Shape-selective remobilization of microparticles in a mesh-based DEP �lter at high throughput

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Introduction
The development and improvement of separation technologies is essential in numerous fields in order to make processes more sustainable or feasible at all.Especially in the lower micrometer and nanometer particle range, classical separation methods are limited as they are often driven by inertia or gravity.Some separation problems in this size range are the recycling of valuable components from waste such as the dust fraction of electronic scrap [1,2], cell separation for analytics and diagnostics [3,4], or the generation of highly specific particle systems, e.g. for solar cells [5].A separation technique suitable for use in this size range is dielectrophoresis.It is labelfree, non-invasive, and highly selective [6], making it a promising alternative to established separation methods.
Dielectrophoresis is the movement of a polarizable particle in an inhomogeneous electric field.It is mostly applied in the biomedical/biotechnological field [7], where commonly microfluidic systems are used that can process sample volumes in the microliter to milliliter range [8].The definition of high throughput is relative, but to give an order of magnitude, in the biomedical field a throughput above around 0.1 mLh −1 can be considered high throughput [9].In order to utilize DEP in a broader variety of fields, especially in technical applications, the throughput has to be increased.The difficulty of scaling DEP processes is based on the inherent physics.The electric field induces a dipole (or multipole [10]) in the particle and the surrounding medium, which results in a net force on the particle in an inhomogeneous field.It is influenced by the gradient of the squared electric field.Consequently the force decreases exponentially with the distance from the electrodes [11], which limits the overall device scale.
In general, the inhomogeneous electric field can be either generated by interdigitated microelectrodes (eDEP) or by insulting structures placed between electrodes with a large distance to each other.Two advantages of such insulator-based (iDEP) devices are that they are less costly to fabricate because there is no need for complex electrode structures and that particles do not usually come into contact with the electrode surface [6,12].Typically, iDEP processes are implemented in microchannels with insulating post structures or constrictions of the channel between widely spaced electrodes [6].So far, macroscopic filter matrices such as packed glass sphere beds [13,14,15] or porous alumina sponges [16,17] were proposed to increase the throughput of DEP filtration processes; however, the devices are unlikely to reach the selectivity of state-of-the-art microfluidic DEP separators [18].
In this manuscript we improve the selectivity of DEP filtration by introducing a mesh-based DEP filter concept.Here, a mesh material serves as an insulating structure between two flat electrodes (indium tin oxide (ITO)coated microscope slides).By using one layer of mesh, the electrode gap is small and comparatively low voltages are necessary to generate a sufficient electric field.A structured porous medium, such as this mesh, will show higher selectivity in trapping compared to sponges or packed beds as further explained in Sec.1.2.A few mesh-based DEP devices have already been introduced, but to the best of our knowledge, they are exclusively eDEP concepts where meshes are used as electrode structures [19,20,21,22].These mesh-based concepts have a great potential for scalability due to the simple design and 3D structure.Also low-cost and commercially available materials can be used.
In our filter type, we apply an operation mode in which particles are firstly trapped and subsequently selectively remobilized from the mesh via a frequency shift.In combination with selective trapping this enables multidimensional trapping.The selective remobilization technique is similar to a frequency hopping method introduced by Modarres and Tabrizian [23].They use a continuous change between two frequencies to separate multitarget particle mixture (shown with three different particle sizes) in a microchannel with interdigitated electrodes and achieved volume flows of around 40 µLh −1 .Other methods such as multistep DEP [24] or dielectrophoretic particle chromatography [4,25,26,27] use frequency or voltage modulation to achieve a time based separation using multiple trap-andrelease cycles.In this manuscript, the feasibility of selective remobilization will be shown in a scalable iDEP setup at a significantly higher throughput.In the future, we aim for combining selective remobilization and selective trapping and thus separate according to several particle properties.So far, such complex multidimensional separations can only be realized using labelbased separation methods, which require rather complicated preparations and procedures or by combining multiple label-free techniques on a single microfluidic chip [28].
Our separation principle, the selective remobilization, is shown on the basis of the particle shape.The particle shape is less frequently investigated than the particle size or material, but receives increasing attention [29].For example, the use of non-spherical polystyrene (PS) particles is being investigated in drug delivery [30] and the shape influence of metal nanoparticles was recently studied for photovoltaic cells [5].In particle synthesis, there are often variations in size and shape, and the subsequent classification according to shape in the microscale is still difficult to realize [29].Several studies have shown that DEP is suitable for shape-selective separations [31,32,33,34].However, these studies varied not only the particle shape, but also the material or volume at the same time, so separability cannot be attributed solely to the particle shape.In this study, ellipsoidal particles are prepared from spherical particles to investigate the shape influence alone.

Theory
For a prolate (pr) ellipsoidal particle with the volume V = 4 3 πa 1 a 2 2 the DEP force [35] is a function of the axes i where a 1 ≥ a 2 = a 3 are the radii of the major and minor axes, ∇( ⃗ E) 2 the gradient of the squared electric field, Re(CM ) the effective polarizability of the particle, and ε m the dielectric constant of the medium surrounding the particle.The effective polarizability, which is the real part of the Clausius-Mossotti (CM) factor, can be calculated for each axis and is a function of the medium's εm and particle's complex permittivity εP ,

Re(CM
with the depolarization factor L a i [35,36].The depolarization factor quantifies the reduction of the electric field inside the polarized particle relative to the external field [37] and is defined further below.The sign of the CM factor determines the direction of the DEP movement.If the particle is more polarizable than the surrounding medium it moves towards regions of highest field strength termed positive dielectrophoresis (pDEP).If a particle is less polarizable than the medium, it moves away from the regions of high field strength termed negative dielectrophoresis (nDEP).The direction is dependent on the frequency f of the applied field as both permittivities depend on f , εm = ε m − jσm ω and εP = ε P − jσ P ω with the imaginary number j, permittivity ε, conductivity σ and angular frequency ω = 2πf .Fig. 1 shows a typical course of the real part of the CM factor for a non-conductive particle like polystyrene (PS) in a very low conductive medium.At low frequencies, the particle experiences pDEP, at the crossover frequency f CO (at which Re(CM ) = 0) it experiences no DEP force and at high frequencies nDEP.If a sufficiently high pDEP force acts on particles in an iDEP channel, they are trapped at the insulating structures, since the regions of highest field strength are located at their sides.For a suspended non-conducting microparticle, the particle conductivity can be calculated as a sum of its bulk conductivity σ B and a surface conductance K S term [38].A suspended particle in an electrolyte with a surface charge attracts ions of the solution and forms an electrical double layer.In this case, the double layer around the particle can also be polarized and contributes to the overall polarizability of the particle.For polystyrene, the contribution due to the bulk material is negligible compared to the surface conductivity [39].For a prolate ellipsoidal particle with the dimensions a 1 ≥ a 2 = a 3 [38] this leads to

Frequency in Hz
The orientation of the ellipsoid in the electric field depends on the CM factors of the individual axes.The axis with the highest CM factor aligns in direction of the electric field [40,41].This alignment corresponds to a minimization of potential energy [37].The depolarization factor for the major axis of a prolate particle can be approximated by [36] L with the eccentricity e = 1 − a 2 a 1 2 [42].
For a sphere with the radius a 1 = a 2 = a 3 = r P and the volume V = 4 3 πr 3 P the depolarization factor is L a 1 = 1 3 , which results in the well know DEP equation for spheres [35].The real part of the CM factor for a spherical particle is defined by In literature, the K S value for a PS bead is often specified to be 1 nS [39].This is only an order of magnitude estimate and a more precise determination is required for the correct design of the process.If the crossover frequency is known or can be determined, the K S value for a spherical particle can be calculated as [43]

Principle of selective remobilization
To separate particles according to multiple characteristics in one filter pass, we aim to not only selectively trap but also selectively remobilize particles.A material-and size-selective separation via nDEP/pDEP differences of particles was already shown elsewhere [44,23,17].In this manuscript, we firstly investigate selective remobilization exclusively and focus on particle shape as a criterion.Here we take advantage of the fact that the particle shapes show different crossover frequencies.Particles of both shapes are initially trapped in the filter at a frequency at which they exhibit pDEP using a sufficiently high voltage.Then the frequency is increased, so that only one of the particle types shows nDEP and is consequently detached from the filter mesh.Finally, the second particle type can be recovered from the filter by switching off the voltage.We explore this approach in the large meshbased DEP filter.As the mesh is characterized by ordered field disturbing structures, it shows less nDEP and mechanical trapping.Compared to the unstructured filter media like sponges or packed beds mentioned above, the selectivity with respect to selective pDEP trapping can be increased.

Results and discussion
A detailed description of the methods and setups used in this paper can be found in Sec. 4. In summary (see Fig. 2), ellipsoidal particles were pro-duced via a stretching process with the same volume as the initial particles and, to ensure comparability, the spherical ones were treated in the same way (except for stretching).In the following, these spheres are termed treated spheres.The particle system was characterized by scanning electron microscopy (SEM) images and experiments in microchannels, and its suitability for investigating shape-selective separation was validated.The determined DEP properties of the particles were used to select suitable separation parameters for experiments in a mesh-based DEP filter at high throughput.In this filter, particles were separated based on their shape via selective remobilization.3. The particles system was selectively remobilized by shape in a new mesh-based DEP filter.The previously determined particle properties were used to select suitable separation parameters.
In this section, we will firstly describe the results of the particle modification and provide the particles' characteristics.Afterwards, we present the results of the experiments in the microfluidic device and the large meshbased filter cell.In this context, we will discuss the principle of selective remobilization and how it can be used for multidimensional separation.In the following, the term remobilization is used when particles are detached from the filter material by a change in frequency and recovery when particles are detached by switching off the electric field.In all figures, the green fluorescence of the ellipsoids is represented by a blue color to be colorblind friendly.The video recordings from the channel in the electronic SI show the original colors.

Particle characterization
The manufacturer's data (see Tab. 1) and the SEM image of the treated spherical particles (inset Fig. 3 a) show that they are highly monodisperse and initially 2.47 µm in size.The stretching process deforms the particles into a noticeably ellipsoidal shape (Fig. 3 a).The determined mean diameter of the major axis is (4.0 ± 1.6) µm and of the minor axis (1.8 ± 0.3) µm.In Table 1: Mean dimensions of particles and their K S values.The mean dimensions of the axes ā1 and ā2 of the ellipsoids and treated spheres were determined from SEM images.For the untreated spherical particles, dimensions are taken from the manufacturer's datasheet.The K S value ranges were obtained via fixed-frequency dielectrophoretic particle chromatography (DPC) experiments (details in SI).[45,46], the stretching method obtained very narrow distributions of the aspect ratios of the ellipsoids by dividing the stretched film into sections of different draw ratios before dissolving.Since we have summarized wide draw ratios of the stretched film into one fraction, the distribution of the aspect ratios of our particles (Fig. 3 b) is broad compared to those in literature.We have chosen the width of the fraction in this way, because we needed large quantities of the fluorescent particles for the high throughput of the mesh-based setup.The stretching process caused a significant lengthening of the major axis and shortening of the minor axis.The major axis length is distributed broadly.

Major axis
The polarizability of polystyrene particles depends strongly not only on size and shape, but also on the surface conductance (K S value), since its contribution to the particle conductivity dominates compared to the low bulk conductivity [47].The determined crossover frequencies and calculated K S values are given in Tab. 1. Ranges are shown because a determination at such low crossover frequencies is not precise with the setup used.Therefore, the determined lower and upper limits of the crossover frequencies were used to calculate K S value ranges and estimate the particles' polarizabilities.The indicated decimal digits result from the calculation and do not correspond to the accuracy of the measurement method.Treatment of the particles reduces the K S value by almost one order of magnitude.The loss of surface conductance is caused by embedding of the particles in polyvinyl alcohol (PVA) for the stretching.Therefore spheres must be treated like the ellipsoids to examine the shape influence alone.Presumably, the loss of surface conductance is caused by a residual amount of PVA on the surface of the particles after dissolution of the PVA film.A residual amount on the surface was also described in literature [48,49], and PVA is known for its reduction of zeta potential (making it less negative) [50].As comparability was ensured by treating both particles similarly, this was not investigated further.The determined K S value ranges of the different shapes with the same treatment differ slightly.The stretched particles have a higher K S value by factor 1.1 to 2.3.For the stretched particles, it must be noted that the aspect ratio distribution also affects the particular K S value.For the calculation using Eq. ( 7), the mean value of the aspect ratio was used for calculating the upper and the lower K S value.Accordingly, the specified K S range is also to be understood as an average.

Shape-selective separation in microchannels
To investigate the influence of the shape on the separation efficiency, experiments were carried out in established microfluidic systems.In iDEP microchannels like the ones use in Ref. [16], we observe a formation of vortex flows on the millimeter scale around the electrodes.These occur over a wide range of process parameters starting at a field strength of around 1 kV pp cm −1 .To reduce vortex formation at the electrodes, we have designed microchannels that narrow significantly before and after the post array (Fig. 4 a and photo Fig. 4 b) to accelerate the fluid flow near the electrodes and to slow it down in the trapping zone.This reduces the influence of the vortices on the laminar flow in the post array, thereby increasing the separation efficiency and reducing fluctuations due to slightly differing electrode placements.The reproducibility of the experiments could be significantly increased compared to channels with a constant width.
The graphs of the real part of the CM factor (Fig. 4 c) of both particle shapes were used to select suitable frequencies for trapping both particles in a DEP channel via pDEP.The Re(CM ) factors are calculated using the K S value ranges and are accordingly also given as ranges.It must be taken into account that ellipsoids that were hardly deformed may be more likely to have a Re(CM ) near the range of the spheres.Likewise, particles stretched more than the average axis diameter can have a much higher value than the displayed ranges.Furthermore, for the ellipsoids, only the values for the major axis are shown as we assume the orientation of this axis in the direction of the electric field (see SI).At a frequency below 20 kHz, both particle shapes reliably show pDEP.In this frequency range, the magnitude of the real part of the CM factor is significantly lower for the spherical particles than for the ellipsoidal particles.The crossover to nDEP also occurs at lower frequencies for the spherical particles.In literature, it was described that the double layer polarization should be more pronounced for non-spherical particles compared to spheres due to their anisotropic shape [33].Therefore, at high polarizabilities (high K S value) the influence of the shape becomes stronger.This dependence is already visible in the Re(CM ) factors over the determined K S range.The difference between the values of the ellipsoids and the spheres at high K S values (dashed lines in Fig. 4 c) is larger than the difference at low K S values (solid lines in Fig. 4 c).At high polarizabilities (high K S value) the influence of the shape is stronger.Accordingly, the reduction of the K S value during the stretching process decreases the shapedbased separability of our particles compared to if they had kept the original K S value.A possibility to weaken the reduction of the K S value or to increase it afterwards would be advantageous for the separation of this model particle system.However, this is rather an academical problem of this specific particle modification method.
A trapping frequency of 15 kHz was chosen at which the spheres should show only weak pDEP, while the ellipsoids should show strong pDEP.The separation efficiency of the ellipsoidal particles at 3 kV pp cm −1 is significantly higher than that of the spherical particles (Fig. 4 d).A higher polarizability of elongated particles was already used by Riahifar et al. for a shapedependent deposition of zinc oxide rods and cubic particles [33] as well as Moncada-Hernandez et al. for sorting S. cerevisiae and E. coli cells [31].The differences in trapping result from the different polarizabilities (height of Re(CM )) of the particle shapes.It should be mentioned that the slightly higher K S value range of the ellipsoids (see Tab. 1) cannot be solely responsible for their higher polarizability.To illustrate this, the real part of the CM factor for both particle shapes with exactly the same K S value range can be found in the SI.There is still a clear difference in the polarizability due to the particles' shapes.Accordingly, the experiments indicate an increased trapping of the ellipsoids compared to the spheres and allow, with appropriate parameter selection, a shape-selective accumulation of one particle type.Furthermore, the experiments in the microchannels show, on a scale established in DEP, that the particle system is suitable for studying shape dependence.

Selective remobilization in large mesh filter
For the selective remobilization experiments in the large DEP filter (scheme and photo in Fig. 5 a and b), we aim to firstly trap both particle shapes in the filter.Then in a second step, we selectively remobilize only one particle type.In the case of a binary mixture, a single selective trapping step would be sufficient for separation.However, we choose the concept of selective remobilization to demonstrate a possibility for multidimensional separation.For the trapping step, a frequency of 10 kHz was selected.Below 10 kHz, a higher DEP force for both particle types is expected, but we assume that more electroosmotic phenomena would occur since the medium conductivity is very low [51,52].
A typical normalized intensity curve (Fig. 5 c) decreases from the initial concentration c 0 for both particle types and reaches a stable low value after applying the electric field of 2.2 kV pp cm −1 .When the frequency at 300 s is increased to the remobilization frequency, both particle types are remobilized in different amounts.This can be observed instantaneously in the filter medium (see video in SI) and with a slight time delay in the intensity curve.The time delay results from the distance between filter cell to the flow-through cuvette.In the example shown, the spherical particles are remobilized to a much higher extent than the ellipsoidal particles.About 100 s later, a stable intensity value is reached again, for the spheres nearly similar to the initial concentration and for the ellipsoids far below because they continue to be trapped.When the voltage supply is switched off at 480 s, a strong increase in the fluorescence intensity can be observed.This time, the amount of ellipsoidal particles recovered is significantly higher.Again after about 100 s, the intensity drops to the initial level for both particle types, as the original particle inflow is re-established.
The results of the entire series of experiments (Fig. 5 d) show that both the trapping step and the remobilization steps can be performed reproducibly.At the trapping frequency and at 2.2 kV pp cm −1 , both types of particles are trapped in the mesh filter with a high separation efficiency, for the spherical particles η 10kHz = 70 % ± 6 % and for the ellipsoidal particles η 10kHz = 79 % ± 7 %.A suitable remobilization frequency was selected via preliminary tests at different frequencies which can be found in the SI.The decision for the selection of a suitable remobilization frequency must be made depending on the purity requirements of the separation task.As we use a model system here, a compromise between a high yield and high purity for both particle types as target particles was selected and a remobilization frequency of 65 kHz was used.Considering Fig. 4 c) it is noticeable that at this frequency the ellipsoids should also show weak nDEP.This is due to the use of the mean axis diameter for the calculation of the polarizability.A large part of the ellipsoids is stretched more strongly (Fig. 3 b), thus have a higher crossover frequency and therefore still show pDEP at 65 kHz.This part of the ellipsoids is trapped in the filter.The less stretched fraction, on the other hand, already shows nDEP and is remobilized with a recovery rate of R 65kHz = 13 % ± 5 %.In comparison, the recovery rate of the spherical particles is much higher R 65kHz = 60 % ± 7 %, which shows the suitability of the selected remobilization frequency.There is a significant enrichment of spherical particles in the filtrate during this first remobilization step.
In the subsequent recovery step, the remaining spheres and ellipsoids are detached from the filter.When looking at the proportion of particles that were recovered in total, a difference between the spheres and the ellipsoids becomes apparent.R total = 86 % ± 8 % of the ellipsoids but only R total = 65 % ± 11 % of the spheres were released from the mesh.A possible reason for this could be the particle shape as well.The ellipsoidal particles may be attached to the mesh structures in such a way that a larger part protrudes into the fluid flow compared to the spheres and they are therefore more easily detached by the drag force.When increasing the flow rate while flushing the channels after each experiment, both particle shapes are detached from the filter by almost 100%.Even after several experiments, there is no strong irreversible accumulation of particles in the mesh.
The quality of the separation was also considered on the basis of the achievable purity and yield.A high purity is achieved if the proportion of the fraction under consideration is high in relation to the total quantity of particles.This value is considered taking the yield of the fraction into account, which indicates how large the proportion of the collected particle quantity is compared to the total quantity of processed particles of this fraction.The purity and yield of the fractions is not only dependent on the remobilization frequency used.It is also influenced by the time window in which the solution is collected during the remobilization steps (Fig. 6).Shortening the collection time t interval strongly reduces the yield, but increases the purity of the filtrate to a certain extend.For the remobilization and recovery step, calculated yield and normalized purity were plotted only for the particle type that would be primarily recovered in this step.If the filtrate is collected for 16 s after the start of the remobilization step (Fig. 6 a), the maximum purity of 74 % is obtained with a yield of 20 %.Extending the capture time to the start of the recovery step can increase the yield of the spheres to 55 %, with purity decreasing to 69 %.For the ellipsoidal particles, the recovery step results in a maximum purity of 81 % after 27 s of collection and a yield of 28 % (Fig. 6 b).In this case, the purity decreases more strongly with the interval length than for the spheres.Increasing the yield by increasing the collection time during the remobilization steps leads in both cases to a reduction in the purity of the two fractions after passing through a maximum.The selec- tion of the collection time should therefore be based on the requirements for purity or yield, which are not given in the case of a model particle system.The purity and yield of the individual fractions can be increased further by changing the particle suspension to a suspension without particles after the trapping step has been completed.In the context of this manuscript, this was not done in order to prevent possible slight parameter changes due to the suspension replacement which could influence the remobilization.An improvement of up to 12 % for the ellipsoid fraction and 4 % for the spheres is achievable in both purity and in yield.
The results show that selective remobilization of particles in DEP filters utilizing a frequency shift can be realized even at a high throughput.In addition to selective trapping of particles, this method can allow simultaneous sorting by several particle properties in one pass step of the filter.For example, pre-classification of material or size can be realized by selective trapping.Subsequently, the retained particles could be additionally sorted via a selective remobilization step, e.g. based on their shape.In this way, a kind of semi-continuous operation mode could be realized to sort particles multidimensionally.

Conclusions and Outlook
Dielectrophoresis is known for its high selectivity and its ability of precise particle manipulations.The benefit of DEP in the (bio-) analytical field has been proven numerous times.Until now, separation based on several particle properties at the same time and, above all, in a scalable process has hardly been taken into account.For the transfer to industrial separation processes of non-biological particles, scalability is essential.This study demonstrates a new field of application for the DEP filtration technique, a selective remobilization, using the example of shape-selective separation.In addition to selective trapping of particles, the subsequent remobilization step can enable multidimensional separations in one pass of the filter.The separability of the particle system due to the shape was shown in the established microfluidic scale first.The selective remobilization technique is demonstrated using a novel mesh-based filter that offers a high potential for further upscaling.Increasing the cross-section of the filter without changing the electrode distance and switching to less expensive electrode materials, such as stainless steel, are conceivable.The observable test cell presented achieves separations at volume flows of 120 mLh −1 , which is 1000 times higher than the throughput we can reach in our microchannels at similar separation efficiencies.
Further research is needed to achieve multidimensional separations.In future studies, we want to examine the combination of selective trapping for example based on particle size or material, and subsequent selective remobilization based on e.g.particle shape.With the help of such a combination, complex interconnections of several separation processes or multiple passes through a DEP filter could be avoided.The method can offer the possibility to work more cost-and time-effectively.Simultaneous sorting by particle shape and particle volume could be used to generate highly specific particle systems or to sort cells by several properties simultaneously.The variation of mesh parameters such as pore size and fibre diameter may be of interest to enable further particle size scales.
For a further scalability and a better handling, a transition to an easily demountable filter design is important.The possibility of increasing the crosssection and the realization of a stack of several electrodes and mesh layers should be investigated in the future.A possible limitation to be considered could be the dissipation of heat generated by joule heating.Especially for a stack system, a possible cooling mechanism should be provided and it should be investigated in which parameter ranges (medium conductivities, frequencies, voltages) the device is able to work.Despite the issues mentioned above, we believe that DEP filtration in macroscopic filter materials has brought us one step closer to industrial-scales for processing of non-biological particles even for complex separation task and at a high selectivity.

Materials and Methods
The raw data of the experiments and the evaluation scripts used in this work can be found in the repository [53].

Generation of ellipsoidal particles
Ellipsoid polystyrene particles were prepared using a process based on a method introduced by Ho et al. [45].This method produces prolate and rotationally symmetric ellipsoids where the two minor axes are equal.Furthermore, the deformation is isochoric [49].We used monodisperse fluorescent polystyrene particles (microParticles GmbH, Berlin, Germany) with a nominal diameter of 2.5 µm as initial particles.The stretching process and materials used are described in detail in the SI, the general procedure is summarized in Fig. 7. Briefly, the particles are embedded into a film that is stretched in an oil bath after hardening.The embedded particles are simultaneously deformed into an ellipsoidal shape and can be recovered by dissolving the film.We experienced that when processing fluorescent particles, the choice of the molecular weight (MW) of the PVA, which is used for the film formation, is critical.We observed a loss of fluorescence when the stretched film has to be dissolved for a long time at high temperatures.When using PVA with a low MW that is highly soluble in water, the stretched film dissolves within a few hours even at room temperature, which reduces the fluorescence loss of the particles.We obtained good results using Parteck COAT (Merck KGaA, Darmstadt, Germany) with an average MW of 40000 gmol −1 .The particles had a sufficient fluorescence signal for our measurement methods.A PVA with a MW of 125000 gmol −1 , Mowiol 20-98 (Sigma-Aldrich Chemie GmbH, Taufkirchen, Germany), which is closer to the PVA used in the original procedure (with 115000 gmol −1 ) worked well only for non-fluorescent particles.To ensure comparability between ellipsoidal (stretched) and spher- ical (not stretched) particles, the same procedure (embedding in a PVA film, heating in an oil bath, dissolution of the film, and washing steps) except for the stretching step itself was also applied to the spherical reference particles.This is required as the K S value of the particles was significantly reduced after the stretching process (which is explained in more detail in Sec.2.1).A total of two batches of ellipsoids and treated spheres were used for the experiments.Care was taken to select comparable batches with respect to K S values and aspect ratios.

Particle characterization
The dimensions and their distribution of the ellipsoidal particles were determined from scanning electron microscopy (SEM) images with the help of ImageJ's (Fiji [54], version 1.53c) measuring tool (n = 600).Dimensions of the spherical particles are known from manufacturer specifications.In addition, the same measurement method as for the ellipsoids was carried out after treatment of the spheres (n = 100) to exclude swelling.
For both spherical and ellipsoidal particles, K S values were obtained via fixed-frequency DPC experiments.Details of this method can be found in the SI.With this procedure, we determine the crossover frequencies of all particles involved, i.e. treated and untreated spheres as well as ellipsoids.The K S value of the spheres is calculated via Eq.( 6).The K S value of ellipsoids is calculated by Eq. ( 7) was obtained by substituting σ P (Eq.( 3)) in Eq. ( 2) and setting Re(CM ) = 0.For the calculation it is assumed that the ellipsoids are aligned with the major axis to the electric field (see Sec. 2.2) and the mean value of the major axis radius after stretching is used.
To select parameters for the separation and remobilization experiments, the courses of the real part of the Clausius-Mossotti factors over the frequency were compared for the two particle shapes.The factors were calculated via Eq. 5 and Eq. 2, respectively and suitable frequencies were chosen for trapping and selective remobilization.

Channel fabrication
Microchannels were fabricated using a standard soft lithography technique [55] using a SU8 master mold and polydimethylsiloxane (PDMS) (Sylgard 184, Dow Corning, Midland, Michigan, USA).The channels were plasma activated and bonded to a plasma activated microscope slide (20 s, Corona SB BD-20ACV, Electro-Technic Products, Chicago, Illinois, USA).A more detailed description of the channel manufacturing is given in ref. [56].
For the large scale mesh-based channels, fluid distributors were 3D printed (Elegoo Mars, Shenzhen, China) using an epoxy resin (Elegoo ABS-Like Photopolymer Resin, Shenzhen, China).As electrically insulating material, we used a polypropylene fabric with a mesh width of 500 µm, a fiber diameter of 340 µm and a fabric thickness of 610 µm (PP-500/36, Franz Eckert GmbH, Waldkirch, Germany).Transparent ITO-coated glass slides (Biotain Crystal Co., Ltd., Fujian, China) with a film thickness of 135 nm and a sheet resistance of 10-15 Ωsq −1 were used as electrodes.To connect the electrodes to the voltage source, wires were attached with a conductive glue (Elecolit 323, Panacol-Elosol GmbH, Steinbach, Germany).To seal the channel sides and the connection to the distributors, a glue based on a modified-silane polymer DEKAsyl MS-2 (Dekalin, Ranstadt, Germany) was used that offers a good compromise between adhesive and sealant.The distance between the ITO electrodes varies due to the adhesive connection between 0.6 mm and 0.8 mm.Three different channels were used for the experiments.

Preparation of suspensions
All experiments were conducted using the same composition of suspending medium: Ultrapure water (Omniatap 6 UV/UF, stakpure GmbH, Niederahr, Germany) containing 0.005 vol% Tween20 (Sigma-Aldrich, Steinheim, Germany) to reduce particle-wall interactions, 6 µM potassium hydroxide to adjust pH, and 0.25 µM potassium chloride to adjust the electrical conductivity to the desired value (1.1 µScm −1 ).Green fluorescent particles were used as initial particles for the ellipsoids (PS-FluoGreen, microParticles GmbH, Berlin, Germany).The spheres exhibit red fluorescence (PS-FluoRed, mi-croParticles GmbH, Berlin, Germany).The total particle concentration in all experiments was 2.5 × 10 5 mL −1 .The initial particle concentration after the stretching or treatment process was estimated.For this purpose, the particle concentration after the stretching process was determined once by counting in a Thoma counting chamber (Paul Marienfeld GmbH & Co. KG, Lauda Königshofen, Germany).This value was used as a reference value for the following batches.
The particle suspension for experiments in the large-scale setup was additionally degassed for 5 min in a vacuum vessel at 70 mbar.This step reduces the gas bubble formation within the capillaries, the mesh filter, and the flowthrough cuvette at high flow rates as far as possible.After degassing, the conductivity of the medium was checked again.

Experimental procedure in microchannels
Imaging of the microchannels was done with an Zeiss Axio Scope A1 (Carl Zeiss Microscopy Deutschland GmbH, Oberkochen, Germany) with a 5×/0.13EC Epiplan lens, a DAPI/FITC/TRITC triple band pass filter (Semrock, IDEX Health & Science, LLC, Rochester, New York, USA) and a Grasshopper3 color camera (FLIR Systems, Inc., Wilsonville, Oregon, USA).The microchannel was mounted vertically to prevent any sedimentation of particles.The microscope objective was placed behind a deflection mirror (CCM1-E02/M dielectric turning mirror, Thorlabs, Inc., Newton, New Jersey, USA), which has no effect on the working distance due to the infinitycorrected microscope optics.The particle suspension was pumped with a syringe pump (TJA-3A, Longer Precision Pump Co., Ltd., Hebei, China) into the microchannel.The syringe holder/delivery unit of the syringe pump was mounted vertically above the set-up using a laboratory stand.The particle suspension was mixed inside the syringe (3 mL) with a magnetic stirrer for the entire duration of the experiment.The electrodes were connected to a voltage amplifier (PZD2000A, TREK, Inc., Lockport, New York, USA) controlled by a signal generator (Rigol DG4062, Rigol Technologies EU GmbH, Puchheim, Germany).
All separation experiments in the microchannels were carried out with a binary particle mixture.Before the experiments, the channel was completely wetted with ethanol.The channel was then flushed with the particle suspension at 1 mLh −1 for 30 min.Before each experiment, any adhering particles were loosened at 10 mLh −1 for 10 s.The flow was allowed to become stationary at 0.1 mLh −1 for 1 min and then the particle flux was recorded for 10 s in each case.The electric field (3 kV pp cm −1 at 15 kHz) was then turned on for 170 s which causes trapping of the particles in the post array structure.Three experiments were performed in different PDMS microchannels (with the same geometry).For each datapoint, three recordings of inlet and outlet were recorded and averaged.
Particle fluxes for each fluorescence color have been calculated using a in-house MATLAB programm in combination with the TrackMate Plugin of Fiji.Details of the tracking procedure are described in reference [56].The separation efficiency for each particle type i was calculated as where ṅin is the particle flux into the channel and ṅout is the particle flux out of the channel.The evaluation period was uniformly chosen to be 20 s before switching off the voltage.

Experimental procedure in large mesh filter
The separation processes in the large mesh filter were observed using an inverted microscope (Eclipse Ts2R-FL, Nikon Corporation, Tokyo, Japan) with a 4×/0.13Plan Fluor lens, a DAPI/FITC/TRITC triple band pass filter and a Grasshopper3 color camera.Since the entire cross-section of the filter cannot be recorded, the evaluation method used in the microchannel experiments cannot be transferred.Instead, the fluorescence intensity in the filter outlet stream was measured inline by a spectrometer (see Fig. 8).The measurement setup consisted of a 110 µL flow-through cuvette (176-765-85-40, Hellma GmbH, Müllheim, Germany), a cuvette holder with four light ports (CVH100, Thorlabs Inc., Newton, New Jersey, USA), an EXFO X-Cite 120 PC Q light source (EXFO Inc., Richardson, Texas, USA) and a SILVER-Nova spectrometer (StellarNet Inc., Tampa, Florida, USA).A wavelength range between 190 and 1110 nm can be recorded.For the fluorescent particles, the light source and spectrometer were placed at a 90 • angle to each other.Again, a DAPI/FITC/TRITC emission filter was used in front of the spectrometer.The electrodes were connected to a voltage amplifier (A400, FLC Electronics, Göteborg, Sweden) supplied by a signal generator (Rigol DG4062, Rigol Technologies EU GmbH, Puchheim, Germany).Fluid input was realized using an Ismatec MCP-CPF IP65 piston pump with the pump head FMI 202 QP.Q0.SSY (Cole-Parmer GmbH, Wertheim, Germany).
Experiments were done with a) particles of only one shape and with b) binary mixtures.Therefore, the number of repetitions is different for both particle shapes; it is indicated in each respective figure caption.The comparability was verified by plotting the intensity curves obtained from pure and binary particle systems against each other.Suitable frequencies for the trapping and remobilization steps were estimated using Clausius-Mossotti factor calculations and selected via preliminary experiments (see SI).
The fluorescence intensity was recorded using a LABVIEW program and evaluated via an in-house MATLAB script.Before each experiment, the channel was completely wetted with ethanol, rinsed for 15 min with medium without fluorescent particles, and the background signal was recorded.The channel was then flushed with the particle suspension for at least 15 min at a flow rate of 240 mLh −1 .Before each recording, the flow rate was increased to 600 mLh −1 for 30 s and then allowed to settle to 120 mLh −1 for another minute.Experiments were started when a stable intensity value was reached.The steady-state particle flux was recorded for 1 min.Particles were trapped in the mesh for 4 min (at 10 kHz) and remobilized for 3 to 4 min at a higher frequency (65 kHz).Full recovery was then recorded for 3 min.
A full wavelength (λ) spectrum at an exemplary time point is shown in Fig. 8 d1.In the case of binary particle suspensions, this is composed of the fluorescence spectra of both particles.To obtain the constituent parts of each particle type, a linear unmixing of the spectrum was performed.We assume that the fluorescence intensity depends linearly on the particle concentration c i and that the total spectrum is a linear combination of the spectra of all individual fluorophores I i , with the total number of reference spectra N [57].Reference spectra were acquired for each fluorescent particle and the best matching combination of particle concentrations were calculated using a genetic algorithm (GA) (from the global optimization toolbox version 4.4) with non-negativity constraints in an in-house MATLAB program.Prior to unmixing, the data were integrated in specific wavelength ranges to speed up the algorithm.The ranges were selected on the basis of the characteristic values of the emission filter used.To validate the unmixing script, recordings were made of selected mixing ratios of the particles.More details of the validation can be found in SI.Using the curves determined over the measurement time, the separation efficiency can be calculated with an equation similar to Eq. ( 8) with the fluorescence intensities of the suspension after passing through the filtration cell without applied (corresponds to c 0 ) and with electric field.The fluorescence intensities 20 s directly before the first remobilization were averaged for the value with the electric field applied (see Fig. 5 c).The recovery rate represents the ratio of released particles (remob) to previously captured particles (trap).We have simplified the calculation and divided the surface area with a positive sign after subtracting c 0 (detachment) by those with a negative The filter consists of two ITO-coated microscope slides and a PP mesh as an electrically insulating structure.The processes in the filter can be observed with a microscope thanks to the transparency of the ITO electrodes.The particle trapping/ release behavior in this panel is shown for the second step.b1.In the first step (t 1 ), all particles are trapped at the trapping voltage U 0 and a low frequency f 1 via pDEP in the filter structure.b2.In the second step, this is followed by an increase in frequency (U 0 , f 2 ) at which one type of particle is selectively remobilized (t 2 ).b3.In the third step, the electric field is switched off and all particles in the filter are recovered (t 3 ).c) Behind the filter outlet, the fluorescence signal is recorded using a spectrometer and intensity values are obtained for each time step over the full wavelength range of 190 to 1110 nm (d1.).
For the first remobilization step, the entire time span up to the point t remob,end at which the intensity signal falls below the signal of c 0 after the beginning of the remobilization was evaluated (see Fig. 5 c).To make the detection method robust against outliers, the intensity signal was smoothed beforehand using a moving average method.To determine the end of the recovery step, a similar procedure was chosen.This recovery rate describes the total number of particles recovered in the whole experiment.The achievable yield Y and purity P of the individual fractions were calculated to assess the quality of separation.Both depend on the time period in which the particle suspension is collected.The values were therefore determined for different time ranges.In each case, the first point of the collecting time corresponds to the first exceeding of c 0 after the start of trapping (beginning of remobilization t purity,start , see Fig. 6 a).The latest point for ending the collection is the beginning of the next step/end of the experiment.The number of particles of the remobilized species (out) is again determined by integration and divided by the particle influx (in) until the end of the time period (t purity,end ) in the case of yield Y i = t purity,end t purity,start c i,out dt t purity,end t=0 c i,in dt (13) and by the total amount of remobilized particles of both species i and k in the case of purity

Figure 1 :
Figure1: Typical frequency dependence of the real part of the CM factor for a homogeneous particle that has a lower permittivity but higher conductivity than the surrounding medium.At very low medium conductivities, this course occurs for non-conductive materials such as polystyrene.

Figure 2 :
Figure2: Overview of experimental work done in this paper.1.A particle system of spherical and ellipsoidal polystyrene particles of the same volume and same treatment was produced.For this purpose, the particles were embedded in a film, stretched at high temperature and recovered.2. The particles were characterized by SEM imaging and DEP experiments in established microchannels.The K S value was determined and the separability of the particles by DEP was verified in an iDEP channel with insulating posts.3. The particles system was selectively remobilized by shape in a new mesh-based DEP filter.The previously determined particle properties were used to select suitable separation parameters.

Figure 3
Figure 3: a) SEM image of PS particles after treatment without stretching step (inset) and after whole stretching process.The majority of the particles have a distinct ellipsoidal shape.b) Distribution and cumulative sum of the diameters a i after the stretching process.The stretching process caused a significant lengthening of the major axis and shortening of the minor axis.The major axis length is distributed broadly.

Figure 4 :
Figure 4: a) Scheme of microchannel (not for scale).The microchannels have a height of 79 µm and a width b a of 2.5 mm.A 10 by 7 array of insulating posts with a diameter h s of 260 µm, a distance d of 360 µm and with a "dove-tail" geometry at each side is located in the center of the microchannel.An electric field E can be applied using two platinum wire electrodes placed d E = 9 mm apart.Before and after the electrodes, the channel narrows to a width b c of 0.7 mm.b) Photo of vertical mounted microchannel.The channel is flowed through in the direction of gravitation supplied by a syringe pump.The microscope objective is mounted behind a deflection mirror so that the particles in the microchannel can still be observed.c) Calculated range of the real part of Clausius-Mossotti factor Re(CM ) of ellipsoids and spheres over frequency f at σ m = 1.1 µScm −1 .The dashed areas indicate the possible range, depending on the variation of the K S value of the particles.For the ellipsoidal particles, the value for the major axis is shown and no length variation is considered.d) Measured shape influence on separation efficiency η in microchannels at σ m = 1.1 µScm −1 and a volume flow of Q = 0.1 mLh −1 .Data were determined at a frequency of 15 kHz and an electric field of 3 kV pp cm −1 from a binary mixture.Standard deviation is shown as error bars (n = 3).

Figure 5 :
Figure 5: a) Scheme of mesh-based filter (not for scale).The particle suspension flows into the channel (Q = 120 mLh −1 ) from above through a distributor structure, then flows through the polypropylen (PP) mesh from left to right and leaves the channel on the underside through a second distributor.The ITO-coated microscope slide electrodes with a distance of d E = 0.6 -0.8 mm are connected to an amplifier.b) Photo of mesh-based DEP filter.c) Typical curve of the normalized intensity I/I 0 over the experimental time t with indication of the evaluation intervals.The starting concentration c 0 of ellipsoidal and spherical particles is determined on the basis of the first 20 s before the electric field is applied.A trapping of both particle types is performed at 10 kHz and 2.2 kV pp cm −1 for 240 s.The separation efficiency (η 10kHz ) is determined using an interval of 20 s before remobilization.At 300 s the frequency f is increased to the remobilization frequency, in this case 65 kHz.The separation efficiency (η 65kHz ) is determined in the same way.The remobilization (R 65kHz ) and total recovery rate (R total at U = 0 V) are obtained in the shown evaluation intervals.d) Mean separation efficiency at 10 kHz, recovery rate for selective remobilization step at 65 kHz and total recovery rate.Experiments were performed at a medium conductivity of σ m = 1.1 µScm −1 and E = 2.2 kV pp cm −1 .Standard deviation is shown as error bars (ellipsoids n = 13/spheres n = 9 for trapping and recovery, ellipsoids n = 4/spheres n = 2 for remobilization at 65 kHz).

Figure 6 :
Figure 6: Calculated yield and purity when collecting particle suspension during each remobilization phase.a) Exemplary curve of the normalized intensity I/I 0 over the experimental time t and indication of the evaluation intervals for yield and purity calculation.The values were determined using the fluorescence intensity curves as described in Sec.4.6.b) Normalized purity P and yield Y over different integration intervals t interval for spherical particles at remobilization step with a frequency f of 65 kHz.c) Purity and yield over different integration intervals for ellipsoidal particles at recovery step.

Figure 7 :
Figure 7: Process schematic of stretching process and used parameters (parts of the figure are based on[45]).The fluorescent PS particles are embedded with the help of a water-soluble PVA in a film, which after drying at room temperature is cut into strips and stretched in a defined manner in an oil bath at 120 • C. The film with the stretched particles is then dissolved in a mixture of water and isopropanol and the ellipsoidal particles are purified via washing steps.

Figure 8 :
Figure8: Scheme of the large mesh-based DEP filter and route of data processing.a) A binary particle suspension is constantly pumped with flow rate Q into the filter cell using a piston pump.b) The filter consists of two ITO-coated microscope slides and a PP mesh as an electrically insulating structure.The processes in the filter can be observed with a microscope thanks to the transparency of the ITO electrodes.The particle trapping/ release behavior in this panel is shown for the second step.b1.In the first step (t 1 ), all particles are trapped at the trapping voltage U 0 and a low frequency f 1 via pDEP in the filter structure.b2.In the second step, this is followed by an increase in frequency (U 0 , f 2 ) at which one type of particle is selectively remobilized (t 2 ).b3.In the third step, the electric field is switched off and all particles in the filter are recovered (t 3 ).c) Behind the filter outlet, the fluorescence signal is recorded using a spectrometer and intensity values are obtained for each time step over the full wavelength range of 190 to 1110 nm (d1.).d) The signal I over time (d2.) is determined by integrating selected wavelength ranges λ eval which lie in the range of the transmission maxima of the emission filter used.The total fluorescence intensity signal is divided into the components of the particles' fluorescence colors by linear unmixing (d3.).
Figure8: Scheme of the large mesh-based DEP filter and route of data processing.a) A binary particle suspension is constantly pumped with flow rate Q into the filter cell using a piston pump.b) The filter consists of two ITO-coated microscope slides and a PP mesh as an electrically insulating structure.The processes in the filter can be observed with a microscope thanks to the transparency of the ITO electrodes.The particle trapping/ release behavior in this panel is shown for the second step.b1.In the first step (t 1 ), all particles are trapped at the trapping voltage U 0 and a low frequency f 1 via pDEP in the filter structure.b2.In the second step, this is followed by an increase in frequency (U 0 , f 2 ) at which one type of particle is selectively remobilized (t 2 ).b3.In the third step, the electric field is switched off and all particles in the filter are recovered (t 3 ).c) Behind the filter outlet, the fluorescence signal is recorded using a spectrometer and intensity values are obtained for each time step over the full wavelength range of 190 to 1110 nm (d1.).d) The signal I over time (d2.) is determined by integrating selected wavelength ranges λ eval which lie in the range of the transmission maxima of the emission filter used.The total fluorescence intensity signal is divided into the components of the particles' fluorescence colors by linear unmixing (d3.).