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 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. At Arizona State University, I have studied a hydrodynamic particle separation technique that employs pinching of particles to a narrow microchannel. In this technique known as pinched flow fractionation (PFF), the particles are subject to a sudden expansion which results in a size-based particle separation transverse to the flow direction (see Yamada and Seki, Anal Chem, 2004). We measure the separation resolution and particle dispersion using epifluorescence microscopy and predict these parameters using a compact theoretical model (see Jain and Posner, Anal Chem, 2008). 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. This work also shows that particles with diameters on the order of the sidewall roughness cannot be separated using PFF.

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Continuous hydrodynamic size-based separation of particles in a pinched microchannel. (a) is the 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 (s A+ sB) and peak distance ( z) determine the separation resolution; (c) inverted epifluorescence photograph (10x, N.A. 0.3) of separation of 5µm and 15µm particles in one such microdevice.

Fabrication of Microdevices using Mylar transparencies and chrome-on-glass mask. (a) are epifluorescent images of the pinched section of a microdevice with a design pinched width of 20µm. The taped Mylar gives the worst quality whereas a glass mask is closest to design specification. (b) is a plot of the ratio of actual aspect ratio and design aspect ratio vs design pinched width for Mylar mask measured (filled circles) , glass mask measured (filled diamonds), estimated (dashed dot line); PDMS devices made from Mylar mask measured (filled squares), estimated (dashed line); PDMS devices made from chrome-on-glass mask measured (filled triangles), estimated (solid line). The design aspect ratio is 30. (c) is a FESEM image of the device made from Mylar. The mean wall roughness is 1.5µm. (d) is a FESEM image of the device made using a glass mask. The mean wall roughness is less than 0.5µm.

Variation of separation resolution with particle size difference for PDMS devices with rough walls and device aspect ratio (a) = 16.65 measured (filled circles) , estimated (solid line), 19.93 measured (filled sqaures) , estimated (dashed line), 23.17 measured (filled diamonds) , estimated (dotted line), 22.95 measured (right triangle), estimated (dash dotted line); smooth walls and a=27.76 measured (open circle) , estimated (* marked solid line), 28.51 measured (open sqaures) , estimated (× marked dashed line). The large particle is 15µm in all measurements. 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.

JAIN A, POSNER J.D. 2008. Particle Dispersion and Separation Resolution of Pinched Flow Fractionation, *Analytical Chemistry*,80(5),pp: 1641-1648. doi

We predict the flow rate ratio required for pinching using the exact analytical solution for fully developed flow in a rectangular duct. The particles also disperse as they advect downstream. We quantify the dispersion as the standard deviation width of a Gaussian distribution s. We determine the total dispersion width sT as the square root of sum of individual variances. The individual sources of measured dispersion include Brownian diffusion, the effects of sidewall roughness, and finite resolution of particle imaging. By summing the individual contributions we get an expression for the total dispersion of a pinched flow fractionation system given as,

where *a* is the device aspect ratio, *k* is the Boltzmann constant, *T* is current temperature, *Lp* is the pinched section length, *wp* is the pinched width,* h* is the height of the channel, *dp* is the diameter of the particle, *QB* is the bulk flow rate, *QP* is the pinched section flow rate, *LR* is mean wall roughness height, k is the wall roughness width and dt is the particle image diameter that we measure. 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

where *z* is the separation between peaks A and B, and sA and sB are their respective standard deviations. We can express the resolution of two particle streams in the pinched separation system as,

where Q=QB + QP.

We measure the critical PDMS channel dimensions by filling the channels with fluorescine dye and recording images using epifluorescence microscopy. The devices are made on Mylar transparencies as well as traditional chrome-on-glass. We find that for the taped Mylar masks the actual microfluidic devices were much larger (30%-90%) than designed because of the poor mask-wafer contact. We measure the dispersion and separation resolution as a function of the device pinched width dimensions (15 µm to 30 µm), device aspect ratio (20 to 30 approximately), and particle diameter difference (2 µm to 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.

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