injected peaks allowed one to check that equal amounts of sample are injected in the different experiments. The σx2-values of the tracer were calculated from the spatial intensity profiles, obtained by averaging the recorded fluorescence intensity over each column of pixels (in the transversal direction) in the obtained CCD images (examples, see Figure 5). For each injection, the intensity profiles were fitted with a normal distribution and were subjected to a moment analysis, using the following expression to calculate the spatial moments:24,25

(23) De Malsche, W.; Eghbali, H.; Clicq, D.; Vangelooven, J.; Gardeniers, H.; Desmet, G. Anal. Chem. 2007, 79, 5915–5926.

(24) Aris, R. Proc. R. Soc. London, Ser. A 1959, 252, 538–550. (25) Neue, A.; Berdichevsky, U. J. Chromatogr., A 1990, 535, 189–198.

Mn )

∫

∞

0

c(x) · xn dx

(3)

Also, the σ2-value can be determined through:

σ2 )

( )

M1 M2 M0 M0

2

(4)

Both methodologies resulted in comparable σx2-values, although those obtained with moment analysis tend to be a few percent higher (2-5%) than those obtained in the normal distribution fittings. Because moment analysis is more sensitive to noise on the data, more scatter was present. For this reason, the σx2values from the moment analysis are only used if the Gauss fit was inaccurate (R2 e 0.995). In practice, this means that only the results from the AR ) 5 distributors are analyzed with moment analysis. Because of their poor performances, they are the least interesting ones anyhow. As the initial variance before the distributor could not be measured due to frame rate limitations of the camera, the peak volumes were checked by calculating the zeroth moment to ascertain a fair comparison

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Figure 4. Scanning electron microscope (SEM) images of a few of the investigated distributors: (a) side-wall region of a radially interconnected distributor and the first part of the separation bed filled with hexagonal pillars; (b) a 180° inlet of a radially interconnected distributor (AR 5) with a uniform width; (c) a bird eye’s view of the mixed size distributor (AR 25 + 5) showing a part of the injection box, the two distributor zones, and the first part of the separation bed; and (d) a zoom of the transition zone with the distributor wedges.

of distributor performance. It was confirmed that the volumes of the injected peaks were identical within a 5% margin. RESULTS AND DISCUSSION Microfabrication Results. Figure 4 shows some of the distributors after etching. Because of the tilted image, Figure 4a,b shows the nearly perfectly vertical sidewalls of the etched pillars in a 25 µm deep bed that can be obtained with the employed DRIE Bosch process. The distance between the pillars, however, was about 0.15 µm larger than in the mask design. This is due to the under-etching that inevitably occurs during the DRIE process. This is not uncommon, and the amount of under-etching lies in the expected range, but might nevertheless lead to a deviation from the expected performance, especially in the side-wall region of the both the bed and the distributor, as it is well-known that this region is very sensitive to small deviations from the optimal design.26,27 As can clearly be noted from Figure 4d, also the shape of the diamond-shaped pillars has changed significantly as compared to the mask designs in Figure 3. The sharp tips of the diamonds have been completely etched away. Instead, the diamonds end in a semicircular shape. This of course creates larger through-pores between two neighboring diamonds. Normally, these pores (indicated by the white arrow in Figure 4d) were designed to be 2.5 µm. Yet, for the AR ) 25 diamonds, this turned out to be about 16 µm. Also, for the AR ) 5 diamonds, the pore width is about 6.5 µm instead of 2.5 µm. The fact that the tips of the AR ) 5 diamonds are etched away to a lesser extent can be attributed to their less elongated shape, making the tip of (26) Vervoort, N.; Billen, J.; Gzil, P.; Baron, G. V.; Desmet, G. Anal. Chem. 2004, 76, 4501–4507. (27) De Malsche, W.; Gardeniers, J. G. E.; Desmet, G. Anal. Chem. 2008, 80, 5391.

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the design much less sharp than in the AR ) 25 case. The difference between design and result is too large to be solely attributed to the under-etching occurring during the DRIE and is most likely also at least in part caused by the resolution of the photomask in the lithography step. The occurrence of these imperfections shows that experimental verification is needed after a theoretical design based on CFD. Influence of Aspect Ratio (AR). Figure 5 compares the CCD camera images of the tracer band profiles eluting from some of the different investigated distributor types for the same flow rate. The data shown for the bifurcating distributor were originally included in a former experimental study,18 but were included here to act as a reference. As can clearly be seen from the sequence in Figure 5a-e, comparing single-sized radially interconnected distributors with pillars with different AR, the most straight and narrow bends are obtained for AR ) 15. When the AR of the pillars is too small (roughly AR e 10, see Figure 5a,b), the bands eluting from the distributor display a strong trans-column warp. The smaller is the AR, the more pronounced is this trans-column warp. This can readily be understood from the fact that, when the AR is too small, the pillars are simply not wide enough to create a sufficiently strong transversal transport. It is well-known from the distributors used in packed bed columns that the performance of a distributor depends strongly on its ability to enhance the transversal over the axial dispersion.16,28 When the pillar AR is sufficiently large, the trans-column warp completely disappears, as can be noted from the fact that the bands shown in Figure 5c-e for AR ) 15, 20, and 25 display a perfectly flat trans-column velocity profile. Some small deviations can be noted near the side-wall located at the top of Figure 5d (28) Lisso, M.; Wozny, G.; Arlt, W.; Beste, A. Chem. Ing. Tech. 2000, 72, 494– 502.

Figure 5. CCD camera images of an injected coumarin dye band eluting from different diverging flow distributors, taken 100 µm after the distributor for a single-size pillar distributor with (a) AR ) 5; (b) AR ) 10; (c) AR ) 15; (d) AR ) 20; (e) AR ) 25; (f) a mixed-size distributor (AR ) 25 + AR ) 5); and (g) a repeatedly bifurcating distributor. Carrier liquid ) methanol, tracer ) Coumarine 440 (5 × 10-3 M).

and the side-wall located at the bottom of Figure 5e for, respectively, the AR ) 20 and 25 cases, as the bands shows a slight forward deviation near these side-walls. These deviations can, however, be explained by a mismatch of a few micrometers or less between the distributor and the channel width on some channels on the mask. However, increasing the AR also invokes a serious drawback, because, as can be noted from Figures 2c-e, the high AR pillar distributors (AR ) 15, 20, and 25) produce bands with a strongly undulating profile. This was already predicted in our numerical studies20 and is a consequence of the fact that the regions in the separation bed that lie in the wake of the pillars making up the last pillar row of the distributor become poorly permeated when the AR of these pillars is too large, thus creating a series of new local flow distribution problems. As can be noted by comparing the images in Figure 5c-e, the local flow maldistribution problem that is generated near the exit points of the distributor becomes ever more pronounced when the AR of the pillars increases, that is, when the number of distributor exit points decreases. From Figure 5 it can be concluded that, at least for the presently considered 1 mm wide channels, the pillars with AR ) 15 clearly offer the best compromise between achieving a high number of distributor exit points (leading to a low local band warp), on the one hand, and the ability to rectify the trans-column velocity profile, on the other hand (leading to a low trans-column band warp). Obviously, and as can clearly be witnessed from Figure 5f, the best distributor performance is obtained when using a mixed-size distributor, starting with a high AR zone (AR ) 25 in the present example) and ending with a low AR zone (AR ) 5 in the present example). This design combines the good radial

dispersion properties of a high AR distributor with the large number of exit points of a low AR distributor, using the so-called distributor wedges (see (3) in Figure 2d) to exclude the liquid from the dead zones that would otherwise form in the wake of the pillars in the last row of the high AR pillar region. The spatial variance of about 1000 µm2 that is achieved for the AR25+5 distributor is, despite the relatively large distance between the pillars (2.5 µm designed on the mask, 2.65 µm in reality because of the underetching), and despite the fact that the distributor length is clearly oversized (see further on), already small enough to be used in combination with high resolution separation beds. Considering that the spatial variance of a separation bed with plate height H and length L is given by σx2 ) H · L, it can easily be verified that a distributor of the AR25+5 type will contribute for only 10% to the total variance if a separation bed with very low plate heigths (1 µm) and a short length (1 cm) is considered. When the bed is 10 cm long, the distributor would even only make up for 1% of the total variance. Figure 5g shows that also the repeatedly bifurcating distributor can produce straight running bands (with some notable exceptions near the side-walls of the channels), without suffering from the strong local band warping problem observed for the AR ) 20 and the AR ) 25 pillars in Figure 5d,e. The latter is of course due to the fact that the number of feeding channels in the bifurcating distributor continuously increases from the distributor inlet to its outlet for the bifurcating distributor. However, the eluting band clearly has a larger overall width. As can be noted from Table 1, showing the internal volumes for all studied distributors, this can most probably be related to the fact that the bifurcating distributor Analytical Chemistry, Vol. 83, No. 2, January 15, 2011

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Table 1. Porosities and Total Internal Volumes of the Different Investigated Distributor Types distributor

ε

V (nL)

bifurcating AR25 AR20 AR15 AR10 AR5 AR25+5

N.A. 0.505 0.506 0.508 0.513 0.526 0.509

4.52 2.38 2.29 2.22 2.06 1.51 2.91

has a much larger overall liquid volume than the radially interconnected distributors, for it is in agreement with one’s physical expectations that the band broadening produced by a given type of flow system increases with its volume.19 It is certainly possible to conceive repeatedly bifurcating distributors with a smaller liquid volume than the one presently tested, but this was not attempted in the present study. Anyhow, it can be anticipated that any attempt to reduce the overall volume will require a reduction of the width of the channels in the first part of the distributor, which in turn will lead to a large increase in local velocity. Another drawback of the repeatedly bifurcating distributor design is that it is very sensitive to local etching errors or local obstructions that form during its use: once a given branch produces a different flow resistance, the fluid flowing through this branch cannot mix with the liquid in the other branches, and will hence leave the distributor at a different time than the rest of the fluid. As can be noted from Figure 6, where the quality of the different flow distributors (all of equal length) is represented by the variance of the eluting band profiles, the observations that can be made from Figure 5 can be generalized over a broad range of flow rates, as the order of the curves connecting the different flow rate data points follows the same trend as observed in Figure 5. Obviously, the AR ) 5 case produces the largest variance of all RI distributors, and the position of the variance curves decreases when increasing the AR up to AR ) 10 and AR ) 15 (see arrow (1) in Figure 6). From this value on, a further increase of the AR starts to have a negative effect (because of the reduction of the number of exit points and the concomitant local warping), as the variance curves for the AR ) 20 and AR ) 25 cases shift upward again (see arrow (2) in Figure 6). It is also interesting to note that the variance of the produced bands is only weakly dependent on the flow rate. In the first place, this follows from the fact that the global warping of the bands is independent of the flow rate, because it is fully determined by the shape of the velocity field, which is independent of the flow rate. This means the velocity only has an effect on the local axial dispersion. For the latter, it is important to note that in a TI distributor the lateral velocity differences are essentially eliminated by convective mixing (in the transversal direction), because it is well-known from the theory of band broadening as formulated by Giddings29 that, when velocity differences are terminated by a convective effect (usually referred to as eddy dispersion), this leads to a band broadening that is independent of the flow rate. This is different from band broadening sources where the lateral velocity differences need to be eliminated by molecular diffusion. (29) Giddings, J. C. Dynamics of Chromatography; M. Dekker: New York, 1965.

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In this case, the band broadening increases linearly with the flow rate (so-called C-term band broadening). Considering the operation of the distributor during separations, it should be noted that the pillars in the distributor region will in general undergo the same coating procedures as the pillars in the bed. However, assuming that the pillars in the distributor are coated in a uniform way (and there is no reason to doubt this), the only effect of the retention inside the pillars is a general reduction of the average velocity with a factor (1 + k′), wherein k′ is the retention factor inside the distributor. Because the global warp of the band is independent of the average velocity (see discussion of Figure 6), a distributor producing straight bands will always do this, regardless of whether the pillars can retain the analytes or not. Uniform Width versus Diverging Distributors. Another important issue in the design of a distributor is its divergence angle. Figure 7 compares a uniform-width distributor with a diverging-width distributor for the AR ) 15 case. In agreement with the literature, the diverging distributor produces a lower variance.11,6 This can readily be explained by the fact that the diverging distributor design eliminates the regions that are the least permeated in the uniform distributor design, that is, the extreme corners at the front of the distributor. Overall, the effect of the divergence angle is relatively small, amounting to some 18% (low flow rates) to 10% (high flow rates). This might of course also be linked to the fact that the considered divergence angle for the AR ) 15 case is still relatively large and close to 180°. It cannot be excluded that other divergence angles might give even better results than the presently considered one, but this will anyhow require a tedious design of the side-walls, and we can currently not conceive of a design wherein the divergence angle can be reduced without creating local dead zones near the pillars closest to the side-wall. Despite their slightly worse distribution performance, 180° distributors might still prove to be useful to prevent clogging at the column inlet. In the current designs of the diverging inlets in distributors with high AR diamonds, only two narrow access points to the column are present (Figure 2d), leading to a high risk of clogging. This risk can be decreased by omitting the first pillar of the first few pillars and ultimately by using a 180° inlet. As already mentioned in the experimental section, we also compared designs with different spacings for the side-wall in the diverging part of the distributors with AR ) 20 and 25 pillars. We started from a zero-shift case where the distance between the sidewall and the first diagonal row of pillars is equal to that in the center of the distributor, and we increased the gap stepwise up to a case where the stepped side-wall was shifted 2 µm away from this first diagonal row of pillars. No measurable or significant positive effects were observed. In the 1.5 µm shift case, a slight reverse warp resulted, which worsened in the 2 µm shift distributor (data not shown). From this observation, we can conclude that such a shift of the side-wall is not necessary for a well functioning distributor, but might improve the performance of a poorly performing radially interconnected distributor. Influence of Reducing Distributor Length. High AR pillar distributors have an additional advantage in the fact that they can be made much shorter than their low AR counterparts. This leads to an additional reduction of the band broadening, because the

Figure 6. Plots of spatial band variance (σξ2) versus liquid velocity (uliq) for different diverging distributors. Repeatedly bifurcating distributor ([), AR ) 5 distributor (0), AR ) 10 distributor (+), AR ) 25 distributor (9), AR ) 20 distributor (2), AR ) 15 distributor (×), and mixed-size distributor AR ) 25 + AR ) 5 (b). Carrier liquid ) methanol, tracer ) Coumarine 440 (5 × 10-3 M). The σξ2-values were determined at a position located 100 µm after the end of the distributor in all cases. Arrow (1) indicates the decrease in variance when AR is increased from 5 to 15, and arrow (2) indicates the increase in variance when the AR is further increased to 25.

Figure 7. Comparison of spatial band variance (σx2) versus liquid velocity (uliq) plots for two distributors with either a diverging inlet (9) or a uniform width (inlet ) 180°, [). CCD images, taken 100 µm after the distributor, of both are shown. The σx2-values were determined 100 µm after the end of the distributor for all cases.

latter increases with the distributor length. Figure 8 shows that reducing the length of a AR 25 distributor does not affect the global warp of the resulting band, as both of the bands are straight. Decreasing distributor length also has a positive effect on column permeability, but because we could not determine the pressure drop with an accuracy better than 5-10% (because the

frequent occurrence of small leakages), we can only conclude that the presence of the distributors does not increase the overall pressure drop by more than a few percent, because we could not observe a significant difference in pressure drop among the channels containing different distributors, nor could we observe a difference with the channels containing no distributor. Analytical Chemistry, Vol. 83, No. 2, January 15, 2011

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Figure 8. Comparison of spatial band variance (σx2) versus liquid velocity (uliq) plots for AR ) 25 distributors with different lengths. The resulting σ2 decreases as L is decreased from L ) 200 µm (2) over L ) 100 µm (9) to L ) 50 (×). The inserted CCD images show that a decrease in distributor length to L ) 50 µm does not affect the global warp, but that local band broadening is reduced in the shorter distributor. The σx2values were determined 100 µm after the end of the distributor for all cases.

The length of the distributor should hence be selected such that it is just sufficiently long to flatten the axial velocity profile. Figure 8 shows that making it longer than this only leads to unnecessary band broadening. For pillars with a low AR, this optimal length is difficult to predict without the aid of numerical computations. However, when the ratio of transversal to axial permeability is sufficiently high, the fluid preferably flows in the transerval direction, and it appears that the number of pillar rows that is needed to achieve a globally flat velocity profile is in this case just equal to the ratio of the column width over the pillar width. This ratio corresponds to the number of splitting points the fluid needs to cross before it can reach the side-wall of the distributor starting from the central inlet. In the case of the AR ) 25 pillars, the 50 µm long distributor of the fluid elapses a lateral distance of 62.5 µm after each splitting point (i.e., after each row of pillars), so that about 8 rows are needed to reach the side-wall just by the subsequent splitting steps. In the present design, two extra rows of pillars were added as a safety factor. Whether or not these last two rows can be omitted is difficult to predict and will certainly depend on the probability of the occurrence of etching errors. From the above transversal splitting argument, it can be concluded that, when designing a distributor for channels with a different width, one can simply select diamond shaped pillars with a lateral width making up at least about 10-15% of the total channel width to meet with the large transversal over axial permeability ratio, criterion needed to force the liquid to proceed through the distributor via subsequent transversal splitting. Depending upon whether one pillar makes up 10% or 15% of the total channel width, 8-10 rows of these pillars should then be put in series. For safety, one or two additional rows can be added 476

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to anticipate etching or fouling problems. After this initial region, the number of exit points needs to be increased by providing one or more regions with pillars with a smaller aspect ratio. The number of rows that are needed in these subsequent zones can again be determined using the same splitting point criterion as that used for the first zone of pillars (replacing the channel width by the distance between two of the neighboring exit points of the preceding zone with the higher AR pillars to calculate the required number of low AR pillar rows). To prevent the formation of dead zones in these subsequent zones, the type of distributor wedges shown in Figure 2d should be used. Finally, Figure 9 shows that when the flow distributor is working properly, that is, succeeds in a producing a globally flat trans-column velocity profile, the band broadening that is measured in the rest of the bed is only determined by the local band broadening properties of the separation bed itself. This is the case for the repeatedly bifurcating and the AR ) 25+5 distributor, as can be noted from the fact that the variance increases in a linearly proportional way with the distance in the bed, indicating a constant source of band broadening (and hence purely due to the pillars in the separation bed). Obviously, this is not the case for the AR ) 5 distributor, as there the variance still varies in a nonlinear way with the distance. This nonlinear variation is a consequence of the fact that, because of the incomplete lateral distribution within the distributor, the first part of the bed also still partly operates as a flow distributor, using the (poor) transversal transport of the bed to further rectify the trans-column profile. CONCLUSIONS Studying a large number of different flow distributor designs, the best performance was obtained with radially interconnected

Figure 9. Plots of spatial band variance (σx2) versus traveled distance (x) for an AR ) 5 distributor (9) for a repeatedly bifurcating distributor ([) and for an AR ) 25 + AR ) 5 distributor (2).

distributors with a diverging inlet section and filled with diamondshaped pillars, oriented perpendicular to the main flow direction and with a high transversal over axial aspect ratio. As compared to repeatedly bifurcating distributors, radially interconnected distributors have the advantage that they can spread the flow over a larger number of channels (thus minimizing the local velocities) and offer many cross-mixing points that allow one to make up for any differences in flow resistance between different parts of the distributor that might occur because of an imperfect fabrication or because of the formation of local obstructions during the use of the device. Preferably, the radially interconnected distributor starts with a diverging section containing some 10-12 subsequent rows of high aspect ratio pillars (with a transversal width making up 10-15% of the final channel width). A simple and effective design criterion for the divergence angle is to select it such that the sloped side-walls run parallel with the sides of the diamond-shaped pillars. After this first zone, one or more regions with pillars with a smaller aspect ratio should be provided to increase the number of exit points. To prevent the formation of dead zones in these subsequent zones, so-called distributor wedges can be used to prevent the formation of any dead zones in the wake of the large aspect ratio pillars of the preceding section. Trying to fabricate pillars with a high AR (axial width ) 5 µm and lateral width ) 75 µm) with standard UV-lithography and DRIE equipment, significant parts of the diamond tips are etched away, resulting in rather blunt-shaped structures. Also, the perpendicular inter pillar distances deviated by about 0.15 µm (or 6%) as compared to the design. Despite these etching issues, despite the relatively large distance between the pillars (2.5 µm designed on the mask, 2.65 µm in reality because of the underetching), and despite the fact that the employed distributor lengths were clearly oversized, spatial band variances in the order of about 1000 µm2 could be achieved. This is already small enough to be used in combination with high resolution separation beds.

Further improvement possibilities can be expected from a further reduction of the pillar and interpillar sizes (by switching to deep UV-lithography techniques for example), from a further refinement of the mixed-size distributors (switching to three instead of two pillar size regions, or improving the design of the so-called distributor wedges), and possibly also from a further optimization of the distribution angle (including design of sidewalls). ACKNOWLEDGMENT J.V. gratefully acknowledges a specialization grant from the instituut voor Wetenschap en Technologie (IWT) from the Flanders region. F.D. is supported through a specialization grant from the Flemish Fund for Scientific Research (FW0). NOMENCLATURE a inlet angle (deg) δ gap width before distributor zone (m) ε external porosity (-) H height of a theoretical plate (m) L column length (m) l distributor length (m) lp axial length of distributor pillars (m) ldom axial domain size (m) Mn nth-order moment σ2x spatial variance (m2) T temperature (°C) uliq liquid velocity (m/s) wdom radial domain size (m) wp radial width of distributor pillars (m)

Received for review May 19, 2010. Accepted October 4, 2010. AC101304P

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