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The transmittable torque of magnetorheological fluid (MRF) clutches can be adjusted by controlling the magnetic field inside the clutch. In order to increase their maximum transmittable torque while decreasing their volume and mass, geometry optimization is often carried out, such as in [1]. Additionally, the MRF used in them can be designed to have a higher yield stress, resulting in a higher transmittable torque. In [2], this was studied by adding micrometer-sized graphite flakes to an in-house created MRF; it was found that the inclusion of graphite flakes led to an increased yield stress. The present research aims to further study this, by investigating the effects that including graphite flakes in a commercially available MRF may have on the transmittable torque of an MRF clutch. Clutch design. The MRF clutch utilized in this research is a drum-type, permanent magnet-based clutch, made from two concentric cylinders. The external cylinder was fabricated from low carbon steel and the internal cylinder was fabricated from aluminum. A cavity for the MRF is formed between these cylinders, with a width of 0.75 mm. The external cylinder formed the main body of the output stage of the MRF clutch. The magnet assembly used to magnetize the clutch consisted of four magnets which have a hollowed-out cylinder shape when assembled together. These magnets were magnetized in the radial direction, with two of them having their south poles in the outer face, while the other two had them in the inner face. The internal cylinder formed the main body of the input stage of the clutch, driven by a DC motor. A mechanism called field blocker, presented in [3], was used to adjust the magnetization level of the MRF inside the clutch. MRF. A commercially available MRF, the LORD MRF-140CG, was used in this study. Four mixtures with 20 μm graphite flakes (282863, Sigma-Aldrich) were prepared, with a graphite content of 0.5% w/w, 1.0% w/w, 2.0% w/w, and 3.0% w/w. Experimental set-up. The MRF clutch was driven by a velocity-controlled DC motor, and its output stage was connected to one end of a 5 Nm T22 HBM torque meter. A lever was attached to the other end of this torque meter, which contacted the testing bench when rotated in one or the other direction. After contacting the bench, this lever forced the output stage of the MRF clutch to remain stationary while the input stage continued rotating. A stepper motor moved the field blocker in or out of the MRF clutch by means of a ball-screw mechanism, covering and uncovering the magnet assembly. The testing set-up is shown in Figure 1 a). Experimental procedure. The testing of the four MRF mixtures together with the MRF without graphite were carried out the following way: 1) The torque output was measured during one second without driving the clutch and with the lever in a free position. 2) The clutch was then driven at the velocity under test for a duration equal to 2 s plus the time required for the clutch to complete a rotation. 3) The clutch was driven backward at a low angular velocity for one second, in order to leave the lever in a free position. This procedure was repeated three times for each combination of five angular velocities, six field blocker positions, with and without the magnet assembly, for a total of 180 measurements per MRF mixture. The average torque value was calculated from the torque recorded during the second testing step, after the first two seconds had passed. The effects on torque due to seal friction and viscosity on the measured torque values were then removed. Results. The results of these tests are summarized in Table 1, Figure 1 b) and c). In Figure 1 b) and c), the average torque values of the tests carried out with the field blocker not covering and covering the magnets are shown (two out of the six positions tested). The torque values are higher in the case were the magnet assembly is uncovered than when it is covered. It is also seen that the difference in torque caused by the graphite content increases as the input angular velocity increases. Higher magnetization levels decrease the difference in torque (the field blocker does not block the magnetic field entirely). The mean, maximum, and minimum torque values over the six magnetization cases are shown in Table 1. It can be seen that on average, the transmittable torque increases with both graphite content and angular velocity, achieving up to 70% torque increase. Conclusion. The inclusion of graphite flakes in a commercially available MRF can be used to increase the output torque of an MRF clutch, a result which aligns to those of [2]. This effect in a clutch with aluminum cylinders is more evident at higher angular velocities.

**References:**

[1] R. M. Andrade, A. B. Filho, C. B. S. Vimieiro, and M. Pinotti, “Optimal design and torque control of an active magnetorheological prosthetic knee,” &lt;i&gt;Smart Mater. Struct.&lt;/i&gt;, vol. 27, no. 10, p. 105031, 2018.&lt;br/&gt;[2] M. K. Thakur and C. Sarkar, “Influence of Graphite Flakes on the Strength of Magnetorheological Fluids at High Temperature and its Rheology,” &lt;i&gt;IEEE Trans. Magn.&lt;/i&gt;, vol. 56, no. 5, pp. 1–10, 2020.&lt;br/&gt;[3] M. A. Fernandez, J. Y. Chang, and C. Y. Huang, “Development of a passive magnetorheological fluid clutch with field-blocking mechanism,” &lt;i&gt;IEEE Trans. Magn.&lt;/i&gt;, vol. 54, no. 11, pp. 1–5, 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/dd1732b1b4985924706ec3392bdc17b8.jpg)
Table 1. Percentage of the average torque values obtained using MRF with graphite above or below the average torque value obtained with the MRF without graphite.

![](https://assets.underline.io/uploads/markdown_image/1/image/53bb62aa46ec33865da9ddf7f003527d.jpg)
Figure 1. The testing set-up is presented in a). The plotted torque values when the magnet assembly was uncovered and covered are shown in b) and c), respectively.

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 A Study on the Effects of Graphite Flakes on Torque Transmission of a Magnetorheological Fluid Clutch

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The transmittable torque of magnetorheological fluid (MRF) clutches can be adjusted by controlling the magnetic field inside the clutch. In order to increase their maximum transmittable torque while decreasing their volume and mass, geometry optimization is often carried out, such as in [1]. Additionally, the MRF used in them can be designed to have a higher yield stress, resulting in a higher transmittable torque. In [2], this was studied by adding micrometer-sized graphite flakes to an in-house created MRF; it was found that the inclusion of graphite flakes led to an increased yield stress. The present research aims to further study this, by investigating the effects that including graphite flakes in a commercially available MRF may have on the transmittable torque of an MRF clutch. Clutch design. The MRF clutch utilized in this research is a drum-type, permanent magnet-based clutch, made from two concentric cylinders. The external cylinder was fabricated from low carbon steel and the internal cylinder was fabricated from aluminum. A cavity for the MRF is formed between these cylinders, with a width of 0.75 mm. The external cylinder formed the main body of the output stage of the MRF clutch. The magnet assembly used to magnetize the clutch consisted of four magnets which have a hollowed-out cylinder shape when assembled together. These magnets were magnetized in the radial direction, with two of them having their south poles in the outer face, while the other two had them in the inner face. The internal cylinder formed the main body of the input stage of the clutch, driven by a DC motor. A mechanism called field blocker, presented in [3], was used to adjust the magnetization level of the MRF inside the clutch. MRF. A commercially available MRF, the LORD MRF-140CG, was used in this study. Four mixtures with 20 μm graphite flakes (282863, Sigma-Aldrich) were prepared, with a graphite content of 0.5% w/w, 1.0% w/w, 2.0% w/w, and 3.0% w/w. Experimental set-up. The MRF clutch was driven by a velocity-controlled DC motor, and its output stage was connected to one end of a 5 Nm T22 HBM torque meter. A lever was attached to the other end of this torque meter, which contacted the testing bench when rotated in one or the other direction. After contacting the bench, this lever forced the output stage of the MRF clutch to remain stationary while the input stage continued rotating. A stepper motor moved the field blocker in or out of the MRF clutch by means of a ball-screw mechanism, covering and uncovering the magnet assembly. The testing set-up is shown in Figure 1 a). Experimental procedure. The testing of the four MRF mixtures together with the MRF without graphite were carried out the following way: 1) The torque output was measured during one second without driving the clutch and with the lever in a free position. 2) The clutch was then driven at the velocity under test for a duration equal to 2 s plus the time required for the clutch to complete a rotation. 3) The clutch was driven backward at a low angular velocity for one second, in order to leave the lever in a free position. This procedure was repeated three times for each combination of five angular velocities, six field blocker positions, with and without the magnet assembly, for a total of 180 measurements per MRF mixture. The average torque value was calculated from the torque recorded during the second testing step, after the first two seconds had passed. The effects on torque due to seal friction and viscosity on the measured torque values were then removed. Results. The results of these tests are summarized in Table 1, Figure 1 b) and c). In Figure 1 b) and c), the average torque values of the tests carried out with the field blocker not covering and covering the magnets are shown (two out of the six positions tested). The torque values are higher in the case were the magnet assembly is uncovered than when it is covered. It is also seen that the difference in torque caused by the graphite content increases as the input angular velocity increases. Higher magnetization levels decrease the difference in torque (the field blocker does not block the magnetic field entirely). The mean, maximum, and minimum torque values over the six magnetization cases are shown in Table 1. It can be seen that on average, the transmittable torque increases with both graphite content and angular velocity, achieving up to 70% torque increase. Conclusion. The inclusion of graphite flakes in a commercially available MRF can be used to increase the output torque of an MRF clutch, a result which aligns to those of [2]. This effect in a clutch with aluminum cylinders is more evident at higher angular velocities.

**References:**

[1] R. M. Andrade, A. B. Filho, C. B. S. Vimieiro, and M. Pinotti, “Optimal design and torque control of an active magnetorheological prosthetic knee,” Smart Mater. Struct., vol. 27, no. 10, p. 105031, 2018. [2] M. K. Thakur and C. Sarkar, “Influence of Graphite Flakes on the Strength of Magnetorheological Fluids at High Temperature and its Rheology,” IEEE Trans. Magn., vol. 56, no. 5, pp. 1–10, 2020. [3] M. A. Fernandez, J. Y. Chang, and C. Y. Huang, “Development of a passive magnetorheological fluid clutch with field-blocking mechanism,” IEEE Trans. Magn., vol. 54, no. 11, pp. 1–5, 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/dd1732b1b4985924706ec3392bdc17b8.jpg)
Table 1. Percentage of the average torque values obtained using MRF with graphite above or below the average torque value obtained with the MRF without graphite.

![](https://assets.underline.io/uploads/markdown_image/1/image/53bb62aa46ec33865da9ddf7f003527d.jpg)
Figure 1. The testing set-up is presented in a). The plotted torque values when the magnet assembly was uncovered and covered are shown in b) and c), respectively.

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Mn-doped ferrite nanoparticles are promising materials for applications in biomedicine as they exhibit better properties for some biomedical applications than non-doped magnetite or maghemite. [1] The thermal decomposition of metal precursors in an organic solvent is arguably the best method in terms of size control and the magnetic properties of the so-obtained materials. It provides hydrophobic nanoparticles that must be transferred to water through surface modification procedures before their use in biomedicine. In this work, Mn-doped ferrite nanoparticles have been synthesized by thermal decomposition changing systematically the Mn/Fe ratio of the metal precursors. Then, they have been transferred to the aqueous phase through ligand substitution with dimercaptosuccinic acid and dopamine. We show that the synthesis and post-synthesis manipulations lead to changes in the composition. During the thermal decomposition process, Mn is incorporated in the nanoparticles in a relatively lower amount than Fe and, then, during the surface modification step both Mn and Fe ions leach out from the nanoparticles (Figure 1). This alteration of the chemical identity of the nanoparticles have substantial implications for their subsequent application because small variations in the Mn/Fe ratio have a strong impact on properties like the saturation magnetization, blocking temperature, contrast enhancement for magnetic resonance imaging, magnetic heating, as well as on the cytotoxicity.[2]

**References:**

[1] L. Yang et al., Chem. Mater., Vol. 29, p.3038 (2017). [2] D. García-Soriano et al., J. Colloid Interf. Sci., Vol. 578, p.510 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a4b3867c47619b2ddabcdcd15281883f.jpg)
Scheme illustrating the changes in composition when the nanoparticles are transferred from an organic dispersion to an aqueous one.

 Cation leaching alters the properties of Mn nanoferrites for biomedical applications

The advances in synthesis methods and the research of new magnetic effects have been the driving forces propelling the use of magnetic nanostructures in several research fields. In biomedical applications, magnetic nanoparticles, usually in the superparamagnetic state, are mainly used in magnetic fluid hyperthermia (MFH) and as contrast agents. In contrast, the novel magnetic nanostructures (MNS) studied in this work present a unique spin arrangement in the magnetic ground state, namely spin-vortex or synthetic antiferromagnetic state. MNS are mainly produced using top-down lithography techniques and physical vapour deposition methods. They are not spherical, rather disc-shaped, like coins with nanometer dimensions. MNS showed promising results in cell separation, as a contrast enhancing agents in MRI and in magneto-mechanically induced cell annihilation. Magneto-mechanically induced cell annihilation is a comparable technique with MFH for cancer therapy, where instead of superparamagnetic particles, micro/nano-discs in the spin-vortex state or synthetic antiferromagnetic nanostructures are employed. The main advantages of this novel approach are the usage of weaker magnetic fields with lower frequencies, as well as the need for a lower concentration of particles. This scenario opens new possibilities in cancer therapy, having triggered a scientific interest for MNS with unique spin configurations suitable for biomedical applications [1]. In this work, we developed one subset of biocompatible magnetic nanostructures that exhibit a spin-vortex state with interest in analysing their application in magneto-mechanically induced cell death [2]. First, micromagnetic simulations, using mumax3 of sub-micron iron discs, were performed for different interdot distance and aspect-ratio (thickness/diameter), to better understand the magnetic behaviour of these nanostructures. Two sets of samples were studied: ideal circular discs and disc-shaped nanostructures (based on images of real samples). By analysing the nucleation and annihilation fields, as well as the magnetic susceptibility, it was found that the (ideal) discs could be considered as isolated for interdot distances greater than twice the radius of the disc (2R) [3]. We also found that discs with an aspect ratio between 5 and 15 should sustain the vortex state in remanence. Iron nano-discs, with a diameter of about 500 nm, were fabricated by electron beam evaporation on a Si substrate pre-patterned by interference lithography [4]. The discs, protected by bottom and top gold layers, were fully characterized with scanning electron microscopy (SEM), X-ray diffraction (XRD), superconducting quantum interference device (SQUID), magneto-optic Kerr effect (MOKE) and ferromagnetic resonance (FMR) techniques. The synthesized nanostructures showed the desired vortex state configuration. The obtained magnetic measurements are in good agreement with the micromagnetic simulations (Fig. 1). Then, the magnetic vortex nano-discs were released from the substrate by chemical etching of a sacrificial layer. Subsequently, cell viability and uptake assays were performed in a human leukaemia monocyte cell line (THP-1). Several concentrations of nano-discs were studied by flow cytometry. As a result, the discs were internalized by the cells and found to be innocuous to them, in the absence of an external magnetic field. Work supported by Horizon 2020 MSCA grant agreement No 734801, AEI PID2019-104604RB, IT1162-19, IF/01159/2015, SFRH/BD/148563/2019, POCI-01-0145-FEDER-028676/PTDC/CTM-CTM/28676/2017 and POCI-01-0145-FEDER-031302/PTDC/FIS-MAC/31302/2017.

**References:**

[1] L. Peixoto, R. Magalhães, D. Navas, S. Moraes, C. Redondo, R. Morales, J. P. Araújo, C.T. Sousa, Magnetic nanostructures for emerging biomedical applications. Appl. Phys. Rev., 7 (2020) 011310., [2] Y. Cheng, M. E. Muroski, D.C.M.C. Petit, R. Mansell, T. Vemulkar, R. A. Morshed, Y. Hana, I. V. Balyasnikova, C.M. Horbinski, X.Huang, L. Zhangc, R. P. Cowburn, M. S. Lesniak, J. Control. Release 223 (2016) 75. [3] L. Peixoto, C. Sousa, D. Navas, and J. P. Araújo, Micromagnetic study of the vortex state in sub-micron iron discs. EPJ Web of Conferences 233 (2020) 05002. [4] B. Mora, A. Perez-Valle, C. Redondo, M.D. Boyano, R. Morales, ACS Appl. Mater. Interfaces 10 (2018) 8165.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/68db60cda0b5971db06d25b5e8aea1a8.jpg)

 Vortex nano-discs: from micromagnetic simulations to cancer cells internalization for magneto-mechanically induced damage applications.

Most patients who develop primary bone tumors require surgical intervention. In this respect, the design of a multifunctional material, used as bone substitute, is of high clinical interest to simultaneously treat cancer and promote bone regeneration. Bioactive glass (BG) nanoparticles are a promising material for bone tissue regeneration because when implanted, a hydroxyapatite layer is quickly formed onto their surface, bonding them to natural bone tissue [1,2]. By coupling the high bioactivity of large specific surface area bioactive glass particles with the heating ability of superparamagnetic iron oxide nanoparticles (SPIONs) under an alternating magnetic field [3], a multifunctional material could be designed and used to selectively destroy remaining or resurging cancer cells through hyperthermia treatment before promoting bone regeneration. In this scope, heterostructures consisting of SPIONs encapsulated in BG have been synthesized by sol-gel synthesis and characterized. The γ-Fe2O3@SiO2-CaO core-shell nanoparticles show promising hyperthermia and bioactivity properties, with a specific loss power (SLP) of 159 W/gFe and hydroxyapatite growth within 3 days [4]. At a concentration of 1 mgFe/mL, a temperature rise of 4 °C was achieved within 3 minutes, which could be suitable for cancer treatment. However, the heating power of these core-shell nanoparticles can still be improved, for example by increasing the SPIONs size. Indeed, the presence of a non-negligible amount of SPIONs with a diameter under 10 nm due to size dispersion is not optimal for hyperthermia [3]. Moreover, as evidenced in Figure 2, this sample present magnetic cores clustering, that is known to induce a decrease of the SLP value due to magnetic dipolar interactions [5]. Single-core NPs with a larger core size would thus be a better candidate for more efficient heating. In that respect, the core-shell particle structure has been modified in order to study the impact of core size and clustering on the hyperthermia properties. Using larger SPIONs led to an increase in SLP and an increasing percentage of single-core heterostructures. Magnetic core aggregation was also controlled by varying SPIONs concentration. The BG shell thickness was also modified, by varying the ratio between the magnetic cores and the silica precursor, because it could affect the heat dissipation of the magnetic particles in fluids [6].

**References:**

[1] J. R. Jones, Acta Biomaterialia, Vol. 9, p. 4457 (2013) [2] C. Vichery and J.-M. Nedelec, Materials, Vol. 9, p. 288 (2016) [3] F. Gazeau, M. Lévy and C. Wilhelm, Nanomedicine, Vol. 3 (6), p. 831 (2008) [4] X. Kesse, C. Vichery and J.-M. Nedelec, ACS Applied Materials & Interfaces, Vol. 12, p. 47820 (2020) [5] D. F. Coral, P. M. Zélis and M. B. Fernández van Raap, Langmuir, Vol. 32, p. 1201 (2016) [6] M. Hu, X. Wang and G. V. Hartland, Chemical Physics Letters, Vol. 372, p. 767 (2003)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b02198782be4bc51a96d6da5e26e6560.jpg)
Schematic representation of bone repair coupled with hyperthermia treatment

![](https://assets.underline.io/uploads/markdown_image/1/image/4483b6fa5add1c82a14e3acf79943747.jpg)
TEM image of γ-Fe2O3@SiO2-CaO core-shell nanoparticles

 Superparamagnetic and Bioactive Nanoparticles for Bone Cancer Treatment

Achieving new possibilities of cell manipulation or of other microbiological species is one of the most important tasks of the latest lab-on-a-chip devices [1-3]. High throughput and precise movement control are the figures of merit for new tools or chip designs. Common concepts consist of labeling biological cells or other biological entities with magnetic nanoparticles to achieve transport by timely and spatially varying magnetic field gradients [4]. In this context, superparamagnetic microbeads (MB) are widely used to imitate the properties of tagged cells or act as carriers for smaller biological species like DNA-strings or proteins. The particles or MBs can be manipulated on top of hard magnets [5] or soft magnetic thin film structures [6]. Recent research has shown many differently designed patterned thin film structures, featuring multiple advantages for the transport of MBs. One of the transport concepts relies on the interaction of their magnetic moment with a stray magnetic field gradient of arranged soft-magnetic thin film elements. Magnetic field sequences create varying potential states, enabling specific MB trajectories. In narrow soft magnetic tracks, magnetic microstructures that exhibit strong local stray field gradients are moved to drag the MBs along certain directions. For example, two-dimensional arrays of soft magnetic elements with various magnetization states varying with applied magnetic fields enable complex MB manipulation [2]. In every case, the maximum speed of the MB is limited by the hydrodynamic drag force, the surface friction, and by the magnetic force. This links the magnetic moments of the thin film elements and the MB, the friction coefficients, and the MB size. Beneficial and applicable unidirectional movement of a MB and a magnetically labeled rat embryonic fibroblast cell is demonstrated. We show the unidirectional transport of MBs and cells independent of the sign of the magnetic stimuli. Oval shaped elements made from a soft magnetic amorphous iron-based alloy are arranged in a one-dimensional chain, allowing MB transport whether clockwise or counter-clockwise in-plane rotating magnetic fields are applied. A directional motion scheme is achieved by exploiting the stray field dependence of the curvature radius of the facing magnetic elements. Three dimensional simulations [7] are used to forecast the motion of a particle along a chain of ovals and provide the theoretical background to the experimental results. Magnetic potential energy landscapes are calculated between the MB anticipated as magnetic dipoles and the micromagnetic structure of the oval elements simulated using mumax3 [8]. We find that an overlap of the potential minima of two neighboring elements for a spacing similar to the diameter of the MB enables a handover of MBs between magnetic elements. The agreement between the numerical simulated bead trajectories and the experimental movement path is shown in Fig. 1. The unidirectional motion scheme of the beads is demonstrated for different starting conditions for clockwise and counterclockwise rotating fields. The motion is independent of the sense of field rotation. The same manipulation options are obtained with a MB engulfed rat embryonic fibroblast cell as shown in Fig. 2. The robust diode-like particle guidance along predefined tracks, formed by chains of elements, holds also great potential for lab-on-a-chip applications, including cell sorting or highly controllable manipulation of biological carriers. The diode-like behavior of the oval elements leaves the direction of magnetic field rotation as a degree of freedom unexploited, permitting its usage for adding-on other application relevant manipulation schemes. Various aspects and options of the motion rectifying magnetic structures will be discussed. J.M., F.B., and U.S. acknowledge funding through the Deutsche Forschungsgemeinschaft grants DFG MC 9/13-1 and MC 9/13-2. C.A. and C.S. thank the Volkswagen Foundation for funding the project "Molecularly controlled, stimuli-sensitive hydrogels for dynamically adjustable biohybrid actuators". S.S. and C.S. acknowledge funding of the Research Training Group RTG 2154 "Material for Brain" through the Deutsche Forschungsgemeinschaft. J.M. thanks S. Gutekunst for stimulating discussions. The authors thank L. Thormählen for magnetic thin film deposition.

**References:**

[1] S. Rampini, P. Li, and G. U. Lee, Lab Chip 16, 3645-3663 (2016). [2] U. Sajjad, E. Lage, and J. McCord, Adv. Mat. Int. 5, 1801201 (2018). [3] B. Lim, P. Vavassori, R. Sooryakumar, et al., J. Phys. D: Appl. Phys. 50, (2016). [4] T. Henighan, A. Chen, G. Vieira, et al., Biophys. Jour. 98, 412-417 (2010). [5] J. Pivetal, D. Royet, G. Ciuta, et al., J. Magn. Magn. Mat. 380, 72-77 (2015). [6] U. Sajjad, R. B. Holländer, F. Klingbeil, et al., J. Phys. D: Appl. Phys. 50, (2017). [7] F. Klingbeil, F. Block, U. Sajjad, et al., Sci. Rep. 10, 1-12 (2020). [8] A. Vansteenkiste, J. Leliaert, M. Dvornik, et al., AIP Adv. 4, 107133 (2014).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/515b7a81ae7380b50d0574aff749114e.jpg)
Fig. 1: Simulation data of a single MB motion for clockwise magnetic field rotation. Snapshots of the unidirectional motion together with the corresponding potential landscape are shown for four magnetic field angles. The corresponding matching experimental behavior for the same parameters are shown. The calculations and experiments were performed at clockwise rotating magnetic fields of 40 mT with a rotation frequency of 1.0 Hz.

![](https://assets.underline.io/uploads/markdown_image/1/image/c9bccb77854ad0f52c7d5fc0767f13c4.jpg)
Fig. 2: Forward transport of a microbead engulfed by a rat embryonic fibroblast cell. The initial position of the cell and the microbead on the upper side of an oval structure is marked, demonstrating a forward motion even under the condition of a starting velocity in the backward direction. Here a counterclockwise rotating magnetic field of 40 mT with a rotation frequency of 0.3 Hz is applied.

 Unidirectional Transport of Superparamagnetic Beads and Biological Cells along an Oval Shaped Magnetic Element Path

We demonstrate the realisation of nanoparticle concentration gradients by means of Halbach arrays positioned below channels dedicated for cell culture studies. The nanoparticles can be magnetic as well as non-magnetic if a biocompatible chelated Gadolinium carrier fluid is used. These gradients are extremely helpful for the dose-response analysis of nano-particle toxicity. Conventionally, concentration ranges are prepared in individual containers (wells). Even though precise, this method is labour intensive both in preparation and analysis and requires considerable space inside the incubator. The use of gradients allows for rapid scanning of the concentration range of interest at small form factor. The Halbach array was realized using 48 commercially available 1.0x1.5x5.0 mm NdFeB magnets. Analytical solutions are given for the forces on magnetic nanoparticles and non-magnetic spheres in a paramagnetic solution. We demonstrate this method on human liver cells inside Ibidi micro-Slide channels of 400 um height using Fe2O3 and silver nanoparticles.

**References:**



**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d7061caed5097b142d18229f01bee10d.jpg)
Fig. 1. Top: Concentration gradient of oxide nanoparticles of 5 nm diameter inside a channel slide dedicated for cell culture analysis. Bottom: Using a paramagnetic fluid, also concentration gradients of non-magnetic particles can be realized.

 Concentration gradients of magnetic nanoparticles in non-magnetic fluids and non-magnetic particles in magnetic fluids for rapid toxicity screening

Electron paramagnetic resonance (EPR) is a non-destructive technique widely used to estimate doses of ionizing radiation [1] in radiological emergencies, medical therapies, industrial processes, etc. An EPR dosimeter detects and quantifies point paramagnetic defects, usually free radicals, that are created by ionizing radiation (photons, neutrons, electrons) incident on an adequate material. The intensity of the EPR signal is a reliable measure of the number of paramagnetic centers induced, which is proportional to the received dose. Several compounds [2] can be used as EPR dosimeters: L-alanine , hidroxyapatite, 2-methyl alanine, lithium formate, glucose, etc. The election depends on the sensitivity, time stability, linearity, and the dose interval of interest (from mGy to kGy). L-alanine [3] is widely used in industrial medium dose applications (50 Gy–10 kGy) or high dose applications (10–50 kGy). The widespread use of alanine in low-dose (below 5 Gy) biomedical applications is due to its tissue equivalent properties. The induced free radicals responsible for the five-line EPR spectrum are very stable and produce a signal that can remain unchanged for years. Its response is reasonably linear in a wide range of doses. The optimal range of detection for alanine commercial sensors is 10 Gy–100 kGy [4]. It is almost insensitive to thermal neutrons and for this kind of radiation it is usual to dope alanine with boron or lithium, with a large neutron capture cross section, to enhance the response [5]. Lithium formate monohydrate (abbreviated ‘LiFo’) is EPR sensitive and has several advantages [6]. LiFo’s atomic composition is closer to that of water, what makes it more similar to organic tissues, has a higher sensitivity (5–6 times), and a simpler (single line) EPR spectrum tan alanine’s. LiFo is receiving considerable attention due to its ability to capture thermal neutrons through the reaction 6Li + n → 4He + 3H. The cross section for thermal neutrons capture of the 6Li isotope (natural abundance 7.5%) is roughly 2 104 times larger than the majority isotope 7Li. Thus, the irradiation of LiFo with thermal neutrons produces the emission of alpha particles and tritium atoms which generate paramagnetic defects that could be detected and quantified by EPR [7]. This is relevant for medical applications that use mixed radiation fields of photons and termal neutrons, as Boron Neutron Capture Therapy (BNCT). An adequate characterization of a BNCT mixed field implies the simultaneous determination of the gamma photon dose and the thermal neutron fluence in a certain position, which is crucial to manage the therapy [8]. A dual dosimeter that would combine the EPR readings of natural Li and 6Li-enriched LiFo was proposed in the past [7]. In this work we investigate the factibility of a L-alanine/LiFo dosimeter without requiring 6Li isotopic enrichment. The γ-doses in our BNCT source go from ~7 Gy to 150 Gy, while the thermal neutron fluences range is 1012 - 2 1013 neutrons cm−2. For calibration purposes we used a 60Co auxiliar source ranging from 0.1 to 50 kGy γ-doses. We used commercial L-alanine pellets and specially prepared (milling and sievieng) natural lithium formate powder samples of specific granulometry, that were irradiated in the 60Co irradiation plant (PISI) and in the mixed flux of the BNCT facility (Fig. 1) placed in the RA6 experimental reactor (Bariloche, Argentina). The EPR study of the irradiated samples was performed by determining the intensity of the spectrum relative to a reference standard constituted by Mn2+ impurities diluted into a MgO single crystal. As expected, L-alanine has revealed to be largely insensitive to thermal neutrons in the investigated range. On the contrary, the EPR intensity of irradiated natural LiFo powders is clearly sensitive to thermal neutrons and has a linear dependence on the γ-dose (Fig. 2). Based on these results we propose a dual dosimeter by combining L-alanine pellets and LiFo powders that would allow to determine the γ-dose and thermal neutron fluence in a selected position. Moreover, we demonstrate that the 6Li enrichment that has been proposed in the past to enhance the performance of Li-based EPR dosimeters is not crucial here. The natural isotopic abundance is enough to obtain a satisfactory sensibility to thermal neutrons in our BNCT irradiation facility for fluences &gt; 1012 neutrons cm-2 This work was supported by Conicet, ANPCyT and UN Cuyo (Argentina). The technical support from R. Benavídes, C. Pérez and M. Guillén is deeply acknowledged.

**References:**

 [1] A. Lund and M. Shiotani, Applications of EPR in Radiation Research (Springer) (2014). [2] A. Lund, S. Olsson, M. Bonora et. al., Spectrochim. Acta A 58, 1301 (2002). [3] D. F. Regulla and U. Deffner, Int. J. Appl. Radiat. Isot. 33, 1101 (1982). [4] www.harwell-dosimeters.co.uk [5] F. Ureña-Núñez , S. Galindo and J. Azorín, Appl. Radiat. Isot. 50, 763 (1999). [6] E. Waldeland, J. Helt-Hansen and E. Malinen, Radiat. Meas. 46 213 (2011). [7] E. Lund, H. Gustafsson, M. Danilczuk et al., Spectrochim. Acta A 60, 1319 (2004). [8] S. Bortolussi, N. Protti, M. Ferrari et al., Nucl. Instrum. Methods Phys. Res. B 414, 113 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c047938f14e7a7c5abc305f0d94feff1.jpg)
Fig. 1. BNCT irradiation set-up. (1) Incoming neutron–photon radiation (2) Bismuth shield (65 cm diameter) to reduce the gamma photon component. (3) Removable cadmium disc for the absorption of thermal neutrons, 2 cm apart from bismuth shield. The other cadmium disc is fixed. (4) Polyethylene disc for the thermalization of neutrons. (5) Sample holder (10 cm × 5 cm × 1.9 cm), in direct contact with the polyethylene discs (not to scale). It holds four quartz tubes and an alanine monitor at the center. (6) Aluminum rod to hold the discs and the sample holder.

![](https://assets.underline.io/uploads/markdown_image/1/image/7a56543402c7e7e4138d4d9778d48ac3.jpg)
Fig. 2. EPR intensity measured on LiFo samples irradiated at the BNCT facility. Average neutron fluences are 1.75 and 12.6 for configurations #1 and #2 respectively, in units of 1012 neutrons cm -2. The triangle corresponds to a LiFo sample irradiated with γ photons at the 60Co source. The line for configuration #3 is a straight line passing through the experimental point and the origin of coordinates. The maximum relative uncertainty in the γ-dose is 6%.

 EPR characterization of the mixed radiation field of a boron neutron capture therapy irradiation facility: a dual natural lithium formate/L-alanine dosimeter

Corona virus 2019 (COVID-19) has already killed more than 1.93 million people around the world, a number which continues to increase daily. This outbreak represents an unprecedented global public health challenge. To limit the spread of COVID-19 and help doctors in clinical decision-making, the detection and real-time monitoring of their symptoms and growth at all (early, intermediate and severe) states is critical. Common symptoms of COVID-19 include: (i) shortness of breath or difficulty breathing, (ii) cough and (iii) fever. Current detectors provide limited information and possess lengthy processing time, or are physically contacted to patients. Therefore, there is an urgent need for developing contactless devices that enable early and fast detection of COVID-19 and track their growth rates in real time. In this study, we have integrated an ultrasensitive magneto-LC resonance (MLCR) sensor technology based on an ultrasoft ferromagnetic microwire [1] with machine learning to develop an innovative, contactless diagnostic device that can sense the breathing symptoms of COVID-19 at multiple stages of disease progress and provide crucial information on the growth rate by patient of this deadly virus. The MLCR sensor can precisely measure and track patients’ breathing patterns and respiratory rates in real-time, thus providing efficient screening and monitoring at a clinic or at home. The sensor converts magnetic oscillations generated from a person’s breathing into impedance spectra, which allows for a deep analysis of one’s breath variation to identify patients being infected by COVID-19 or other types of virus. We add predictive analytics, with the help of machine learning, to provide a good understanding of what can and cannot be said about a patient’s health condition status and a possible treatment plan, based on the available data. Actual tests were performed on various subjects. We have demonstrated that the MLCR sensor can track a person’s breathing pattern very precisely in real time over the course of multiple states (normal breathing, holding breath, and sleeping). Owing to its ultrahigh sensitivity, the sensor yielded a distinct breathing pattern for each person tested and revealed abnormal breathing, which is superior to existing respiratory monitoring devices. Figure 1 shows how we explored the ultrahigh sensitivity of the MLCR sensor for real-time tracking of a patient’s breathing in multiple/complex states from holding breath (Stage 1) to the release of breath (Stage 2) and the return to normal breathing (Stage 3). We have found that when getting older, one usually manifests weaker breathing marked by an increasing breathing rate. He/she tends to hold his/her breath for a shorter period of time and often experiences more with respiratory issues than younger people. People become more relaxed, thus breath more regularly and slowly while sleeping as compared to the wake-up mode. Our highly sensitive magnetic respiratory monitor provides not only valuable information on a patient’s current health status, but also a novel breathing control tool for improving our health and physical performance. Finally, we have demonstrated the integration of the MLCR sensor with machine learning for the fast screening and real-time monitoring of COVID-19 progress.

**References:**

O. Thiabgoh, T. Eggers, and M. H. Phan, A new contactless magneto-LC resonance technology for real time respiratory motion monitoring, Sensors and Actuators A 265, 120 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f1ebef3a76dea2956522c1caf5be7bcb.jpg)
Figure 1. Breathing patterns of a tested subject at three different stages; Stage 1: breath holding, Stage 2: breath releasing, and Stage 3: normal breathing. A detailed analysis of the complex breathing stages provides valuable information on the patient's health status.

 A Novel Magnetic Respiratory Sensor for Real-Time Tracking of Coronavirus Progress 

Implementing magnetophoresis in microsystems inspired vivid interest in biomedical applications as it meets a need for trapping and separation methods enabling specific and continuous isolation of biological objects for further analysis. Magnetophoresis, referring to the motion of an object in a magnetic field gradient, is a highly selective and versatile sorting method and, contrary to concurrent methods such as immunoaffinity or dielectrophoresis, it doesn’t depend on the medium properties (pH, temperature, ionic strength...). Downscaling the size of the magnetic flux source considerably increases the generated magnetic field gradients generated [1], but inevitably reduces the interaction distance. Therefore integrating micrometric magnetic structures, within a microfluidic system is the best compromise, while offering portable and compact systems. Permanent micro-magnets generate their own stray magnetic field and gradient at remanence state, leading to autonomous systems. However, the fabrication of microscale permanent magnets by conventional thin-film techniques requires a precise control over the shape, size and material microstructure and involves complex and expensive processes. In addition, their implementation in polymer-based devices brings up heterogeneous integration issues. To overcome this technological challenge, we present a simple fabrication process based on NdFeB particle self-ordering in a polymer matrix. The NdFeB@polydimethylsiloxane (PDMS) microstructure was simulated on Comsol® to determine the generated magnetic forces. The calculations were consistent with colloidal probe atomic force microscopy (AFM) measurements and showed magnetic forces up to few nN at contact. In particular, we showed that enhanced magnetic forces could be achieved at large distance by adding an external permanent magnet (25x8x2 mm3). Finally, the micro-magnets were integrated at the bottom of a microfluidic channel and efficient magnetic bead trapping was demonstrated thanks to the beneficial effect of two-scale permanent magnets. The integrated permanent micro-magnet array inside a polymer membrane was obtained using a previously described method [2]. The principle rests on an organized agglomeration of magnetic powder inside a polymer matrix by submitting the composite to an external magnetic field pattern during the polymer reticulation. NdFeB particles organize in chain-like agglomerates characterized by a diameter of 5 µm, a length of 75 µm and an areal density of 1500 agglomerates/mm2. The composite membrane was then sealed to a microfluidic channel by O2 plasma bonding. In addition, magnetic force measurements were conducted by colloidal probe AFM to assess magnetic performances of the permanent micro-magnets. Finally, magnetophoretic trapping ability of the micro-magnets, acting as micro-traps, was demonstrated with 12-µm superparamagnetic beads at increasing flow rates (0.5-4 mL/h). In particular, we investigated the effect of adding an external permanent magnet (25x8x2 mm3) at the bottom of the micro-traps on the system magnetic performances. Magnetic field gradients generated by the NdFeB agglomerates were estimated from numerical simulations (Comsol Multiphysics®) and the effect of an external permanent magnet was studied. As illustrated in Figure 1-A, micro-traps alone generate magnetic gradients as high as 105 T/m at contact, 104 times higher than the gradients produced by the external magnet alone, whereas the external magnet permits to reach higher magnetic gradient values for larger distances from the traps (20 µm). These observations were confirmed by colloidal probe AFM measurements. As shown in Figure 1-B, magnetic forces generated by the micro-magnet at contact are comprised between 0.5 and 2 nN, while adding an external magnet permits to widen the force range to 4 nN, which surpasses forces of several pN usually encountered in microfluidic devices. Finally, the micro-traps were integrated in a microfluidic channel and successful capture of superparamagnetic beads was achieved. Trapping efficiency measurements as a function of flow rate are depicted in Figure 1-C. At 1 mL/h, trapping efficiency reached 75% with the micro-traps and the additional external magnet, while it was 50% and 35%, with the micro-traps alone and the magnet alone, respectively. Results demonstrate the benefit of combining micrometer-scale and millimeter-scale permanent magnets to enhance magnetic performances. Indeed, the high magnetic force range of the external magnet attracts beads located in the upper part of the channel while the high localized gradients generated by the micro-traps lead to their trapping. We have presented a low-cost and easy-to-handle fabrication process to integrate large density arrays of permanent micro-magnets in a microfluidic system. In particular, we highlighted the beneficial effect of combining two-scale magnetic sources as strong magnetic field gradients are produced by the micro-magnets and large magnetic force ranges are obtained with an additional external magnet. This novel approach could lead to autonomous and compact magnetophoretic trapping devices.

**References:**

 [1] O. Cugat, J. Delamare, and G. Reyne, IEEE Trans. on Magn. 39, 3607-3612 (2003). [2] L. Descamps, S. Mekkaoui, M.-C. Audry, A.-L. Deman and D. Le Roy, , AIP Adv., 10, 015215 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b59a4d294c084f06bca90f3d7475c6d6.jpg)

 High magnetic sorting efficiency in a microfluidic device

* Corresponding Author: ozan.akdogan@eng.bau.edu.tr Magnetically actuated milli swimmers/robots, especially in biomedical field, are used in many applications such as cargo delivery and sensing applications. In this study, magnetically actuated small-scale swimmers have been developed by using Fe flakes embedded in photocurable polymeric resin. Our future aim will be to merge the developed small-scale swimmers with minimally invasive biomedical applications. The 3D printed structures were fabricated using a photocurable polymeric resin acquired from Wanhao (China). In addition to monomers and oligomers, the chemical composition of this resin includes a photo initiator that responds to a certain wavelength of UV light (405nm) to change the polymerization conformation of the resin into a solid state. Then, structures were printed by using the Anycubic Photon digital light processing (DLP) 3D printer with an exposure time of 10 seconds and a layer thickness of 0.05 mm. Different sizes and shapes of (length of the ship1, ship2 and square, 5.6 mm, 2.7 mm and 0.6mm, respectively) the magnetically actuated swimmers were 3D printed; two ellipsoid shaped swimmers with different sizes and a cubic shaped swimmer. An ellipsoid and cubic shape were chosen for its unique morphology that gives it hydrodynamic superiority over traditional spheres [1]. The combination of polymeric materials such as resins with magnetic particles expand the robot’s functionality [2]. The Fe flakes have been previously tested with functional polymer composites for extrusion-based 3D printing [3]. In this study, Fe flakes (100-200nm thickness and ~10μm lateral size) were incorporated into the photocurable resin to actuate robots in response to the magnetic field. The X-Ray Diffraction and vibrating sample magnetometer analysis of Fe flakes showed that Fe flakes have BCC crystal symmetry and soft ferromagnetic response, respectively. (Fig 1a and b). A 0.2 g of Fe flakes and 40 ml of the polymeric resin were mixed to synthesize 0.5% wt/vol concentration. The printed structures were cured by UV light exposure. The incorporated Fe flakes were visualized by a light microscope (Fig.1c, d and e). The movement characteristics of the swimmers in a magnetic field gradient were tested by a homemade electromagnetic setup with a maximum field of 336 Gauss. The 3D printed magnetic structures’ movement speed in DI water were calculated experimentally as 12.27±1.89 mm/s, 11.92±1.9mm/s and 8.29±1.5mm/s for milli ship1, milli ship 2 and sub-mm square, respectively. The theoretical swimming speed values were calculated according to the equations below; the magnetic force acting on the robots by a gradient, in which m and B are the magnetic moment and the field, respectively (3) and the drag force (Stoke’s Law), in which, η, the viscosity of DI water (8.9x10-4 Pa.s), R and v are the hydrodynamic radius and velocity of the objects, respectively (4). Fm = ▽ (m . B) [3] Fd= 6π η R v [4] Theoretical speeds calculated for milli ship1, milli ship2 and sub-mm square were 13.54 mm/s, 9.9 mm/s and 10 mm/s, respectively. The different shaped milli swimmers were actuated by electromagnetic system and tracked (Fig.2). Magneto-responsive robots movement abilities will be tested against specific obstacles with different shapes and magnetic materials as well. Acknowledgements This work was supported by BAP.2019-03.11(Bahcesehir University).

**References:**

1. Carrasco, B. et al., Hydrodynamic Properties of Rigid Particles: Comparison of Different Modeling and Computational Procedures., Biophysical Journal, 76, 3044–3057, (1999) 2.Song, S. W., Jeong, Y. & Kwon, S., Photocurable polymer nanocomposites for magnetic, optical, and biological applications., IEEE J. Sel. Top. Quantum Electron. 21, 324–335, (2015) 3.Zirhli, O. et al. Fabrication and Characterization of Fe16N2 Micro-Flake Powders and Their Extrusion-Based 3D Printing into Permanent Magnet Form., Adv. Eng. Mater. 22, (2020) 4. Pankhurst, Q. A. et al., Applications of magnetic nanoparticles in biomedicine., J. Phys. D. Appl. Phys. 36, 167-181, (2003) 5. L.D. Landau, I.Akhiezer, M.Lifshitz, Chapter XV-Viscosity, General Physics, 341-366, (1967)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fcd27136415135330892ad5e005270ef.png)
Figure 1. a) VSM and b) XRD analysis of Fe flakes given. Light microscopy image of Fe flakes nanoparticle distribution 3D-printed structures c) Milli square. d) Milli ship. e) Texture of printed structures.

![](https://assets.underline.io/uploads/markdown_image/1/image/66e69fa67a75757fe051df0e36d11fd7.jpg)
Figure2. The swimming pathway of structures in the DI water are shown in the figure respectively. a) Square, b) Ship 1 and c) Ship 2 (0.6 mm 5.6 mm, 2.7 mm, respectively). d) The swimming trajectory snapshots of robots under the magnetic field.

 Development and characterization of magnetically actuated milli-robots by Stereolithography

Magnetic fluid sealing is a high-performance sealing technique compared to traditional sealing methods, but is limited to a few working conditions. Here we present a novel sealing method using nano-micron magnetic powders as sealing medium. Nano and micron-sized magnetic particles of different materials and size distribution were prepared and mixed. Packing process of magnetic particles was simulated by DEM. Leakage rate was calculated by Darcy’s Law. Finally, the static sealing experiment showed a high pressure resistance and a rather low leakage rate of this novel sealing method. 1. Introduction Sealing with magnetic fluids has been a commonly used high-performance sealing technique with its unique advantages like low friction torque, no leakage and long lifetime. However, it is not capable of resisting high pressure difference or working under extreme temperatures. Magnetic powders are mixture of nano- and micron-sized particles which can be magnetized by an external magnetic field. This research prepared nano-micron magnetic powders of great magnetic and rheological properties. Then the packing process of magnetic powders was simulated and leakage rate was calculated. A static sealing device was designed to test the sealing behavior of this novel sealing method. 2. Methods 2.1 Preparation of magnetic powders Chemical precipitation was used to prepared magnetic nanoparticles. Experimental conditions were adjusted to acquire nanoparticles of different materials, sizes and magnetic intensity. Micron particles were prepared by high-energy ball milling method. Surfactants were coated on particles to control the interparticle forces. 2.2 Simulation of packing process Interparticle forces of magnetic particles are complex and so is the packing process of magnetic powders. In this research, packing process of nano-micron magnetic powders was simulated by DEM using Hertzian-Mindlin model with JKR. Fraction, sizes, magnetization and surfactants of powder preparation, leads to changes of interparticle forces, especially cohesive and magnetic forces. Magnetic particles follow the basic equation: midvi(t)/dt = mig + Fid(t) + Fic(t) + Fim(t) vi(t) is the ith particle's velocity at time t; Fid(t), Fic(t), Fim(t) are the total drag force, net contact force and magnetic force of the ith particle, respectively. 2.3 Calculation of leakage rate by Darcy's Law Darcy's law is commonly used to describe the flow of a fluid through a porous medium. We established a microscopic model to estimate the permeability for calculation of leakage rate of the sealing device. The permeability κ is calculated by the equation: κ = μÛh / △p μ is the fluid viscosity; Û is the outlet velocity; h is the computational zone height; △p is the pressure difference. 2.4 Design and experiments of static sealing device A static sealing device was designed, where magnetic field distribution was simulated to maximize the magnetic flux density in the sealing gap. For each magnetic powder example, sealing capacity and leakage rate were measured. 2.5 Results The simulation results showed that the permeability decreased rapidly with the decrease of particle sizes, and appropriate mixture of nano- and micron-sized particles further decreased the permeability. For the powders prepared, the permeability could be as low as 5.09E-18 m-2. Considering the size of the sealing device, the calculated leakage rate was 2.22E-9 m3/s. Experiments indicated a sealing capacity ≥ 0.5 MPa and leakage rate ≤ 1E-6 Pa×m3/(s×cm). 3. Discussion By selecting magnetic materials, mixture of particles of different sizes and coating particles with surfactants, nano-micron magnetic powders can possess great magnetic and rheological properties. Proper size distribution and interparticle forces lead to a denser packing of magnetic powders. Further, a denser packing leads to a rather low leakage rate, which is verified by both simulation and sealing experiments. A novel sealing method using nano-micron magnetic powders shows distinctive property and may be a promising sealing technique.

**References:**

[1] J. Kafashan, J. Wiacek and N. Abd Rahman, Granular Matter, Vol. 21, p.80 (2019) [2] R.A. Sperling, W.J. Parak, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 368, p.1333-1383 (2010) [3] M. Neouze, U. Schubert, Monatshefte für Chemie - Chemical Monthly, Vol. 139, p.183-195 (2008) [4] R. Aboul Hosn, L. Sibille and N. Benahmed, Computers and Geotechnics, Vol. 95, p.30-39(2018) [5] K. Chen, Y. Tian and L. Shan, Smart Materials and Structures, Vol. 22, p.97001 (2013)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/dc98b54b36276cc5bab66afb1c8b1a3a.jpg)
Fig.1 Prepared magnetic powders

![](https://assets.underline.io/uploads/markdown_image/1/image/ab3ec5f9c5d8047ad3aa9245e09e70f4.jpg)
Fig.2 A microscopic model to calculate permeability

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