Increasing flow rates in polydimethylsiloxane-based deterministic lateral displacement devices for sub-micrometer particle separation

In this study, we show the design and manufacturing of microfluidic deterministic lateral displacement (DLD) devices for sub-micrometer particle separation. For that purpose, devices with pillar gaps of 4 µm and a periodicity of 50 were designed. After photolithographic manufacturing of SU-8 masters with different heights (15 and 30 µm) and vertical sidewalls for soft-lithographic replication with polydimethylsiloxane (PDMS) the influence of flow rate on the separation efficiency of 0.45 and 0.97 µm particles was investigated. The 15 µm devices were operated at 0.125 and 0.5 µl/min sample flow rate and the 30 µm devices at 0.5 and 2.0 µl/min, respectively. Excellent separation efficiencies were observed for both device heights at the lower sample flow rates, while separation efficiencies decreased at the respective higher sample flow rates. The decrease in separation efficiency was attributed to deformation of the soft PDMS pillars, which causes an increase in pillar gaps at the higher sample flow rates as shown by microscopy imaging. The advantage of the 30 µm devices over the 15 µm devices is clearly shown by the separation of 0.45 and 0.97 µm particles at 0.5 µl/min. Due to reduced hydrodynamic resistance in the 30 µm devices and thus less pillar deformation, the displacement efficiency of 0.97 µm particles was above 99% compared to 46–57% for the 15 µm devices. Our 30 µm devices demonstrated excellent separation at a tenfold higher sample flow rate with 0.5 µl/min compared to comparable PDMS-based devices operating in the same size regime.


Introduction
Microfluidic devices are miniaturized setups to control the flow of liquids or dispersions with high precision and minimal sample volumes under continuous flow (Whitesides 2006). As such, they are useful tools to study and control chemical reactions (Kessler et al. 2020;Shastri et al. 2015), create emulsions, double emulsions and solid particles with very high precision (Abate and Weitz 2009;Amstad 2017;Datta et al. 2014;Perrotton et al. 2019), or study self-assembly phenomena (Vogel et al. 2015;Wang et al. 2018). One of the most important areas of application is in the biomedical field (Azizipour et al. 2020;Sia and Whitesides 2003;Velve-Casquillas et al. 2010). Benefits of microfluidic devices include the potential to mimic biological conditions (Azizipour et al. 2020;Velve-Casquillas et al. 2010) leading to more realistic experimental conditions, enormous integration possibilities for Lab-on-a-Chip (Azizipour et al. 2020;Gupta et al. 2016) and Organ-on-a-Chip (Azizipour et al. 2020;Boyang Zhang et al. 2018) devices, as well as the opportunity to exploit properties that are only or more easily accessible at the microscale (Boyang Zhang et al. 2018). A laminar flow profile is an important example of such a property, which is often encountered in microfluidic devices (Azizipour et al. 2020;Sia and Whitesides 2003;Velve-Casquillas et al. 2010). This laminar flow profile provides highly regular conditions that can be exploited in sophisticated applications of microfluidic devices. In particular, deterministic lateral displacement (DLD) devices exploit this regular laminar flow for particle separation based on their hydrodynamic diameter. The working principle of DLD was first described by Huang et al. in 2004(Huang et al. 2004. In a DLD device, particles are separated by a flow profile that results from a precisely arranged pillar array. The separation arises from a lateral displacement of particles above a critical diameter while particles below the critical diameter can traverse the DLD device without lateral displacement (Salafi et al. 2019). This results in a spatial separation of particles based on their diameter.
Since the first description of the DLD principle numerous devices have been designed, simulated and tested in the fields of blood fractionation (Inglis et al. 2008(Inglis et al. , 2011, circulating tumor cell separation (Jiang et al. 2017;Liu et al. 2013) or filtering satellite droplets of microfluidic droplet generators (Joensson et al. 2011;Tottori et al. 2017;Tottori and Nisisako 2018).
Separation down to 20 nm is possible (Wunsch et al. 2016), but requires expensive, complex and time-consuming fabrication of silicon devices. A widely used and simple alternative are PDMS-based devices, with PDMS being one of the most used materials for microfluidic devices (Raj M and Chakraborty 2020). PDMS offers several attractive properties including biocompatibility, transparency, ease of device manufacturing and the possibility to rapidly replicate microfluidic devices from a master substrate.
However, the soft nature of PDMS poses great challenges to accurately reproduce small feature sizes required for the separation of nanoscale particle systems (Sia and Whitesides 2003;Velve-Casquillas et al. 2010). To date PDMS-based DLD devices capable of sub-micrometer particle separation reported in literature are scarce (Tottori et al. 2020;Zeming et al. 2018) and usually shallow to avoid pillar deformation and bending at smaller pillar gaps with increased height. The reported devices had channel heights of 3 µm (Zeming et al. 2018) and 4 µm (Tottori et al. 2020), respectively. These shallow heights can limit the device's throughput (Hochstetter et al. 2020) as the hydrodynamic resistance scales inversely with the channel height.
This study aims to investigate the separation of submicrometer particles at varied flow rates in PDMS-based DLD devices. As the separation of sub-micrometer particles requires small pillar gaps, the hydrodynamic resistance of the resulting DLD device increases (Hochstetter et al. 2020) compared to a device for separation of larger particles. Devices with higher hydrodynamic resistance must be operated with higher pressure to achieve the same flow rate, which can lead to pressure-induced deformation of pillars in PDMS-based devices (Inglis 2010). Therefore, overcoming hydrodynamic resistance is a key challenge to increase flow rates in DLD devices. To investigate the influence of the hydrodynamic resistance for separation of sub-micrometer particles, devices with different heights (15 and 30 µm) and a designed pillar gap of 4 µm were manufactured. The devices were then run at different flow rates (0.125, 0.5 and 2 µl/min) with mixtures of 0.45 and 0.97 µm fluorescent polystyrene particles. The displacement efficiencies of the devices for the differently sized particles at different operation parameters were determined.

Design of DLD devices
First, the design of the DLD device and, in particular, the shape, geometry and fabrication of the pillar array is introduced (Fig. 1).
The inlet region of the DLD devices was designed with three individual ports. The two outer inlet ports were used for a buffer solution, while the centered inlet port was used for the sample particle dispersion. Each buffer port is connected by five channels, and the sample port by one channel to the pillar array, respectively. The width of all inlet channels was 200 µm. However, since the buffer channels consist of five parallel-connected channels, the hydrodynamic resistance is reduced to one-fifth of the sample channel's hydrodynamic resistance. To ensure parallel flow entering the pillar array, all channels should have the same resistance , thus, the length of the buffer channels is fivetimes the sample channel length.
All outlet channels were designed with a width of 140 µm. Since the same number of channels was connected in parallel for each outlet port, the length of all outlet channels was the same (Fig. 1). All inlet and outlet channels were separated by 25 µm walls at the closest.
The critical diameter, above which particles are being displaced in the device, is mainly influenced by two geometrical pillar array factors, as proposed by the model of Davis ). The first geometrical pillar array factor is the pillar gap G (Fig. 1a) between two neighboring pillars perpendicular to the fluid flow direction and the second factor is the periodicity ( N ) of the pillar array. The periodicity results from a shift of the lateral pillar position in each adjacent pillar row perpendicular to the fluid flow direction. Estimation of critical diameters D c in this work is based on the model by Davis and can be calculated with the following equation ): To reduce the critical diameter G can be reduced or N can be increased. Increasing N has the advantage that larger pillar gaps can be designed, which are easier to realize and fabricate accurately by photolithography, especially when further considering increased device heights of 15 and 30 µm. However, Davis recommends, as a rule of thumb, (1) D c = 1.4 GN −0.48 that N should not be greater than 50 , which was chosen as the periodicity for the DLD devices in this work to maximize the required pillar gap. To achieve a submicrometer separation, a pillar gap of 4 µm was designed, leading to a critical diameter of 0.9 µm. The pillar height was chosen to be 15 µm and 30 µm to increase the applicable flow rate compared to typical device designs (Tottori et al. 2020;Zeming et al. 2018), and pillar diameter was designed to be 25 µm to ensure feasible aspect ratios and stable operation conditions. Also, the critical height of lateral collapse (Zhang et al. 2006) for PDMS pillars with the designed dimensions was estimated as shown in the supplementary information. Based on the estimation pillars should start to collapse around 74 µm, so that the designed pillars should be sufficiently stable for manufacturing.

Manufacturing of DLD devices
The DLD devices were replicated from in-house manufactured master wafers by PDMS molding. Master wafers were manufactured with SU-8 2050 photoresist (MicroChem, U.S.A.) ( Fig. 1c) on 150 mm silicon wafers in a clean room. SU-8 was chosen due to the possibility of achieving thick photoresist layers (> 200 µm) in a single spin coating step (Campo and Greiner 2007). The SU-8 was spin coated with 4000 and 6000 rpm for 60 s to produce different layer thicknesses and structured by standard photolithography with a mask aligner MA6 (Süss GmbH, Germany). An i-line filter was used to ensure vertical sidewalls of the SU-8 (Campo and Greiner 2007). After hard baking, the step height was measured with a P-16 + stylus profilometer (KLA-Tencor, U.S.A.) at six different locations spread over the wafer. The measured thicknesses were 30.3 ± 1.5 (30 µm) and 15.4 ± 0.9 µm (15 µm) for 4000 and 6000 rpm, respectively. Therefore, the resulting aspect ratios in our pillar arrays were 1.2:1 and 0.6:1. A focused ion beam (Helios G4 PFIB CXe, ThermoFisher Scientific, U.S.A.) cross section image of the SU-8 master wafer, highlighting the accurate vertical walls, is shown in (Fig. 1c). More information on the processing parameters can be found in the supplementary information. An anti-sticking layer of Trichloro-(1H,1H,2H,2H-perfluorooctyl) silane (Sigma-Aldrich, U.S.A.) was applied to facilitate PDMS separation from the master wafers.
For PDMS molding Sylgard 184 (Dow Corporate, U.S.A.), which consists of a base and curing agent that were mixed in a ratio of 10:1 by weight, was used. After mixing, the PDMS was degassed in a desiccator and then poured onto the master wafers. After curing at 50 °C for at least 20 h, the PDMS was peeled off the wafer and the inlet and outlet holes were structured with a 1.5 mm biopsy punch.
The structured PDMS DLD devices were permanently bonded onto a glass microscope slide. Both the PDMS and glass were treated for 30 s with a mixture of argon Fig. 1 a Exemplary image of a PDMS-based DLD device with schematic magnifications (not to scale) of the inlet and outlet region as well as the pillar array with pillar gap G and pillar diameter D. b Microscopy image of a replicated pillar array in PDMS with a pillar gap of 4 µm and periodicity of 50. c Focused ion beam cross-section of a SU-8 master on a silicon wafer, manufactured using an i-line filter during exposure. Platinum, deposited for cross-section preparation, and some preparation artefacts are visible 2 Page 4 of 10 and oxygen plasma. Afterwards the treated surfaces were brought into contact for irreversible bonding and the finished DLD devices could be used.

Operation of DLD devices
To investigate the performance of the DLD devices, a dispersion of 0.45 ± 0.10 and 0.97 ± 0.03 µm fluorescently labelled polystyrene particles was used (Microparticles GmbH, Germany). Particles were purchased in a concentration of 2.5 wt.-% and 0.5 µl of the 0.45 and 0.75 µl of the 0.97 µm particles were diluted in 5 ml of water. The 0.45 µm particles were labeled with a green pyrromethene fluorescent dye and the 0.97 µm particles were labeled with a red squaraine fluorescent dye. DI water was used as the buffer fluid. To avoid clogging, 1 vol.-% Tween-20 (Sigma-Aldrich, U.S.A.) was added to all used fluids.
Two Fusion 100 Touch syringe pumps (Chemyx, U.S.A.) were used to run the DLD devices. First, the buffer was applied into the DLD devices. After the buffer fluid filled the entire inlet region of the DLD devices, the sample particle dispersion was connected to the DLD devices. The DLD devices were flushed with the particle dispersion prior to inserting pipette tips for sample collection. The flushing and operation of a DLD device is also illustrated in supplementary video 1. An overview of all experimental parameters is given in Table 1. For each set of parameters, two runs were conducted.
The chosen sample flow rates for the 15 µm devices were 0.125 and 0.5 µl/min, while the 30 µm devices were operated with 0.5 and 2.0 µl/min. The reason for not applying the lowest sample flow rate of 0.125 µl/min to the 30 µm device was that the flush time in 15 µm device already had to be doubled and had to be increased further for the 30 µm device due to the greater volume of the devices. On the other hand, an applied sample flow rate of 2.0 µl/min to the 15 µm device led to the tubing being pushed out of the inlets due to the increased pressure.

Characterization of DLD device separation
The displacement efficiencies of the DLD devices were characterized by confocal fluorescence microscopy (TCS SP5, Leica, Germany). Displacement efficiency in this work is defined as the fraction of particles measured in outlet 1 (collecting displaced particles) divided by the total amount of particles of the same size measured in all three outlets. For a reliable separation, the displacement efficiency of larger particles should be as high as possible while it should be as low as possible for smaller particles.
For particle detection, a 1 µl droplet of the collected sample fluid from the outlets was dried on a cover slip. The entire area covered by the dried particle dispersion was scanned with a fluorescence microscope. The 0.45 ± 0.10 µm particles labeled with green fluorescent dye were excited with a laser emitting at 488 nm and the 0.97 ± 0.03 µm particles labeled with red fluorescent dye were excited with a laser emitting at 633 nm. The emitted light of the particles was collected in the range of 500 to 550 nm for the green fluorescent dye and in the range of 650 to 700 nm for the red fluorescent dye. Images were analyzed with Fiji (Schindelin et al. 2012) (version 1.53c) to determine the total number of particles in the dried droplet. For that purpose, the fluorescent images were converted into binary images and individual particles were counted (details in supplementary information and Fig. S1).

DLD device structures and separation characteristics
Prior to displacement experiments, the pillar diameter and gap of the molded DLD devices were determined. For that purpose, three microscopy images of molded DLD devices were taken for each height. The pillar diameter was calculated from the pillar area, which was determined by image analysis from the microscopy images. With the designed pillar center to pillar center distance of 29 µm, the pillar gap was then calculated: Results and design parameters as well as resulting critical diameters for the devices according to Eq. (1) are shown in Table 2.
The evaluation of the microscopy images showed slightly different pillar diameters and hence also different pillar gaps from the two different master wafers for the different device heights. However, as the pillar gaps of the replicated PDMS (2) G = 29 μm − D. devices were slightly smaller than expected from the design, the calculated critical diameters for both device heights ( Table 2) were shifted to smaller values. To demonstrate the successful separation of sub-micrometer particles, we therefore chose particle populations with sizes that were equally spaced from this critical diameter and used 0.97 µm particles and 0.45 µm particles. After the theoretical critical diameters were evaluated, the devices were operated with a dispersion containing 0.45 and 0.97 µm particles. As an example, the measured particles for a 30 µm device run at 0.5 µl/min and another one run at 2 µl/min sample flow rate, respectively, are shown in Fig. 2.
At a sample flow rate of 0.5 µl/min, the larger particles (d = 0.97 µm) were displaced in outlet 1, while the 0.45 µm particles were found in outlet 2 (Fig. 2a). The displacement efficiency was high (> 99%) for the 0.97 µm particles and low (< 5%) for the 0.45 µm particles, indicating an efficient separation. When the sample flow rate was increased to 2.0 µl/min, the displacement efficiency of the 0.97 µm particles decreased to ~ 69% (Fig. 2b).
The flow-rate dependent displacement efficiencies of 0.45 and 0.97 µm particles in all devices are summarized in Fig. 3. For the lower flow rates (0.125 µl/min for 15 µm and 0.5 µl/min for 30 µm) an excellent separation of the differently sized particles was achieved, as more than 97% of the 0.97 µm particles and less than 5% of the 0.45 µm particles were displaced. An increase in flow rate by a factor of four, however, decreased the displacement efficiency of the 0.97 µm particles for both device heights to approximately 45-60 and 65-75%, respectively, whereas the displacement efficiencies of the 0.45 µm particles remained below 5%. A reason for the minor effect of increased flowrate on the displacement efficiency for the 0.45 µm particle could be that the displaced 0.45 µm particles are primarily agglomerates, which are already displaced at low flow rates. Increasing the flow rate and thus reducing the critical diameter therefore does not affect their displacement. This is also supported by the average measured size of 13.3 ± 2.2 px 2 compared to 4.6 ± 1.5 px 2 for 0.45 µm particles in outlet 1 compared to outlet 2, respectively.
These findings imply that the separation of the differently sized particles in the centered outlet was reduced, while the separation of the larger particles into outlet 1 was still high. In absolute numbers, the displacement of 0.97 µm particles per time was even higher compared to the lower flow rate, since the flow rate was increased by a factor of four while the displacement efficiency only reduced to 65-75% for the 30 µm device. For applications requiring only the separation of larger particles, a higher throughput can be achieved by increasing the flow rate.
Another advantage of the higher flow rates was an easier handling of the collected fluids. While microfluidic devices can manage extremely small volumes, it can be difficult to manage those volumes outside of the devices. This was also the reason for the doubled flushing and sample collection time for the 15 µm devices at 0.125 µl/min sample flow rate (Table 1).
Compared to a device by (Tottori et al. 2020), separating 0.5 and 1.0 µm particles, the flow rate in the 30 µm  device was 10 times higher at 0.5 µl/min. However, the device by Tottori et al. was driven by withdrawal while the devices in this work were run by infusion. While the flow rate of devices operated in withdrawal is directly limited by the device's resistance with a maximum negative pressure difference of 1 bar to atmospheric pressure, the flow rate by infusion operated devices can be higher, since higher pressure differences can be applied. To compare the devices more accurately, the hydrodynamic resistance of the pillar arrays was calculated and compared. According to ) the hydrodynamic resistance of the pillar array ( R ) can be estimated based on the fluid viscosity ( μ ), pillar array length ( β ), width ( ), height ( H ), and pillar gap ( G ) as follows: An overview of parameters as well as the resulting hydrodynamic resistance of the pillar arrays is given in Table 3. As DLD devices in this work and Tottori's were run with water, a viscosity of 1 mPa•s was used for calculations.
Based on the calculated resistances the hydrodynamic resistance of the devices in this work was one order of magnitude lower compared to the device by Tottori et al. When applying the same pressure, the flow rate for the devices in this work should be higher. These differences showed that the increased pillar height in our devices allowed a significant increase in flow rate.

Flow-rate-induced phenomena
To investigate the observed reduction in displacement efficiency at higher flow rates, the DLD devices were run under a microscope to directly observe the response of the device to different flow rates (Fig. 4). Microscopy images were taken at the start of the experiment, after the pillars were wetted, and after the flushing time specified in Table 1 to equilibrate the system at the different flow rates. The images show the beginning of the pillar array near the inlet.
The images show a change of the pillar gap between the lower and higher flow rates, which we attributed to increased pressure. This change in pillar gap was assumed to contribute to the reduction in displacement efficiency, since a bigger pillar gap also shifts the critical diameter upwards. For better visualization of the pillar gap changes by the applied flow rate, overlays of pillars at the different conditions are shown in Fig. 5.
The overlays underline changes in the pillar gaps at the different flow rates. For the pillar gaps after wetting and at the lower flow rate only minor difference could be seen (Fig. 5). However, the overlays of pillars at higher flow rate on wetted pillars clearly showed that the pillars at the higher flow rate were reduced in diameter (Fig. 5) and hence the pillar gap increased. To calculate the change in critical diameter, the difference in pillar dimensions before and after application of flow were quantified by image analysis (Fig. 4, Table 4). Based on the measured changes in pillar gap at the three different operation conditions, the critical diameter for particle separation at those conditions was re-calculated. As the images showed the pillar gap increased with increasing flow rate. The difference between the just wetted and lower flow rate was minor (Fig. 5). With increasing flow rate, the change in pillar gap became more significant and led to an increase in the calculated critical diameter. For the 15 µm device, the calculated critical diameter increased from 0.6 to 0.9 µm. The critical diameter was thus shifted towards the diameter of the large particles, which caused the reduced displacement efficiency. Note that the critical diameter was calculated for an ideal device based on ideal pillar gap and periodicity. Any defects, inhomogeneities, clogging or particle-fluid and particle-particle interactions could potentially influence the separation characteristics. Furthermore, the channel walls could also influence the separation characteristics (Inglis 2009) as no channel wall correction was designed. However, as shown by Pariset et al. (Pariset et al. 2017) the channel wall influence decreases with the number of pillars in a row perpendicular to the flow direction. As the number of pillars in a row for the used devices was 85 the channel wall influence should be minor. Also, the particles were not perfectly monodisperse (0.97 ± 0.03 µm). Hence, a reduction in displacement efficiency is reasonable when particle size and calculated critical diameter of a DLD device are close together.
For the 30 µm devices, the change in critical diameter was even more pronounced, as the critical diameter rose from 0.8 to 1.1 µm, even exceeding the size of the 0.97 ± 0.03 µm particles. The remaining displacement of these particles, which was not predicted by the pillar dimensions at high flow rates, may have resulted from the drop of pressure downstream in the device. As the pressure dropped down the device, also the deformation of the pillars was less pronounced (Supplementary Fig. S2) and thus the critical diameter decreased towards the outlet region. At some point in the pillar array, the critical diameter became again smaller than the particle size and the particles started to get displaced. However, since the remaining displacement distance was shorter, only partial displacement was achieved.
When looking closely at the displacement efficiency of 0.97 µm particles at the higher flow rates in the 15 µm devices a lower efficiency was achieved compared to the 30 µm devices, even though the critical diameter of the 15 µm device was lower ( Fig. 3 and Table 4). Dincau et al. 2018 showed that the formation of vortices at higher Reynolds numbers ( Re ) could increase the apparent pillar size and hence reduce the resulting pillar gap. To evaluate whether this effect may have contributed in our devices, the Reynolds numbers for the different device parameters and operation modes were estimated (McGrath et al. 2014): with The calculated values are shown in Table 5. For the density and viscosity of water values of 1•10 3 kg/m 3 and 1•10 -3 kg/m•s were used, respectively. The hydrodynamic diameter D h of the channels was calculated with device heights H and pillar gaps G at the respective flow rate ( Table 4). The fluid velocity was estimated by the applied collective flow rate Q col (Table 5)   cross section area A and number of pillar gaps, n of 85, in a pillar row: The resulting Re were 0.03 and 0.11 for the 15 µm device at lower and higher flow rates and 0.06 and 0.25 for the 30 µm device, respectively. While Re for the 30 µm with the higher flow rate was indeed the highest of the calculated Re values, the absolute value was probably too low (below 1) to explain the higher displacement efficiency of the 30 µm devices compared to the 15 µm devices. As in the works by Dincau et al. (2018) and Kottmeier et al. (2019) the effect of Re on the displacement started at values above 1 and increased with increasing values demonstrated at Re of 10 and above.
Further, the displacement characteristics could be influenced by the device height. Higher devices could possibly compensate perturbations better in the flow profile, which can be caused by particles (Beech 2011) between pillars. So, a particles perturbation between pillars influences relatively less of the total volume for higher devices as the volume increases with device height compared to shallower devices. Also, the effect of clogging, as another perturbation (Beech 2011), could be reduced as a clogged particle in a higher device should be less influential as in a shallower device. As the influence of perturbations is reduced, more stable operation conditions, benefiting the device's separation characteristics, are encountered. In the end, increased height leading to more stable operation conditions may contribute to the increased displacement of 0.97 µm particles in the 30 µm devices.

Conclusion
This work investigated the influence of flow rates, and associated with it, total throughputs on the displacement efficiency of PDMS-based DLD devices for sub-micrometer particle separation. For this purpose, devices with different heights exceeding the typical vertical dimensions of (6) = Q col ∕(n ⋅ A).
PDMS-based devices (Zeming et al. 2018;Tottori et al. 2020) were manufactured and operated at different flow rates.
By increasing the height of the DLD device a significant increase in throughput, while keeping excellent separation, was achieved. For 0.97 µm particles displacement efficiencies of 97 and 99% for devices with heights of 15 and 30 µm were obtained, even though the flow rate for the 30 µm devices was increased by a factor of four to 0.5 µl/ min compared to devices with a height of 15 µm operated at 0.125 µl/min. Tottori et al. 2020 reported a PDMS-based DLD device for the separation of 0.5 µm and 1.0 µm particles operating at a flow rate of 0.05 µl/min. In comparison, for our device with a height of 30 µm a ten-fold increased flow rate was achieved.
At even further increased flow rates of 0.5 µl/min and 2.0 µl/min for devices with a height of 15 µm and 30 µm, respectively, a reduction in displacement efficiency was seen and investigated. The reduction in displacement efficiency was mainly attributed to flow-rate-induced pillar deformation. This deformation led to larger pillar gaps and hence an increased critical diameter of the devices. Noteworthy, the 30 µm devices showed a smaller reduction in displacement efficiency compared to the 15 µm devices, showing that the increased device height of 30 µm also led to more stable operation conditions. So, our study showed that increasing the device height enables the separation of sub-µm particles at higher throughputs. Further throughput increases building on these findings can be readily envisioned by combining higher device structure with asymmetric pillar arrays (Zeming et al. 2016), parallelization of devices (Hochstetter et al. 2020;Tottori and Nisisako 2018) or their combinations.
Acknowledgements The authors thank Susanne Beuer for performing the FIB cross-section preparation and imaging.
Author contributions TD, NV and MR: supervised the work and reviewed and edited the manuscript. JM: performed the experimental work, visualization of data and wrote the initial draft of the manuscript.
Funding Open Access funding enabled and organized by Projekt DEAL.

Conflict of interest
The authors declare that they have no conflicts of interest.
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