Anal. Chem. 2008, 80, 1641-1648
Particle Dispersion and Separation Resolution of Pinched Flow Fractionation Abhishek Jain and Jonathan D. Posner*
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, Arizona 85287
This paper investigates a hydrodynamic particle separation technique that employs pinching of particles to a narrow microchannel. The particles are subject to a sudden expansion which results in a size-based particle separation transverse to the flow direction. The separation resolution and particle dispersion are measured using epifluorescence microscopy. The resolution and dispersion are predicted using a compact theoretical model. Devices are fabricated using conventional soft lithography of polydimethylsiloxane. The results show that the separation resolution is a function of the microchannel aspect ratio, particle size difference, and the microchannel sidewall roughness. A separation resolution as large as 3.8 is obtained in this work. This work shows that particles with diameters on the order of the sidewall roughness cannot be separated using pinched flow fractionation. Rapid and high-resolution analysis of biological cells and macromolecules are of prime interest for biological research as well as the development of point-of-care and environmental monitoring technologies. The separation technique employed to separate particles depends upon various particle properties including the particle size, mass, surface charge, dielectric constant, surface modification, and stiffness. Each separation method can be evaluated based on the separation time, efficiency of particle separation, throughput, and applicability to particle properties. In the 90s, Manz et al. pioneered the micro-total analysis system concept of performing several labor and time intensive steps such as sample preparation, mixing, detection, and separation on a single microfabricated device.1 Over the past 15 years there has been significant progress in the development of microchip based particle separation techniques based purely on fields, hydrodynamics, or both fields and hydrodynamic flow. Here, we briefly review separation techniques employed on rigid and semirigid particles and neglect long chain biopolymers such DNA, RNA, and proteins for which separation science is well developed.2-5 We also neglect various chromatographic techniques such as high performance liquid chromatography (HPLC) which * To whom correspondence should be addressed. E-mail: Jonathan.Posner@ asu.edu. Phone: (480) 965 1799. Fax: (480) 965 1384. (1) Manz, A.; Graber, N.; Widmer, H. M. Sens. Actuators, B: Chem. 1990, 1, 244-248. (2) Yu, X. B.; Xu, D. K.; Cheng, Q. Proteomics 2006, 6, 5493-5503. (3) Liu, S. R.; Guttman, A. TrAC, Trends Anal. Chem. 2004, 23, 422-431. (4) Khandurina, J.; Guttman, A. Curr. Opin. Chem. Biol. 2003, 7, 595-602. (5) Andersson, H.; van den Berg, A. Sens. Actuators, B: Chem. 2003, 92, 315325. 10.1021/ac0713813 CCC: $40.75 Published on Web 01/26/2008
© 2008 American Chemical Society
uses stationary phases such as gels or functionalized surfaces for particle affinity and steric interactions. Field based particleseparation methods include electric field based methods that use electroosmosis and electrophoresis,6-8 dielectrophoresis,9-12 and electrowetting.13 In addition, ultrasound radiation14-16 and optical fields17 have been used to separate particles. Field flow fractionation (FFF) uses both a velocity gradient and a transverse field to separate particles. The purpose of the transverse field is to migrate the particles into different regions in the velocity profile. Their location in the velocity determines their velocity and thus the elution time. A wide variety of transverse fields have been demonstrated with FFF, including electric,18-20 thermal,21-23 dielectrophoresis,24-26 and asymmetric flow(AsFFF).27,28 Split-flow (SPLITT) field based fractionation methods have also been demonstrated.29-32 (6) Gascoyne, P. R. C.; Vykoukal, J. Electrophoresis 2002, 23, 1973-1983. (7) Radko, S. P.; Chrambach, A. Electrophoresis 2002, 23, 1957-1972. (8) Johann, R.; Renaud, P. Electrophoresis 2004, 25, 3720-3729. (9) Fatoyinbo, H. O.; Hughes, M. P.; Martin, S. P.; Pashby, P.; Labeed, F. H. J. Environ. Monit. 2007, 9, 87-90. (10) Kralj, J. G.; Lis, M. T. W.; Schmidt, M. A.; Jensen, K. F. Anal. Chem. 2006, 78, 5019-5025. (11) Kumar, A.; Acrivos, A.; Khusid, B.; Jacqmin, D. Fluid Dyn. Res. 2007, 39, 169-192. (12) Li, Y. L.; Dalton, C.; Crabtree, H. J.; Nilsson, G.; Kaler, K. Lab Chip 2007, 7, 239-248. (13) Cho, S. K.; Zhao, Y. J.; Kim, C. J. Lab Chip 2007, 7, 490-498. (14) Masudo, T.; Okada, T. Curr. Anal. Chem. 2006, 2, 213-227. (15) Nilsson, A.; Petersson, F.; Jonsson, H.; Laurell, T. Lab Chip 2004, 4, 131135. (16) Yasuda, K.; Umemura, S.; Takeda, K. J. Acoust. Soc. Am. 1996, 99, 19651970. (17) MacDonald, M. P.; Spalding, G. C.; Dholakia, K. Nature 2003, 426, 421424. (18) Gale, B. K.; Caldwell, K. D.; Frazier, A. B. IEEE Trans. Biomed. Eng. 1998, 45, 1459-1469. (19) Kantak, A. S.; Srinivas, M.; Gale, B. K. Anal. Chem. 2006, 78, 2557-2564. (20) Graff, M.; Frazier, A. B. IEEE Trans. Nanotechnol. 2006, 5, 8-13. (21) Edwards, T. L.; Gale, B. K.; Frazier, A. B. Anal. Chem. 2002, 74, 12111216. (22) Janca, J. J. Liq. Chromatogr. Relat. Technol. 2002, 25, 683-704. (23) Janca, J. Int. J. Polym. Anal. Charact. 2006, 11, 57-70. (24) Muller, T.; Schnelle, T.; Gradl, G.; Shirley, S. G.; Fuhr, G. J. Liq. Chromatogr. Relat. Technol. 2000, 23, 47-59. (25) Wang, X. B.; Yang, J.; Huang, Y.; Vykoukal, J.; Becker, F. F.; Gascoyne, P. R. C. Anal. Chem. 2000, 72, 832-839. (26) Yang, J.; Huang, Y.; Wang, X. B.; Becker, F. F.; Gascoyne, P. R. C. Biophys. J. 2000, 78, 2680-2689. (27) Yohannes, G.; Sneck, M.; Varjo, S. J.; Jussila, M.; Wiedmer, S. K.; Kovanen, P. T.; Oorni, K.; Riekkola, M. L. Anal. Biochem. 2006, 354, 255-265. (28) Kang, D. J.; Moon, M. H. Anal. Chem. 2004, 76, 3851-3855. (29) Williams, P. S.; Levin, S.; Lenczycki, T.; Giddings, J. C. Ind. Eng. Chem. Res. 1992, 31, 2172-2181. (30) Giddings, J. C. Sep. Sci. Technol. 1985, 20, 749-768.
Analytical Chemistry, Vol. 80, No. 5, March 1, 2008 1641
Figure 1. Continuous hydrodynamic size-based separation of particles in a pinched microchannel. (a) Schematic of separation microdevice. Particles are introduced from the lower inlet and the bulk flow from the upper inlet such that the particles are pinched to the sidewall. The particles move along their center streamline and accordingly separate in the transverse direction due to the linear expansion of streamlines in the expanded chamber. (b) The particle widths (σA + σB) and peak distance (∆z) determine the separation resolution. (c) Inverted epifluorescence photograph (10×, NA 0.3) of separation of 5 and 15 µm particles in one such microdevice (see Supporting Information for a movie of the separation).
Pure flow based separation methods include diffusion based methods such as the H-filter33 and the T-filter.34 Hydrodynamic chromatography35,36 as well as mechanical obstacles37,38 are other examples of pure hydrodynamic separations using laminar flow. A similar concept was developed by Yamada et al. called pinched flow fractionation (PFF).39 In this method, the particles are separated based on size transverse to the flow direction. A variant of this technique has been conducted by Zhang et al. which uses (31) Moon, M. H.; Kim, H. J.; Lee, S. J.; Chang, Y. S. J. Sep. Sci. 2005, 28, 1231-1236. (32) Narayanan, N.; Saldanha, A.; Gale, B. K. Lab Chip 2006, 6, 105-114. (33) Schulte, T. H.; Bardell, R. L.; Weigl, B. H. Clin. Chim. Acta 2002, 321, 1-10. (34) Kamholz, A. E.; Weigl, B. H.; Finlayson, B. A.; Yager, P. Anal. Chem. 1999, 71, 5340-5347. (35) Blom, M. T.; Chmela, E.; Oosterbroek, R. E.; Tijssen, R.; van den Berg, A. Anal. Chem. 2003, 75, 6761-6768. (36) Chmela, E.; Tijssen, R.; Blom, M.; Gardeniers, H.; van den Berg, A. Anal. Chem. 2002, 74, 3470-3475. (37) Huang, L. R.; Cox, E. C.; Austin, R. H.; Sturm, J. C. Science 2004, 304, 987-990. (38) Davis, J. A.; Inglis, D. W.; Morton, K. J.; Lawrence, D. A.; Huang, L. R.; Chou, S. Y.; Sturm, J. C.; Austin, R. H. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 14779-14784. (39) Yamada, M.; Nakashima, M.; Seki, M. Anal. Chem. 2004, 76, 5465-5471.
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a varying channel width with improved separation resolution.40 In subsequent work, Yamada and co-workers improved the lateral separation by adding asymmetrical outlet branches to their device.41,42 Previous work on PFF demonstrates its efficacy but does not specifically address the sources of dispersion or the separation resolution. Here we focus on measuring and predicting the dispersion and separation resolution of PFF devices. We present a compact theory for predicting the dispersion and separation resolution and show that these quantities are dependent on the device geometry, particle size, and device sidewall roughness. THEORY In pinched flow fractionation, a particle laden stream is pinched to a microchannel sidewall in a narrow channel. The particles in the narrow channel are pinched to the wall at a distance equal to their radius and will move along streamlines that pass through their hydrodynamic centers. After the pinched section, the flow (40) Zhang, X. L.; Cooper, J. M.; Monaghan, P. B.; Haswell, S. J. Lab Chip 2006, 6, 561-566. (41) Takagi, J.; Yamada, M.; Yasuda, M.; Seki, M. Lab Chip 2005, 5, 778-784. (42) Sai, Y.; Yamada, M.; Yasuda, M.; Seki, M. J. Chromatogr., A 2006, 1127, 214-220.
undergoes a rapid expansion where the laminar flow streamlines are amplified. The particles travel along their streamlines and are separated in the transverse direction as shown in Figure 1a. The separation resolution is a function of the distance between the centers of the two particle peaks and the particle dispersion widths as shown in Figure 1b. Figure 1c shows an image of 5 and 15 µm particles being separated with a design pinched width of 25 µm and design aspect ratio of 30. The microfluidic channels with large width to depth ratios (e.g., the expanded channel) can be approximated as two closely spaced parallel plates similar to a Hele-Shaw cell. At low Reynolds numbers, the depth averaged Navier-Stokes equation reduces to the Laplace equation for pressure (Darcy’s law). This equation is a potential flow equation and based on this assumption, the streamlines will linearly expand with the channel dimensions. Nearly linear amplification of streamlines has also been experimentally observed by Yamada et al.,39 and therefore, the distance between the particle centers in the broadened section is given as
∆z )
a∆dp 2
(1)
where a is the aspect ratio of the device defined as the ratio of broadened section width and pinched section width (wb/wp) and ∆dp is the difference of the particle diameters.39 Equation 1 assumes that the particles are completely pinched to the wall of the pinched section before entering the broadened section. Yamada et al.39 use the assumption of large width to depth ratio (wp/h . 1) microchannels for developing a compact relation that predicts the ratio of bulk streamflow rate QB and particle streamflow rate QP required for pinching the particle laden stream to the channel wall. This equation assumes that the velocity profile can be modeled as two infinite plates and does not account for the transverse velocity profile. Yamada’s relation underpredicts the actual flow rate ratio required to pinch the particle stream to the wall. Using the exact analytical solution for fully developed flow in a rectangular duct,43 we can predict the required flow rate ratio with greater accuracy. This analysis is given in the Supporting Information section S1. Here we use the flow rate ratios predicted using this theory. The particles also disperse as they advect downstream. We quantify the dispersion as the standard deviation width of a Gaussian distribution σ. We determine the total dispersion width σT as the square root of the sum of individual variances.44 The individual sources of measured dispersion include Brownian diffusion, the effects of sidewall roughness, and finite resolution of particle imaging. We have specifically neglected any electrostatic effects due to repulsion of the thin electric double layers. We obtain a order of magnitude estimate of the dispersion of particles due to diffusion using a one-dimensional penetration depth, δ2 ) 2Dt, where δ is the mean distance the particles move in time t, with a diffusivity D. The diffusivity of a small particle in a viscous fluid can be described by the Stokes-Einstein relation.45 (43) Shah, R. K.; London, A. L. Laminar Flow Forced Convection in Ducts; Academic Press: New York, 1978. (44) Giddings, J. C. Unified Separation Science; Wiley-Interscience: New York, 1991. (45) Einstein, A. Investigations on the Theory of Brownian Movement; Dover: New York, 1956.
The appropriate time scale for diffusion is the advective time that a particle spends in the pinched section. The residence time of the particle can be calculated using the velocity at the center of the pinched particle. The particle undergoes Brownian motion and thus samples velocities across the depth of the channel. Here, we take the depth averaged velocity (detailed analysis presented in Supporting Information section S2) and the residence time scale can be represented as Lp/up where Lp is the length of the pinched channel and up is the average velocity at the particle center. The compact solution for the length scale δ of particle Brownian motion within the pinched section, therefore, is given as
δ)
x
2kTLpwp2h
9πµdp2(QB + Qp)
(2)
where h is the channel depth. We assume that the dispersion due to Brownian motion in the expanded section is amplified by the aspect ratio of the device such that
σdiffusion ) aδ
(3)
The significance of diffusion in a system is determined by the Peclet number Pe ) UL/D, where U is the characteristic velocity. Later we show that for the flows studied here, the Pe . 1 and the Brownian motion contributes very little to the dispersion. We have included this theory for completeness and so that the final expressions will be applicable to a wide variety of conditions. Rough channel sidewalls in the pinched section force the particles to stand off the mean wall position and can also cause dispersion for small particles. Small particles can sit in the hills or valleys of the wall roughness which results in a variability of their position in the pinched section. The dispersion may depend on the mean roughness height LR, particle size dp, and the mean wall roughness spacing κ. The mean wall roughness spacing κ is the average distance between the roughness peaks in the x-direction. If the particles are large compared to the wall roughness spacing (κ/dp , 1), they will not fall into the crevices of the rough wall, they will travel straight along the wall, and the dispersion due to roughness may approach to zero. If the particles are small compared to roughness spacing (κ/dp . 1), the particles may fill the interstitial space of the roughness and the dispersion in the pinched section may approach to mean roughness height LR. Therefore, we propose the dispersions due to wall roughness vary roughly linearly with the wall roughness LR, can be amplified by the aspect ratio a, and scale with the wall roughness spacing normalized by the particle diameter (κ/dp). It is given as
()
σwall ) aLR erf
κ dp
(4)
Physically the wall roughness should have no effect when κ/dp is small, should vary linearly with κ/dp, and asymptote to unity at large κ/dp. The error function (erf) is used as a phenomenological scaling for this effect and is incorporated into the wall dispersion in eq 4. The measured dispersion depends on the physical dispersion described above and sources related to the optical measurement Analytical Chemistry, Vol. 80, No. 5, March 1, 2008
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system. In the case of optical microscopy, there is a source of measured dispersion due the particle size itself and diffraction as observed in a particle image. The image of a single particle depends on the diameter of the particle, the optical magnification (M), and the point response function of the lens ds.46 The point response of a diffraction limited lens is given by the Airy function as
ds )
1.22(M + 1)λ NA
(5)
dτ ) xM2dp2 + ds2
(6)
The standard deviation of a Gaussian can be approximated as onefourth its total width. Therefore, we approximate the normal standard deviation of a particle image by taking one-fourth of the particle image diameter which gives
dτ 4
(7)
By summing the individual contributions we get an expression for the total dispersion of a pinched flow fractionation system given as
σT )
x( a2
2kTLpwp2h
)(
9πµdp2(QB + QP)
( ))
+ aLR erf
κ dp
2
+
dτ2 16
(8)
Equation 8 predicts a compact scaling argument for the total measured dispersion caused by particle transport in the pinched separation system as a function of particle size, device geometrical parameters, flow rate, and wall roughness. This expression includes the effects of the imaging system. The equation for the physical dispersion is eq 8 in the absence of imaging considerations by removal of the last term on the right-hand side. Here, we use separation resolution to quantify the conditions under which particles can be efficiently separated and individual particle groups can be captured without contamination of other size groups. The separation resolution is defined as
Rs )
∆z 2(σA + σB)
(9)
where ∆z is the separation between peaks A and B, and σA and σB are their respective standard deviations as shown in Figure 1b.47 Using eqs 1-9, we can express the resolution of two particle streams in the pinched separation system as (46) Adrian, R. J. Annu. Rev. Fluid Mech. 1991, 23, 261-304. (47) Robards, K.; Haddad, P. R.; Jackson, P. E. Principles and Practice of Modern Chromatographic Methods; Academic Press: San Diego, CA, 1994.
1644
4
(x
(
a2
(
)
2kTLpwp2h 9πµdp12Q
( ))
κ aLR erf dp1
2
) (x
a(dp1 - dp2) +
+
dτ12 16
+
(
a2
(
)
2kTLpwp2h 9πµdp22Q
aLR erf
( )) κ dp 2
2
+
+
)
dτ2 2 16
(10)
where Q ) QB + QP.
where λ is the wavelength of light and NA is the numerical aperture of the objective used. The particle image diameter dτ is given as46
σparticle )
Rs )
Analytical Chemistry, Vol. 80, No. 5, March 1, 2008
EXPERIMENTAL METHOD AND SETUP Microdevice Design. Four different sizes of devices were designed as shown in Table 1. The inlet channels were designed with a 50 µm width and a subtended angle of 60°. The pinched section length (Lp) and the depth of the devices (h) were kept constant as 200 and 26 µm, respectively. We designed the devices to have a constant aspect ratio while we varied the pinched width and broadened width. As detailed below, the actual aspect ratio does vary due to the microfabrication process. Microfabrication. The devices were fabricated using soft lithography of PDMS.48,49 We use an SU8 (2025 MicroChem. Corp., Newton, MA) master template fabricated on a Si (100) wafer (University Wafer Corp., Boston, MA) using photolithography. Slygard 184 PDMS prepolymer (Dow Corning, Midland, MI) is then cast on a silanized master. The PDMS is then cured at 80 °C in a convection oven for 50 min. The cured PDMS is peeled off from the master and permanently bonded to a glass slide using oxygen plasma treatment (Tegal Plasmaline Asher 421, Rocklin, CA). We examine the effect of wall roughness on separation resolution by fabricating structures using both printed Mylar masks and standard chrome-on-glass masks (Photo Sciences Inc., Torrance, CA). The Mylar transparencies were printed on a 50 000 dpi resolution printer (Fineline Imaging, Colarado Springs, CO) and were taped to a blank glass plate using Kapton tape. The photolithography system used was EVG 620 mask aligner (Tempe, AZ). Experimental Setup. We used epifluorescence microscopy (Nikon TE-2000) to image the polystyrene fluorescent particles and determine the critical dimensions of the devices. The images were recorded on a CCD camera (Cascade IIb, Photometrics). The particle separation images were taken with a 10× objective with a numerical aperture (NA) of 0.3. We used two independent syringe pumps with 1 cm3 syringes (Fisher Scientific, Waltham, MA) and 23 gauge needles (0.5 in.′′ long, type 304, i.d. 0.017 in.′′, o.d. 0.025 in.′′) to pump the bulk fluid and the particle suspensions. The bulk flow rate (QB) was kept 1 cm3/h, and particle flow rate was kept 0.02 cm3/h for all measurements. Fluidic connections were made using Tygon tubing (i.d. 0.02 in.′′, o.d. 0.06 in.′′, 0.02 in.′′ wall; supplier, VWR, Brisbane, CA) and stainless steel tubes (0.025 in.′′ o.d. × 0.017 in.′′ i.d., 0.500 in.′′ length; supplier, New England Small Tube, Litchfield, NH). Materials and Reagents. The base solution used was deionized water with Triton-X and particle volume fraction was kept in (48) Duffy, D. C.; McDonald, J. C.; Schueller, O. J. A.; Whitesides, G. M. Anal. Chem. 1998, 70, 4974-4984. (49) McDonald, J. C.; Duffy, D. C.; Anderson, J. R.; Chiu, D. T.; Wu, H. K.; Schueller, O. J. A.; Whitesides, G. M. Electrophoresis 2000, 21, 27-40.
Table 1. Comparison of Microfluidic Device Widths, Design vs Measured Using a Mylar Mask and a Glass Mask design pinched width (µm)
measured pinched width (µm) using mylar mask
measured pinched width (µm) using glass mask
15 20 25 30
27.5 30.65 32.55 39.93
17.45 22.45 27.01 31.58
design broad width (µm)
measured broad width (µm) using mylar mask
measured broad width (µm) using glass mask
450 600 750 900
458.68 609.81 760.11 908.24
451.27 603.46 752.77 900.18
Figure 2. Fabrication of microdevices using Mylar transparencies and chrome-on-glass mask. (a)Epifluorescent images of the pinched section of a microdevice with a design pinched width of 20 µm. The taped Mylar gives the worst quality whereas a glass mask is closest to design specification. (b) Plot of the ratio of actual aspect ratio and design aspect ratio vs design pinched width for Mylar mask measured: b, glass mask measured; [, estimated (dashed dotted line); PDMS devices made from Mylar mask measured, 9, estimated (dashed line); PDMS devices made from chrome-on-glass mask measured, 1, estimated (solid line). The design aspect ratio is 30. (c) FESEM image of the device made from Mylar. The mean wall roughness is 1.5 µm. (d) FESEM image of the device made using a glass mask. The mean wall roughness is less than 0.5 µm.
the range of 0.02-0.1%. We used green polymer microspheres with diameters 2 (G0200), 5 (G0500), 10 (G1000), and 15 µm (354) (Duke Scientific Corp., Fremont, CA). RESULTS AND DISCUSSION Inspection of Microdevices. We measure the critical PDMS channel dimensions by filling the channels with fluorescine dye and recording images using epifluorescence microscopy. A fluorescent micrograph of a device is shown in Figure 2a. Here we show the pinched section for a designed pinched width of 20 µm fabricated with a taped Mylar mask, an untaped Mylar mask, and the glass mask. The measured device dimensions vary from the design values as shown in Table 1 because the actual device is larger than designed due to limited mask-wafer contact during
photolithography. We see that the device pinch width is always larger than designed. This difference is largest for the taped Mylar mask based devices. In addition, there is uncertainty in the measurement of the device dimensions due to wall roughness, optical diffraction limited imaging, and digitization of image. For the taped Mylar masks, the actual microfluidic devices were much larger (30%-90%) than designed because of the poor mask-wafer contact. The Kapton tape that is used to adhere the mask to the glass plate is approximately 200 µm thick and forces the mask to stand off the photoresist. To confirm the effect of Kapton tape, we also fabricated structures with Mylar masks that are not taped to the glass. Figure 2b shows a comparison of Mylar and glass masks and PDMS device aspect ratios made from Mylar and glass Analytical Chemistry, Vol. 80, No. 5, March 1, 2008
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masks. The measured aspect ratio is normalized by the design aspect ratio adesign ) 30. The pinched widths of the Mylar and glass masks were measured using a differential interference contrast (DIC) microscopy (Olympus, model BH2-UMA). We see that for higher design pinched widths, the ratio approaches unity and the devices are close to their design specification. These results also show that the Mylar and glass mask dimensions agree well with their design specifications. The difference between the measured and designed structures can be attributed to a variety of sources including (1) microfabrication sources such as poor mask-wafer contact during photolithography (∆litho) and sidewall roughness (∆rough) and (2) sources of the measured devices such as optical diffraction (∆diffract)50 and image digitization (∆digital). We can therefore deduce that the measured ratio will follow the trend
wb + ∆ aactual wp + ∆ ) adesign wb wp
where
the
total
uncertainty
Figure 3. Measured separation resolution (Rs) by averaging an ensemble of 100 epifluorescent images. The data is fit using a sum of two Gaussian equations, and separation resolution is determined using the Gaussian parameters.
(11)
is
∆
)
2 2 2 +∆2rough+∆diffract +∆digital . x∆litho
The lithographic uncertainty, ∆litho, is due to the poor wafer-mask contact. We determine the actual channel dimensions from an ensemble average of 25 epifluorescence images. The uncertainty varied with the device dimensions and ranged from 1.5 to 9 µm for devices made of glass mask and Mylar mask, respectively. The roughness, ∆rough, was measured using SEM and ranged between 0.5 and 1.5 µm. The objective used for determining pinched widths was 40×, NA 0.6 with a diffraction limited spot ∆diffract of 1.3 µm and ∆digital is 0.26 µm calibrated using a microscale. The relation in eq 11 is plotted along with the data in Figure 2b. Another consequence of poor mask-wafer contact is sidewall roughness. Field emission scanning electron microscopy (FESEM) images of PDMS devices for a Mylar mask and a glass mask are shown in parts c and d of Figure 2, respectively. The PDMS devices made from Mylar masks result in a mean wall roughness (Lr) of about 1.5 µm whereas it is less than 0.5 µm for glass masks. The mean wall roughness spacing κ is measured from the SEM images as 1.5 µm. Later we show that the sidewall roughness has a dramatic effect on the dispersion and resolution of these devices. Measurement of Dispersion and Separation Resolution. We determine the separation resolution by measuring the particle position distribution in the expanded section. The measurements are made from an ensemble average of 100 epifluorescent images of particle streams undergoing separation. We average the image intensities along the x-axis to obtain the particle intensity distributions as a function of z. An exemplary particle intensity with a bimodal Gaussian fit is shown in Figure 3. We obtain the dispersion widths (s1,s2) and the particle stream centers (z1,z2) from the Gaussian fit. (50) Inoue, S. Spring, K. R. Video Microscopy, 2nd ed.; Plenum Press: New York, 1997.
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Analytical Chemistry, Vol. 80, No. 5, March 1, 2008
Figure 4. Variation of total dispersion with change in particle diameter for PDMS devices with rough walls and device aspect ratio (a)) 16.65, measured, b, estimated (solid line); 19.93, measured, 9, estimated (dashed line); 23.17, measured, [, estimated (dotted line); 22.95, measured, 2, estimated (dashed dotted line); smooth walls and a ) 27.76, measured, O, estimated (/ marked solid line); 28.51, measured, 0, estimated (× marked dashed line).
The measured centers and widths are used to calculate the resolution as
Rs )
z2 - z 1 2(s1 + s2)
(12)
Figure 4 shows a plot of the measured and estimated ratios of normalized dispersion as a function of the particle diameter for both Mylar and glass masks. We see that the ratio of dispersion to particle size decreases with particle size and increases with aspect ratio. As predicted, the dispersion also decreases with the wall roughness so that the chrome-on-glass mask results in the lowest dispersion. This is due to the fact that the mean sidewall roughness of the final PDMS device fabricated with a glass mask is a third of that produced by a mylar mask. With the flow rates used, the Peclet number (Pe) ranged from 108-109 and, therefore, the value of σdiffusion was very small (1-10 nm) and can be neglected in eq 10. It can be seen that for small size particle (2 µm diameter), the predictions are typically higher than the measured values. This can be attributed to the fact that due to
Figure 5. Particle peak displacement from the sidewall for PDMS devices with rough walls and device aspect ratio (a) ) 16.65, measured, b, estimated (solid line); 19.93, measured, 9, estimated (dashed line); 23.17, measured, [, estimated (dotted line); 22.95, measured, 2, estimated (dashed dotted line); smooth walls and a ) 27.76, measured, O, estimated (/ marked solid line); 28.51, measured, 0, estimated (× marked dashed line).
high Peclet numbers (Pe) near the wall, the particles may not be falling into the crevices as predicted by our simple theory. We predict the separation distance of the particles away from the wall using the linear theory of streamline amplification as proposed in eq 1 and developed by Yamada.39 Figure 5 shows a plot of measured and predicted distance as a function of the particle diameter. The distance between the particle stream center and the wall increases with increasing diameter as expected. Large particles, however, move 20-60% closer to the sidewall than expected. The chrome-on-glass devices result in larger aspect ratio devices than the Mylar mask devices for identical designs. As we expect, the chrome-on-glass devices result in particle peaks that have larger z values. However, these values are still lower than what is predicted by the simple theory. Figure 6 shows the separation resolution as a function of particle diameter difference ∆dp for six devices and three particle size combinations. We fix the large particle size to 15 µm in all our experiments. It can be observed that the separation resolution increases with the particle diameter difference. However, for large particle difference, which implies a small second particle, we see that the theoretical curve decreases after reaching a maximum. The decrease is due to the large predicted wall roughness dispersion for particles whose diameter approaches the wall roughness spacing. As observed in the dispersion measurements of Figure 4, here the resolutions are larger for devices made from glass masks compared to mylar masks because of the reduced wall roughness. It is also illustrative to plot the separation resolution with respect to the measured device aspect ratio as shown in Figure 7. As we predict, the resolution increases with aspect ratio. The largest particle that can be used is limited by the pinched width of the device. In our work, the largest particle is 15 µm and the smallest compatible pinched width was 27 µm. For smaller devices, the 15 µm particle would jam at the pinched section inlet. Because of the constraint of not being able to use smaller pinched width devices, we have only two measurements using glass masks. Glass masks result in higher aspect ratio
Figure 6. Variation of separation resolution with particle size difference for PDMS devices with rough walls and device aspect ratio (a) ) 16.65, measured, b, estimated (solid line); 19.93, measured, 9, estimated (dashed line); 23.17, measured, [, estimated (dotted line); 22.95, measured, 2, estimated (dashed dotted line); smooth walls and a ) 27.76, measured, O, estimated (/ marked solid line); 28.51, measured, 0, estimated (× marked dashed line). The large particle is 15 µm in all measurements.
Figure 7. Variation of separation resolution with aspect ratio for PDMS devices having rough walls and particle size difference (∆dp) ) 5, measured, b, estimated (solid line); 10, measured, 9, estimated (dashed line); 13, measured, [, estimated (dashed dotted line); smooth walls and ∆dp ) 5, measured, O, estimated (× marked solid line); 10, measured, 0, estimated (3 marked dashed line); 13, measured, ], estimated (+ marked dashed dotted line).
structures and smoother walls and thus higher resolution separations. A separation resolution value of greater than unity is required to completely separate and capture particles. Our measurements show that for high aspect ratios and large particle differences, the value of resolution is greater than unity. We have achieved a maximum resolution of 3.8. CONCLUSIONS The present work focuses on quantifying the dispersion and separation resolution of a continuous hydrodynamic particle Analytical Chemistry, Vol. 80, No. 5, March 1, 2008
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separation technique. We have developed a compact analytical expression for particle dispersion and separation resolution that accounts for Brownian motion and wall roughness. We measure the dispersion and separation resolution as a function of the device pinched width dimensions (15-30 µm), device aspect ratio (2030 approximately), and particle diameter difference (2-15 µm). We show that the device wall roughness plays a key role in the dispersion and separation resolution. Mylar masks result in rough side walls and compromised device performance. We observe that particles appear closer to the sidewall than predicted by linear theory which results in lower separation resolution. In this study, dispersion due to wall roughness is a limiting factor for obtaining high-resolution separations. Our results suggest that particles whose diameters are of the order of the wall roughness cannot be separated using PFF. The results show separation resolutions greater than unity can be obtained for devices having aspect ratios larger than 20 and particle size differences greater than 10 µm. A better theoretical model for dispersion due to wall roughness is needed that incorporates the effect of advection of particles near the wall that may depend on the Peclet number in this region.
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Analytical Chemistry, Vol. 80, No. 5, March 1, 2008
Future work may also include high fidelity computational modeling that will predict why particles move closer to the wall than predicted by linear theory. ACKNOWLEDGMENT Microfabrication work was partially performed at the Center for Solid-State Electronics Research (CSSER) cleanroom facility at Arizona State University (ASU). A.J. thanks Seth Wilk, Leo Petrossian, and Punarvasu Joshi for their assistance in fabricating the devices. SUPPORTING INFORMATION AVAILABLE Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs. org.
Received for review June 29, 2007. Accepted November 30, 2007. AC0713813
