Influence of the filter grain morphology on separation efficiency in dielectrophoretic filtration

Recovery of noble materials from waste is essential for industries around the globe. Dielectrophoretic (DEP) filtration, an electrically switchable particle separation technique, can be applied to tackle this challenge. It is highly selective regarding particle size, material or shape. Expanding the scope of DEP towards high throughput and improving the trapping efficiency are vital to make DEP a viable robust alternative to conventional separation methods. DEP filtration works by selective immobilisation of particles in a porous medium by the action of an inhomogeneous electric field. The field inhomogeneity comes from scattering an electric field at the phase boundary between the particle suspension and the filter surface. In this article, we show how the filter structure affects the DEP separation. We study fixed bed filters of three different grain types and find that the morphology of the grains highly influences the DEP filter efficiency. Specifically, grains with irregular surface structure and high perceived angularity show high separation efficiency. We believe these insights into the design of DEP filtration will pave the way towards its application in, for example, the recovery of valuable materials from electronic waste dust.


INTRODUCTION
The recovery of valuables from electronic waste is an important aim for many countries [1].Because of an evergrowing amount of such waste, an efficient solution to extract precious metals, which would be otherwise lost, is required [2].Electronic scrap, generally, consists of plastics, metals and glass [3].A typical recycling process usually involves three stages, pre-treatment, separation using size reduction and physical processing and metallurgical or chemical purification [3].The recovery of submicron metal particles from electronic dust generated during the recycling of such waste remains a challenging problem.For instance, physical recycling techniques are relatively simple but possess a high metal loss (10%-35%) due to a lack of metal liberation [3].Gravity separation depends on both density and size of the particles.It is not suited for the separation of small particles as differences in settling velocity are drowned out by particle diffusion.Electrostatic separation, while widely used, relies on the amount of charge that particles carry.Dielectrophoresis allows to access a richer set of properties of the target particle and enables particle sorting without relying on the particle charge [4,5].It has a long tradition in biomedical applications, for example in cell separation [6][7][8][9][10][11] but, theoretically, is also well suited for complex non-biological separation tasks such as recovery of metals from dust [12,13].
The dielectrophoretic (DEP) force is directly proportional to the volume of the particle and, for a spherical particle, can be expressed as [14] ⃗  DEP = 2 m  3  p Re where  p is the radius of the particle,  m is the dielectric constant of suspension,  CM is the Clausius-Mossotti (CM) factor and ⃗  is the root-mean-square amplitude of the applied electric field.As follows from Equation (1), to generate a DEP force, the electric field must be nonhomogeneous.
The relative polarisability is described by the CM factor [14,15].It determines strength and direction the DEP force.This factor depends on both complex permittivities of the particles and the medium in which they are suspended (ε p and εm ): where  and  are conductivity and permittivity of the particle or suspension, and f is the frequency of the applied ac field.If Re[f CM ] is positive, the particle is more polarisable than the surrounding medium.In this case, it experiences positive DEP (pDEP), a force along the field gradient towards local maxima of the electric field [16].If Re[f CM ] is negative, the particle is less polarisable than the surrounding medium.It then experiences negative DEP (nDEP), a force that pushes it away from the maxima of the electric field, against the gradient of the electric field.Because the complex permittivities and thus also Re[ CM ] depend on the frequency, particles can experience a cross over from pDEP to nDEP or vice versa.At high frequencies, the behaviour is entirely dominated by the real-valued permittivities, at low frequencies the behaviour is entirely dominated by the conductivities [16].Specifically, at low field frequencies, Re[f CM ] can be expressed through conductivities of the particle and surrounding medium ( p and  m , resp.) alone: Two different particles can be separated when they experience significantly different DEP forces.This can be accomplished because of differencies in size, shape or due to differencies in Re[f CM ].While the conductivity and permittivity of the particle are, mostly, fixed, it might be possible to vary both the suspension conductivity and applied field frequency in order to obtain a significantly different Re[ CM ] for two different particle types.This enables a material-selective separation in a particle mixture.
DEP separators can be categorised by how they generate the required non-uniform field.Two main principles exist, electrode-based DEP (eDEP) and electrodeless or insulator-based DEP (iDEP).In eDEP, the required field inhomogeneity comes from an asymmetry in the electrode structure.The most popular electrode-based designs are interdigitated microelectrodes that are found on the bottom of a microchannel [17].Generally, traditional eDEP devices are well established on the microfluidic chips and are often applied in fields that do not require high volumetric throughputs, such as cellular analysis [18,19].However, they do not allow for the preparative scale throughputs that are usually well beyond the µL/min range [17].Our group showed a pathway out of this throughput limitation for eDEP setups by using custom-designed printed circuit boards which significantly reduced the fabrication costs and allowed for a scale up, currently up to 6 mL/min [20].In iDEP, the two electrodes are placed outside of the region of DEP manipulation [21].To generate the required non-uniform field, the void space is filled with an insulating material which creates a spatial variation of the electric field by scattering the superimposed electric field [22].This generates minima and maxima of the field inside on the surface of the insulating material.Insulator-based DEP benefits from a simple fabrication process without the need of complex electrode patterns and without a risk of reduced setup performance due to a fouling of electrode surface [23].It can be used on a microfluidic scale, but its very promising scalability for higher throughput was shown in some recent publications of our group [24][25][26].A macroscopic iDEP approach is DEP filtration, which is investigated here.
In DEP filtration, a porous medium is sandwiched between two macroscopic electrodes (Figure 1).The field inside the porous medium will be highly inhomogeneous due to the scattering of the field at the solid-liquid boundary of each pore.Such design is easily scalable by increasing the cross-sectional area available for the flow.In previous studies, we used a monolithic alumina sponge as porous filtration matrix and investigated how pore size, flow rate and applied voltage influence the separation efficiency [24].Other researchers usually use micron or mm-sized glass beads [10,27].The electric field is directly influenced by the pore structure of the filter.As the DEP Two examples of porous filters pressed between two macro-electrodes (acting as a packed bed filter) are presented on the right as 'filter matrix'.The spatial non-uniformities of the electric field required for DEP immobilization come from this medium.The concentration of fluorescent particles at the outlet is determined by online fluorescence photometry based on a signal intensity (measured in counts per second, cps) that is linearly proportional to the particle concentration.
force depends on the gradient of the electric field squared (Equation ( 1)), the DEP filtration strongly depends on the design of this porous structure [26].In particular, the DEP force will increase with inhomogeneity of the porous structure [24].
In previous studies, to find the influence of the pores on separation efficiency in DEP filtration, we modelled a filter by a regular array of insulating posts in a microfluidic chip.We investigated quasi two-dimensional individual posts in a setting that is close to microfluidic iDEP and showed that the maxima of the electric field were located at sharp edges of the structure and that the intensity of the field maxima increased with the sharpness of the structure [28,29].Transferring these findings from microfluidics requires taking into account an influence of the pore shape itself (which is directly influenced by the grain morphology and surface), which to the best of our knowledge has not yet been researched in detail for DEP filtration.Given how strongly the gradient of the electric field is influenced by the shape of the obstacle in iDEP, it is conceivable that the morphology and geometry of the grains (and the shape of the pores they form) strongly influence the DEP filtration process.
In this work, we research the impact of filter matrix parameters on the DEP separation effect.We show how the geometry and size of randomly distributed packed beds of grains influence the separation efficiency in DEP filtration.We investigate three materials that are similar in their material composition but different in grain structure and in the shape of the pores that they form (namely, spherical and angular grains).We investigated two types of angular grains, sand and crushed (milled) glass, which differ in the number of edges they show, and one type of spherical grains, glass beads.Here, the term angular refers to a property of sharpness of the corners that the single grain shows [30].In this study, we use angularity as a qualitative marker only.The crushed glass sample enables a proper shape comparison between grains that are identical in terms of their materials (glass beads and crushed glass are both made of soda-lime glass) and different in their grain morphology (spherical and angular grains, respectively).We investigated three size fractions for each grain type, with modal grain diameters between 200 and 500 µm.

MATERIALS AND METHODS
We characterised individual grains according to the particle size distribution (PSD) and shape.We analysed the packed beds using micro-computed X-ray tomography (µCT) and image analysis.Finally, we compared the efficiency in DEP particle trapping at the different voltages and discussed how the individual grain shape influences the efficiency in DEP filtration.

Particle size analysis
The filter grains were analysed using laser diffraction (Mastersizer 2000, Malvern Panalytical Ltd., UK).The analyser was equipped with stirring and dispersion units running at 2500 rpm.Filter particles were dispersed in water and the measurement started when the obscuration was between 3% and 15%.The analyser was emptied and cleaned between each measurement.To ensure consistency, each fraction was stirred before the sampling in the storage reservoir for 10 s and then taken out for the test.This procedure was repeated three times for each sample.

Sieving
To classify the grains into different fractions, we used a Retsch Vibrotronic Type VE 1 sieving device (Retsch GmbH, Germany).The grains of each material (glass beads, sand and crushed glass) were separately sieved through a standardised set of sieves.The division was made in three size fractions (for the separation of each fraction two sieves were always in use: 150 and 250, 250 and 355 and 355 and 500 µm).The material retained on the smallest sieve (i.e.150, 250 or 355 µm) was collected and labelled as a sample (mesh 150, 250 and 355, respectively).

Micro-CT (µCT) analysis of the packed beds
The sand and glass beads were packed in the same amounts as they were used in DEP experiments into 3D printed plastic containers of dimension 8.3 × 20 × 30 mm 3 with a wall thickness of 0.5 mm.Scans with a resolution of 7.85 µm/voxel were performed on an Xradia 520 Versa X-ray microscope (ZEISS, Oberkochen, Germany).The pictures were produced by the attenuation of X-rays as they travel through the porous filter.Following that, a reconstruction technique was used to get a 3D spatial representation of the item based on the helical route along which the objective has travelled [31].Each voxel in the reconstructed image, with its 16-bit greyscale value, indicates an X-ray attenuation coefficient related to the sample density.Scans were performed with 1600 projections per rotation and a 4× objective length.The obtained 16-bit computer tomography (CT) image was processed in order to segment these porous structures (Section S6).

2.4
Experimental setup

Grained filter matrix preparation
The sand was purchased from Wolf and Mueller Quarzsande GmbH, Germany.According to the company's information, the material composition of the sample is SiO 2 ≥ 97%, Fe 2 O 3 0.1%, Al 2 O 3 1.67%.The glass beads were purchased from SiLibeads series of soda-lime glass (Sigmund Lindner GmbH, Germany).According to the company, they contain approximately 70% of silica.The crushed (milled) glass was obtained by milling 2 mm diameter soda-lime glass beads using a planetary mill (FRITSCH GmbH, Germany).We determined that the rotation speed of the mill needs to be smaller than 400 rpm and that 2 min of milling is sufficient to crush enough glass, which can be further conveniently sieved into our three size fractions (mesh 150, 250 and 355, respectively).

Particle suspension
We assess the DEP separation performance of all samples using fluorescently labelled carboxylated polystyrene (PS) particles (Polysciences Fluoresbrite Yellow-Green Carboxylate Microspheres, Polysciences Europe GmbH, Germany).They have a diameter of 0.5 µm and coefficient of variation (COV) 3% (as measured by the manufacturer).We prepared the particle suspension by mixing PS particles with ultrapure deionised water (OmniaTap 6 UV/UF, Stakpure GmbH, Germany) to a concentration of 2.2 × 10 6 particles/mL.We then added a small amount of Tween 20 (Sigma-Aldrich, Germany) to a final concentration of 0.002 vol.% to the suspension to reduce unspecific adsorption of particles.The suspension's temperature and conductivity were recorded in every experiment.

Experimental details
The DEP experimental setup equipment consisted of a suspension beaker, peristaltic pump (REGLO Analog, Ismatec, Switzerland), filter cell with two stainless-steel electrodes (manufactured in-house) and fluorescence spectrometer (FluoroMax 4, Horiba Scientific, Japan).The suspension beaker was connected to the pump.From the pump, there were two Teflon tubes: one connecting the pump to the filter cell and another one connecting the pump directly to the spectrometer (and referred as bypass in this manuscript).It was possible to switch between either of the tubes using a three-way valve.The filter cell (where the DEP manipulation region is located) has a dimension of 8 × 29 × 18 mm 3 , a tapered inlet and outlet section and is manufactured from polytetrafluoroethylene.It features two macroscopic stainless-steel plates which function as electrodes positioned 8 mm apart from each other inside this cell (Figure S2).The filter setup is identical to the one in our previous works [24,26].
Between the electrodes, the porous-grained filter was loaded in a form of a packed bed which had dimensions of the filter cell.The electric field was generated by applying a sinusoidal voltage (300, 450 and 600 V rms at 1 kHz) across the electrode distance using a voltage amplifier (PZD700A, TREK Inc., USA) and a function generator (HM8131, Hameg Instruments GmbH, Germany).The current was measured during all experiments using a power analyser (LMG670, ZES ZIMMER Electronic Systems GmbH, Germany).Particle concentration was measured on-line using a fluorescence spectrometer and a quartz flow-through cuvette (176.762-QS,Hellma).The excitation/emission wavelength of the PS particles were 441 and 486 nm, and the concentration of the particles was linearly proportional to the intensity signal (counts per second, cps) [24].All experiments were repeated at least three times.Before each experiment, the setup was flushed with ethanol and subsequently with pure deionised water at a flow rate of 11 mL/min (to ensure that the filter material is wet at the beginning of each experiment).
Further experimental details can be found Section S4.

Loading of the filters
Each sample was installed inside the filter cell as follows.
Grains were weighted to an amount of 13 g, loaded to the filter, and kept in place by a polyamide mesh (with a regular pore size of ≈110 µm).The mesh sealed the 8 × 18 mm gap of the fluid flow (an example is shown in Figure S2).Then, the cell was assembled, carefully closed on top, rotated 90 • and flushed with ethanol and pure deionised water through the inlet before the experiment started.To ensure that the loading procedure did not influence trapping efficiency, we have loaded and unloaded the cell several times and recorded the separation efficiencies (Section S4 and Figure S3).Recorded separation efficiencies were comparable among all runs, indicating that trapping is indeed independent of the reproducibility of the filter loading.

Measuring trapping efficiency
Before each measurement, the background signal of pure water was recorded.First, the suspension was connected to the bypass and directed to the measurement device without passing the filter.This was done to determine the concentration of the particles without any trapping caused by the presence of the filter ('mechanical' trapping).The suspension was pumped through the bypass for more than 2 min at the constant flow rate of 11 mL/min.Then, the pump was connected to the filter cell.We recorded the initial concentration of the particles inside this cell,  0 .When the particle concentration was stable (usually, after 120 s), we switched on the electric field across the porous filter.In response, due to DEP, the particle concentration dropped until it reached its DEP minimum at the applied voltage,  e .Then, the electric field was switched off, the particle concentration peaked and slowly returned back to its initial value,  0 [24].The separation efficiency  in % was calculated using the ratio of particle concentration when DEP was applied and initial concentration (the initial concentration was measured at the filter cell outlet, therefore, it already accounts for 'mechanical' trapping):

Particle size distribution
We studied the PSD for the three size fractions of each filter material.We refer to the three size fractions as 150, 250 and 355 mesh, respectively, according to the smallest size of the mesh (in µm) they were collected from after the sieving (as described in Section 2.2).Full details on of each sample can be found in Table S1.Generally,  50 represents the median diameter, that is 50% of all grains have a diameter smaller than this value.Analogous to  50 , 90% of all grains have a smaller diameter than  90 and  10 means 10% of all grains have a smaller diameter than this value.These parameters are the standard parameters for the PSD which allow for a characterization of the particle sizes inside an investigated sample.We note that the mesh size does not correspond to the median particle diameter, that is  50 of the sand sample is 365.2 µm, whereas the sieving mesh size is 250 µm.The label mesh size only indicates the smallest sieve's grain diameter in the sample rather than the median diameter.
Based on a volume-bases analysis, all three packed bed samples are polydisperse with monomodal distribution (Figure 2).The PSDs of the samples are comparable and  50 of the sand and glass beads are in a good agreement, especially, at the small grain size (with a variation of 1.8% for mesh 150).For the crushed (milled) glass, the  50 is significantly larger, especially at the larger grain sizes.For instance, the  50 of the crushed glass is 21% larger than the  50 of the glass beads at mesh 250 and 16% larger at mesh 355.We believe that this difference comes from a slightly wider Gaussian distribution in crushed glass and, moreover, occurs due to a manufacturing method (the material was not available commercially, was milled in-house, and sieving of the non-spherical crushed glass is challenging due to its highly non-uniform shape).We further investigated the COV for the key parameters of each fraction.The COV correlates well with the variations below 3% for  50 and below 5% for  10 and  90 in the cases of glass beads and sands (Table S1) [32].The crushed glass sample satisfies the same correlations for  50 and  10 , too, in the mesh 250 and 355 fractions.The smaller fraction of the crushed glass (mesh 150) shows not only a wider dispersion but also the coefficient of the variation of the key parameters falls outside of the limits mentioned above.This might be caused by the agglomerations of the small particles inside the storage reservoir and the results could be further improved by selecting a more reliable sampling method.

Micro-CT analysis of the packed bed samples
We used µCT to morphologically compare one glass beads sample against one sand sample (both with mesh 250) and two sand samples with two different mesh sizes (250 and 355).
The 3D µCT images of three different samples (glass beads mesh 250, sand mesh 250 and sand mesh 355) and their segmented porous structures are shown in Figure 3 (details for segmentation and analysis can be found in Section S6 and the online repository [33]).
The full analysis is summarised in Table S4 and Figure S4.Briefly, among the sand fractions, porosities are similar (35% for mesh 250 and 38% for mesh 355).The sample of glass beads (mesh 250) has a porosity of 43%, thus, is around 8 percentage points larger than the comparable sand sample.The smallest hydraulic pore diameter is found in the sand (mesh 250).Interestingly, the hydraulic pore diameter of the mesh 250 glass beads sample is 157 µm and is comparable to the mesh 355 sand sample, which is 151 µm; both values are roughly 20 µm larger compared to the mesh 250 sand sample, which is 132 µm.The sample of sand mesh 250 has the highest surface area which can be explained by its smallest grain size and pore diameter.For both sand samples, the sphericity of the pores is three orders of magnitude lower compared to the pores formed by the glass bead sample.We account this to the higher angularity of sand compared to the spherical glass beads.
From our previous studies on DEP filtration, we learned that the DEP trapping efficiency increases with decreasing the pore size.Consequently, because the average pore diameter of the smallest sand fraction (mesh 250) is lower than this parameter for mesh 350 glass beads, we would expect the smallest fractions of the sand to demonstrate the highest DEP efficiency among these three samples.Further, based on the comparison of the pore diameters formed by the structure (Table S4), we expect the mesh 355 sand sample and the mesh 250 glass bead sample to show similar DEP trapping efficiencies, unless the morphological structure of the grains and grain shape would have a significant impact on the trapping (i.e.due to the presence of more edges on the grain which, potentially, can be beneficial for the DEP effect).

Scanning electron microscopy
We have also obtained scanning electron microscope (SEM) pictures of individual grains of glass beads, sand and crushed glass in the size fraction of mesh 150 (Figure 4).The glass spheres are almost perfectly spherical (Figure 4A).In contrast sand and crushed glass (Figure 4B,C) have more small steps and kinks on the surface, that is they have a higher angularity.

Comparison of the filter efficiencies of the different filter matrices
PS particles show pDEP at the used frequency of 1 kHz (Section S2).Because these particles are three orders of magnitude smaller than the pore sizes of the filter, trapping without electric field is low (Section S3).In this study, we refer to this trapping rate without DEP as mechanical trapping.It occurs, for example, when particles are being trapped in dead-end pores or through electrostatic or van  der Waals forces [34].Figure 5 summarises our trapping experiments.
With decreasing grain size and, thus, decreasing pore size, DEP separation efficiency increases for all the materials (Figure 5A-C).Further, the separation efficiency increases with voltage for all grain types and sizes.This correlates well with our previous findings that separation efficiency increases with decreasing pore size, because the electric field gradient is larger at smaller pore sizes and because particles have to travel shorter distances to become trapped [24].At the lowest voltages (300 V rms ), the separation efficiency for different size fractions of each material is almost similar and always below 50%.
When comparing angular grains (sand and crushed glass) with spherical grains (glass beads), one can see that with increasing angularity of the filter grain, the separation efficiency increases (Figure 5D).Comparing the efficiencies at 600 V rms , the glass beads (green line in Figure 5D) show the lowest DEP trapping efficiency among all samples, followed by the sand (red line) and, finally, the crushed glass shows the highest efficiency (dark blue line).Generally, differences between the grain types are more substantial than pore size differences for a single grain type (Figure 5D, lines have larger differences between each other compared to left and right points of each individual line).Notably, the hydraulic pore diameter of the filter of mesh 350 (sand sample) is comparable to the hydraulic pore diameter of the filter of mesh 250 (glass beads sample), 151 and 157 µm, respectively (Section 3.2 and Table S4).However, the DEP performance of the glass bead sample is considerably lower than of the sand sample.This indicates that the role of the grain shape and grain surface has a strong influence on the DEP efficiency because the strength of the field gradient directly depends on grain morphology.Some aspects of the study from Crowther and Hayes in 2017 align well with this hypothesis.In their research, the most DEP-efficient insulator design was an elliptically shaped one with additional small insulators across the base [35].We note that at the high applied voltages (especially, at 600 V rms and above), an inducedcharge electroosmotic flow (ICEO) can additionally affect the behaviour of the target particles [36].Due to the conditions of the experiment, that is the filter cell being sealed on top, we cannot rule out or observe any ICEO-induced vortices.For a detailed characterisation and a full visualisation, a change in the design of the setup would be required.Similarly, some signs of a possible electrothermal motion were indicated also at high voltages (600 V rms ) while applying the electric field for a long time.However, in general, this effect is not to be expected to notably affect the DEP trapping due to the use of low fluid conductivities in our experiments (≤2 µS/cm) [37].
Comparing our DEP results to SEM pictures (Figure 4), it also confirms the hypothesis that increasing angularity and roughness of the grain increases the trapping efficiencies.Interestingly, this increase is independent of pore size.In our previous publication, we suggested that sharp edges of insulating posts in iDEP are only beneficial when the distance between the posts is small [29].For the three investigated pore sizes of this study, we cannot find indications for this behaviour in macro-scale filters.Instead, we see that the DEP trapping efficiency increases with grain angularity and roughness for all three-grain size classes (being a subject for a further detailed investigation, devoted to the quantification of angularity of these grains).

CONCLUDING REMARKS
We showed that DEP trapping efficiency is highly influenced by shape factors of the grain filter, such as the angularity of the filter grains and their surface topography.
We investigated three filter materials with different surface morphology, that is glass spheres, sand and crushed (milled) glass.We showed that differences in grain morphology have a more substantial influence on DEP filtration than the differences in the grain size of the filters in use.We also demonstrated that in packed bed filters the grain angularity is beneficial regardless of the grain size (when looking at modal grain sizes between 200 and 500 µm).This is in contrast to a previous study looking at design of insulating posts in insulator-based positive dielectrophoresis, which suggested that sharp edges at the post surface are only beneficial when the post-to-post spacing is narrow.It indicates that a regular array of posts in a microfluidic chip might not be an adequate simplification to model DEP filtration.Thus, more research is essential to elucidate a link between grain shape, pore size and particle trapping in DEP filtration.The results from this study give us a better understanding of the design of macro-scale DEP filters.Prospectively, this allows us to compound effective DEP filters for applications which require a high purity separation at industrial-scale throughputs.

C O N F L I C T O F I N T E R E S T S TAT E M E N T
The authors have declared no conflict of interest.

D ATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are openly available in a Zenodo repository at https://doi.org/10.5281/zenodo.7601041.

F I G U R E 1
Schematic representation of the dielectrophoretic (DEP) experimental setup (left) and main components of the setup (right).

F I G U R E 2
Particle size distribution of the three different grain types: (A) mesh 150, (B) mesh 250 and (C) mesh 355.

F
I G U R E 3 A visualisation of the grain segmentation process, demonstrated on glass beads and sand samples: greyscale micro-computed X-ray tomography (µCT)-based models of three different filter structures ((A) glass beads mesh 250, (B) sand mesh 250 and (C) sand mesh 355) and segmented grains of these samples ((D)-(F), respectively).

F I G U R E 4
Scanning electron microscopy (SEM) images of the three grains investigated in this study, (A) glass beads, (B) sand and (C) crushed (milled) glass.

F I G U R E 5
Trapping efficiency of different packed bed filters at 11 mL/min flow rate and frequency of 1 kHz.(A-C) Separation efficiency as a function of voltage and grain size for (A) crushed glass beads, (B) sand particles and (C) glass beads.(D) Separation efficiency as a function of grain size and grain shape at 600 V rms for three different filter materials (dark blue -crushed glass, red -sand and green -glass beads).The error bars represent standard deviation in all the cases.
This work was supported by the German Research Foundation (DFG) through the research training group 'Micro-, Meso-, and Macroporous Non-Metallic Materials: Fundamentals and Applications' (GRK 1860).The authors would like to explicitly acknowledge the research grant received by M. Kepper from MAPEX Center for materials and processes (MAPEX-CF) for µCT measurements at their facilities.M. Kepper would like to thank J. Giesler, L. Weirauch, S. Sinko, K. Sandmann, A. Kyrloglou, T. Guo, A. Rother, W. A. Kahl for the fruitful discussions and M. F. Ziemann and A.P.G.De Alwis for their assistance in the laboratory.Open access funding provided by IReL.