A microfluidic band-pass filter for flexible fiber separation

Abstract

The control of particle trajectories in structured microfluidic environments has significantly advanced sorting technologies, most notably through deterministic lateral displacement (DLD). While previous work has largely targeted rigid, near-spherical particles, the sorting of flexible, anisotropic objects such as fibers remains largely unexplored. Here, we combine experiments and simulations to demonstrate how tilted pillar arrays enable efficient, length-based separation of flexible fibers. We discover that these arrays act as band-pass filters, selectively inducing lateral migration in fibers whose lengths are close to the array period. Fibers significantly shorter or longer exhibit minimal lateral deviation. This migration arises from the interplay of fluid-structure interactions between fibers and the complex flow and steric interactions with the pillars. Depending on their length, fibers exhibit distinct transport regimes: short fibers zigzag in between pillars following the flow, intermediate length fibers exhibit wrapping and jumping from one pillar to another, leading to lateral displacement, and long fibers deform extensively, following mixed zigzag-jump trajectories with minimal lateral migration. We identify the mechanical tension that develops in the fiber when wrapped around the pillars as the driving mechanism of cross-streamline transport. Leveraging this band-pass effect, we designed a highly efficient separation device to collect monodisperse fiber suspensions. Our findings not only expand the functional scope of DLD-like systems but also open new avenues for understanding transport of anisotropic objects in porous media.

Figures (5)

• Figure 1: Geometry of the channel and examples of fiber dynamics. (A) A 3D schematic of the experimental channel (not to scale), with a magnified top-view bright-field image of the pillar array shown alongside. In the experiments, $H_{\rm{ch}}= 50\,\unit{\um}$, $R=10\pm1\,\unit{\um}$ and $\lambda=30\,\unit{\um}$ (these geometric parameters are identical in numerical simulations, see Methods). (B and C) Chronophotographs of fibers from experiments (top row) and simulations (middle row) at a tilt angle between flow and array directions of $\alpha = 35^\circ$. The bottom row presents the corresponding fiber CoM trajectories extracted from the simulation (solid lines) and experiment (dots). Colors indicate the time. The shaded gray regions indicate the flow lanes between pillars $P_{\rm{n}}$ and $P_{\rm{n+1}}$, separated by a stagnation point at pillar $P_{\rm{n+2}}$ (red cross). (B) The fiber length is $L = 9.6 \,\unit{\um} = 0.32\lambda$. (C) The fiber length is $L = 48 \,\unit{\um} = 1.6\lambda$. In both cases, the initial conditions for the simulations are extracted from experiments. In the experiments actin filaments are suspended in an aqueous solution of $45.5\,\unit{\percent}$ (w/v) sucrose, with a viscosity of $\mu = 5.6\,\unit{\milli\pascal\second}$. Note that the fiber CoM can be located inside the pillar when it is wrapped around.
• Figure 2: Characterization of the flow field and Poincaré map in a unit cell. (A) Velocity field at various tilt angles $\alpha$ measured by µPIV (top) and simulated by LBM (bottom). Colors indicate the velocity magnitude normalized by the maximum value in each unit cell, while arrows and curves represent the streamlines. The cyan arrows are the flow directions (B) Definition of Poincaré maps. The gray region indicates the non-accessible area on the Poincaré map of the tracers. The normalized position (scaled by the unit cell size $\lambda$) of a streamline as it enters the unit cell is ($\eta_{\rm i} = y_{\rm{in}}/\lambda$) and ($\eta_{\rm i+1} = y_{\rm{out}}/\lambda$) as it exits the unit cell Kim2017. (C) Poincaré maps of the fiber CoM in the experiments (top row) and simulations (bottom row) at various tilt angles $\alpha$. Crosses show the Poincaré maps of streamlines computed from LBM simulations. Colors correspond to the contour length of the fibers, with two lengths shown in the simulation plots: $L=0.4\lambda$ and $L=1.6\lambda$. Orange ellipses at $\alpha = 35^\circ$ outline the separation of longer fibers from shorter ones and from streamlines. Quarter circles in each corner of the plots represent the surface of the pillars. The Poincaré maps from experiments were derived from over 270 fiber trajectories, each comprising more than 50 fiber instances reconstructed from image frames.
• Figure 3: Cross-streamline migration during the wrapping phase of the fiber around a pillar at a lattice tilt angle $\alpha=35^\circ$. (A) Experimental and numerical snapshots captured during the wrapping phase. In the numerical snapshots, arrows indicate the velocity directions of both the fiber tip (marked with a star) and the flow at the tip's position. (B) The upper panel displays chronophotographs of a longer and a shorter fiber, with normalized tension represented by a color scale. Black stars indicate the downstream leading ends of the fibers. Notice that the CoM of the longer fiber moves more slowly than that of the shorter one. The lower panel presents the maximum normalized tension over time corresponding to the chronophotographs above. Orange indicates periods when the fibers are in contact with the pillars, while green indicates no contact.
• Figure 4: (A) Experimental relationship between fiber lateral migration angles $\beta$ and fiber lengths from experiments using the separation setup shown in SI Appendix, Fig. S1, with $\lambda/R=3$. The error bars denote the group average with a bin width of $\Delta L/\lambda = 0.12$. (B) Simulated angles of migration $\beta$ of the fibers as a function of their length. Data are averaged over 50 runs for each length. Vertical black lines represent the standard deviation. Inset shows the definition of the migration angle $\beta=\arctan\left(y_{\rm f}/x_{\rm f}\right)$, with $y_{\rm f}$ the lateral position of the fiber CoM at $x_{\rm f}$ downstream from the start of the pillar array. Black line is the averaged fiber CoM trajectories over the 50 runs.
• Figure 5: Chip-scale statistics. (A) Typical examples of simulated chronophotographs and trajectories observed in the 3 regimes, along with a representation of the modes of transport of the fiber over time. The chronophotographs only show the first timesteps of the simulations. (B) Fractions of the zigzag and jump modes averaged over 50 realizations for each fiber length. Vertical black lines show the standard deviation. Pink circular symbols represent the averaged maximum ensemble average of normalized tensions over 50 realizations for each length. Green diamond symbols denote the migration angle $\beta$.