Bridging the scales in high-throughput dielectrophoretic (bio-)particle separation in porous media

Dielectrophoresis (DEP) is a versatile technique for the solution of difficult (bio-)particle separation tasks based on size and material. Particle motion by DEP requires a highly inhomogeneous electric field. Thus, the throughput of classical DEP devices is limited by restrictions on the channel size to achieve large enough gradients. Here, we investigate dielectrophoretic filtration, in which channel size and separation performance are decoupled because particles are trapped at induced field maxima in a porous separation matrix. By simulating microfluidic model porous media, we derive design rules for DEP filters and verify them using model particles (polystyrene) and biological cells (S. cerevisiae, yeast). Further, we bridge the throughput gap by separating yeast in an alumina sponge and show that the design rules are equally applicable in real porous media at high throughput. While maintaining almost 100% efficiency, we process up to 9 mL min−1, several orders of magnitude more than most state-of-the-art DEP applications. Our microfluidic approach provides new insight into trapping dynamics in porous media, which even can be applied in real sponges. These results pave the way toward high-throughput retention, which is capable of solving existing problems such as cell separation in liquid biopsy or precious metal recovery.


Quantification of the finite size effect
The experimentally determined separation efficiency shows increasing deviation from the simulations with decreasing post-to-post spacing. In other words, the simulation predicts a monotonically increasing separation efficiency with decreasing spacing, whereas the experiments suggest an ideal post-to-post spacing. We assume this deviation is because the simulation neglects the particles' finite size. Since the simulation only calculates the trajectories of volume-less particle centers, particles will always be immobilized directly on the posts' surface. In reality, however, when the particle is immobilized its center will be one radius away from the post's surface. The force balance (i.e., DEP force vs. drag force) will be substantially different in both cases (see Fig. S 2). A balance between drag and DEP force (Fig. S 3,left) reveals that in the real case, the DEP force is not always strong enough in order to keep the particle irreversibly on the post's surface. Especially at low values of q, the drag force is larger than the DEP force which would forbid trapping at that location. This is not considered in the simulation. The gravity of this effect can be expressed in terms of the intersection angle q0 which gives the point on the posts surface at which the DEP force becomes larger than the drag force. Figure S 2: DEP and drag force directly on the surface of the particle (dotted particle outline, as it occurs in the simulation) and one radius away from the post (red particle, is it occurs in reality). Because of the parabolic flow profile and the no-slip boundary condition, the drag force is zero directly on the post's surface. With increasing distance from the post, the force balance shifts from DEP to drag. Figure S 3: It is possible to quantify the finite size effect by comparing the DEP force against the flow direction -FDEP,x with the drag force that opposes the particle trapping FDrag,x on all locations the surface of the post (actually, one particle radius away from it) as expressed by the angle q (a). At q = 0, thus directly at the pore throat, the fluid velocity is highest (due to the constriction). At the same time, FDEP,x = 0, since all DEP force only points in y direction. With increasing q, the FDEP,x increases while simultaneous FDrag,x decreases (because the pore widens due to circular post design). The angle q = q0 where -FDEP,x becomes larger than FDrag,x is the intersection angle. At values q < q0, albeit being predicted by the simulations, no trapping can occur since the drag force would wash particles away. Thus, a large value indicates a strong overprediction of the simulated separation efficiency compared to the experiments. As expected, q0 is low for all d at Q = 0.05mL h -1 . It is increasing with decreasing d and increasing Q since both parameter variations would cause a shift of the force balance toward higher drag forces.
It is possible to shift this force balance toward DEP by varying the cross-sectional aspect ratio (AR, width-to-height ration of the cross section) of the posts (that is, skewing the post's cross section so that the longer axis would be aligned perpendicular to the applied field). This will cause substantially higher DEP forces close to the immobilization points as it is obvious from a decreasing value of q0 ( Fig. S 4, left). This decrease is more pronounced for Q = 0.1 mL h −1 than for Q = 0.2 mL h −1 . This should cause a decreasing deviation between the experiments and the simulation for AR > 1. From Fig. S 4 (right), it is obvious that both, simulated and experimentally determined separation efficiency increase with increasing aspect ratio (due to the larger overall DEP forces). Nevertheless, it is possible to observe that the deviation between experiment and simulation decreases with increasing aspect ratio (due to the shift in the force balance from drag to DEP and thus the decreasing intersection angle q0). As an example, the deviation is over 15 % for AR = 1 and Q = 0.1 mL h -1 but less than 5 % at AR = 1.6. This directly supports the theory that the neglect of the particles finite size causes the overprediction of the simulation results. We assume that the finite size effect also depends on the particle size. With decreasing particle size the ideal spacing should shift towards smaller values. (2) of the main document). Since we only simulated four data points per d, the fit is rather poor. We argued that a value of C close to 0 indicates a geometry well-suited for particle separation. With increasing magnitude of C, the Sshape of the curve (where h switches from 0 to 100%) moves towards higher values of ̅ (less efficient separation). Clearly, decreasing d causes an increase in C. This is especially evident from    The pore window diameter was determined from manual counting on an incident light microscopy image (also Keyence VK-X200, Figs. S10 and S11). The counting was performed by placing 300 ellipses on the image using the software ImageJ and by measuring their resp. half axis. The filter are produced using a foaming technique and consist of 45 % alumina and 55 % sintered mullite.       Fig. 3(b). All points are numbered and the corresponding parameters can be found in Table S2.

Cell viability before and after separation experiments
The cell viability in all cases was determined using the BacLight LIVE/DEAD viability assay from Thermo Fisher Scientific. This assay uses SYTO 9 (green fluorescent) as cell stain for all cells and propidium iodide (PI, red fluorescent) stain for dead cells. Hence, after labeling, all cells are labeled with green fluorescent color whereas, additionally, only dead cells are labeled by red fluorescent color.
Before the experiment, we use 3 µL of a 1 to 1 mixture of both components, SYTO 9 and PI (as obtained from the supplier) per 1 mL of cell suspension (concentration of the cell suspension is roughly 5×10 6 cells/mL). After 20 minutes incubation the cells are washed one time using pure water via centrifugation for 10 minutes (to remove all residual cell stain in suspension).
Since all residual dye is washed off, after experiments we collect 10 mL of the effluent (that we want to determine) and add another 3 µL of a 1 to 1 mixture of both components. This is again incubated in the dark for 20 minutes. Since the cell concentration is too low to find enough cells for a quantitative analysis using a fluorescence microscope together with microscope slide and a cover slip, we filled a spare PDMS channel with the stained cell suspension. This allows to find a sufficient number of cells on one image for quantitative analysis. At this stage we do not remove the residual dye because the concentration of cells is too low for centrifugation (no pellet is formed).
We performed viability analysis of the released cells in the filtration experiments for two data points of Fig. 4C, namely, 300 V and 6 mL/min flow rate and 150 V and 1 mL/min flow rate. Both data points have approximately the same separation efficiency of ~80 %. In both cases the cell viability of the released cells is very high, almost 100 % (see Figs. S14 and S15).  The triangular support structures can be seen in the picture. Obviously, most cells show only green fluorescence, indicating a viability of above 95% after the experiments. Image taken using a 5x EC Epiplan objective lense (Carl Zeiss) on an upright microscope (Carl Zeiss Axioscope A.1), and red and green fluorescence filter sets. Note that the cells appear smaller compared to Fig. S13 because the pictures were taken with a 5x lense instead of a 10x lense. A high amount of background fluorescence is visible since the residual dye was not washed off. Pictures taken with a Lumenera Infinity 3S-1URM monochrome camera with 30 ms exposure time and combined using ImageJ. Figure S 15: Combination of the green (all cells) and red (dead cells) fluorescence channels of the released cells of an experiment performed with 300 VRMS and at a flow rate of 6 mL/min. The cell suspension was filled in a PDMS microchannels as used for the microchannel experiments in the paper. The triangular support structures can be seen in the picture. Obviously, most cells show only green fluorescence, indicating a viability of above 95% after the experiments. Image taken using a 5x EC Epiplan objective lense (Carl Zeiss) on an upright microscope (Carl Zeiss Axioscope A.1), and red and green fluorescence filter sets. Note that the cells appear smaller compared to Fig. S13 because the pictures were taken with a 5x lense instead of a 10x lense. A high amount of background fluorescence is visible since the residual dye was not washed off. Pictures taken with a Lumenera Infinity 3S-1URM monochrome camera with 30 ms exposure time and combined using ImageJ.