fluids

Article Experimental Study of Sidewall Pressure Induced by Ferroparticles in Fluid under a Pulsating

Or Werner, Asaf Azulay, Boris Mikhailovich and Avi Levy *

Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, 8410501 Beer-Sheva, Israel; [email protected] (O.W.); [email protected] (A.A.); [email protected] (B.M.) * Correspondence: [email protected]

 Received: 13 May 2020; Accepted: 20 June 2020; Published: 22 June 2020 

Abstract: For several decades, magnetic nano- and microparticles have been used in various applications, as they can be attracted and controlled using external magnetic fields. Recently, carbonyl iron microparticles were used in a feasibility study of a new cardiac pacing application. The particles were inserted into a heart, attracted to its sidewall using a pulsating magnetic field, and applied pulsating pressure on its sidewall. The magnitude of the sidewall pressure is a critical parameter for the success and safety of the application, and it was evaluated analytically using a simplified model. In the present study, the behaviour of carbonyl iron microparticles in a water chamber was studied experimentally. Several masses of these particles were attracted to the sidewall of the chamber using an external pulsating magnetic field; the behaviours of the masses of particles, the particle–particle interaction, and the influence of fluid dynamics on them were examined during different periods of pulses. The sidewall pressure during their attraction was measured using an in-house piezoelectric polyvinylidene fluoride sensor. The relations between the measured sidewall pressure and the mass of the particles, their sizes, and the magnetic field exposure time were investigated. The obtained results suggest an asymptotic sidewall pressure value for the specified magnetic field. The measurements of the sidewall pressure are compared with evaluated results from the analytical model, showing that the model over-predicts the sidewall pressure.

Keywords: pulsating magnetic field; ferromagnetic particles; magnetic attraction; polyvinylidene fluoride (PVDF) sensor

1. Introduction Suspensions of ferromagnetic particles have been used in research and applications, as they can be attracted and controlled by external magnetic fields. Two primary medical applications being investigated currently are the elimination of tumours with local hyperthermia and drug delivery [1]. Ferromagnetic particles are also used in mechanical applications such as dumpers and film bearings [2,3], as well as in magnetic field sensors [4]. Another mechanical use of suspended magnetic particles is as a heat transfer medium [5,6]. Recently, the feasibility study of a new medical application was presented: leadless cardiac pacing [7]. In this application, ferromagnetic particles are injected into the vascular system and maintained in the right ventricle using an external (DC) electromagnetic field. Subsequently, electromagnetic pulses are applied to the heart to attract the particles to the sidewall of the heart and to release them. During their attraction, the particles apply pressure on the sidewall, thus stimulating the heart muscle and provoking pacing. The above study focuses on the functioning

Fluids 2020, 5, 98; doi:10.3390/fluids5020098 www.mdpi.com/journal/fluids Fluids 2020, 5, 98 2 of 15 of the heart when the pulses are applied, while the behaviour of the particles is outside the scope of the study. The pressure that the particles apply on the sidewall, a critical parameter for the success and safety of the above application, was not measured. In order to successfully provoke cardio pacing, a local pressure as low as 2 kPa is required. However, controlling the pressure is crucial, since impacts that exceed 250 kPa can cause tissue ∼ damage [7,8]. The sidewall pressure in Reference [7] was evaluated to be 146 kPa for a given magnetic field and gradient of 0.4 T and 64 T/m. This pressure was evaluated using a simplified model, ∼ which relied on two main assumptions. The first is that the of the particles is at saturation, which for the specified magnetic field is in line with results from Reference [9]. The second assumption is that the aggregation of particles may be modelled as a solid body, a sphere with 1 mm radius and a uniform magnetization. Two parameters discussed in Reference [7], which may influence the sidewall pressure, are the diameter of the particles and the duty cycle of the electromagnetic pulse. However, the influence of these parameters on the aggregation of particles and thereby on the sidewall pressure has not been discussed. In the current work, the influence of these two parameters on the sidewall pressure is investigated. In several studies, a magnetic field was used to attract suspended particles. In Reference [10], a planar coil was used to accumulate suspended ferromagnetic particles on a microelectromechanical systems (MEMS) sensor, as a device to detect the appearance of ferromagnetic particles in liquid. In Reference [11], a high-gradient magnetic separation technique was used to capture weakly magnetic mineral particles. In three studies [12–14], the percentage of attracted particles was measured in order to rate the success of the attraction. However, the behaviour of the particles during the attraction was not investigated in the studies presented above. The behaviour of particles in a colloidal suspension called ferrofluid was investigated in References [15,16]. The ferrofluid was injected into a horizontal cell filled with colloidal silica and subsequently attracted to a sidewall using a magnetic field. In these studies, the particles did not settle because of the design of the experimental setup. In addition, an experimental method for measuring the pressure that ferrofluids apply on the sidewall was presented. The disadvantage of this method is that it is designed for static measurements of pressure and may not be suitable for dynamic measurements. The response of ferrofluid flow to various configurations of a steady magnetic field is discussed in Reference [17]. The accumulation of ferrofluids, after it was attracted to the sidewall of a horizontal pipeline, is presented in References [18–20]; a similar accumulation of larger particles in a vertical pipeline is presented in Reference [21]. The pressure that the particles apply on the sidewall was not measured in those works, and the magnetic field was constant during the experiments. In addition to the experimental investigations above, several numerical models were used to compute the attraction of particles in fluids [15,18,19,22–24]. These models did not include particle-particle interaction, and they were validated qualitatively, or not at all. A model that included particle-particle interaction is presented in Reference [21], but the in-phase magnetic interaction was not included. Experimental and numerical studies described earlier did not report the measurement of pressure that magnetic particles apply on a sidewall, under the effect of a magnetic field. In addition, the behaviour of the particles near the sidewall in a pulsating magnetic field was not investigated. Therefore, those two subjects are investigated in the current study. To study the behaviour of the particles in a pulsating field an experiment was performed, and the pressure the particles applied on the sidewall during the experiment was measured. This study is intended to explain the dependence of the sidewall pressure on three primary parameters: the amount of the particles involved, their sizes, and the duty cycle of the pulsating magnetic field, at a given frequency in the study. The particles used for this study are the same particles as in Reference [7] (US5004, US Research Nanomaterials, Inc., Houston, TX, USA), and evaluated results from a simplified model are compared with recent experimental results. FluidsFluids 20202020,, 5,, x 98 33 of of 15 15

2. Experimental 2. Experimental To focus on the behaviour of the particles in a pulsating , the experiment To focus on the behaviour of the particles in a pulsating electromagnetic field, the experiment was was performed in a neutral system: a system that eliminates factors that could affect the particles, performed in a neutral system: a system that eliminates factors that could affect the particles, such as such as moving walls and induced flow. In the experiment, suspended particles were attracted to a moving walls and induced flow. In the experiment, suspended particles were attracted to a sidewall sidewall using a pulsating magnetic field. The behaviour of the particles was qualitatively analysed using a pulsating magnetic field. The behaviour of the particles was qualitatively analysed using video using video records of 50 frames/s (CamRecord 1000, Optronis, Kehl, Germany). In addition, the records of 50 frames/s (CamRecord 1000, Optronis, Kehl, Germany). In addition, the pressure that the pressure that the particles applied on the sidewall during their attraction was measured, using an in- particles applied on the sidewall during their attraction was measured, using an in-house piezoelectric house piezoelectric pressure sensor. pressure sensor.

2.1.2.1. Experimental Experimental Setup Setup An illustration of the experimental system is presented in Figure 1. The primary part of the An illustration of the experimental system is presented in Figure1. The primary part of the system is the experimental chamber, of internal dimensions 76 mm × 76 mm × 200 mm . It system is the experimental chamber, of internal dimensions 76 mm 76 mm 200 mm. It contains contains acrylic glass windows from all sides to enable a clear video recording× × of the experiment. In acrylic glass windows from all sides to enable a clear video recording of the experiment. In one of the one of the windows, a pressure sensor was inserted, 10 cm from the bottom of the chamber. An windows, a pressure sensor was inserted, 10 cm from the bottom of the chamber. An electromagnet was electromagnet was positioned behind the sensor from outside of the chamber to attract the particles positioned behind the sensor from outside of the chamber to attract the particles in the chamber toward in the chamber toward the sensor. The electromagnet was contributed to this research after it was the sensor. The electromagnet was contributed to this research after it was used in another work, used in another work, of which its details are presented in Reference [7]. Briefly, it contains 900 of which its details are presented in Reference [7]. Briefly, it contains 900 windings on a permendur core windings on a permendur core of 40 mm diameter, and the core ends with a tip of 5 mm diameter, of 40 mm diameter, and the core ends with a tip of 5 mm diameter, to increase the magnetic field and its to increase the magnetic field and its gradient [25]. An iron cylindrical bar was inserted in the gradient [25]. An iron cylindrical bar was inserted in the window, between the electromagnet and the window, between the electromagnet and the sensor. The bar touches the tip from one side, and ends sensor. The bar touches the tip from one side, and ends 3 mm from the inner sidewall on the other side. 3 mm from the inner sidewall on the other side. This arrangement increases the magnetic field near This arrangement increases the magnetic field near the sidewall, especially where the sensor is located. the sidewall, especially where the sensor is located. The magnetic field in the experimental system, The magnetic field in the experimental system, induced with current of 20 A, is presented in Figure2; induced with current of 20 A, is presented in Figure 2; the magnetic field as a function of the distance the magnetic field as a function of the distance from the sensor is presented in Figure2a, and the from the sensor is presented in Figure 2a, and the time-varying magnetic field during a pulse is time-varying magnetic field during a pulse is presented in Figure2b. The time-varying magnetic field, presented in Figure 2b. The time-varying magnetic field, as well as time-varying sidewall pressure as well as time-varying sidewall pressure presented in the following section, was processed with a presented in the following section, was processed with a low-pass filter with a cutoff frequency of low-pass filter with a cutoff frequency of 50 Hz (the frequency of the power grid). 50 Hz (the frequency of the power grid).

FigureFigure 1. IllustrationIllustration of of experimental experimental system system.. Fluids 2020, 5, x 4 of 15 Fluids 2020, 5, 98 4 of 15

Figure 2. Characterization of the electromagnetic field. (a)—Electromagnetic field and its gradient, Figureagainst 2. distance Characterizatio from then inner of the wall. electromagnetic (b)—The pulse field. of the(a) electromagnetic– Electromagnetic field field varies and in its time. gradient, against distance from the inner wall. (b) – The pulse of the electromagnetic field varies in time. 2.2. Electrical Instrumentation 2.2. Electrical Instrumentation The magnetic field in the current study was induced by an electromagnet, connected to a programmableThe magnetic DC field power in supplythe current (Gen 60-25,study TDK-Lambda,was induced by Karmiel, an electromagnet Israel) in the, connected ‘current mode’, to a programmablein which a DC signalpower providedsupply (Gen to the 60- power25, TDK supply-Lambda controls, Karmiel, the current. Israel) in The the provided ‘current signalmode’, was in whichin the shapea voltage of pulsessignal ofprovided a positive to stepthe power function. supply The pulsescontrol weres the characterisedcurrent. The provided by three parameters:signal was inthe the magnitude shape of pulses of the current,of a positive frequency, step function and duty. The cycle pulses of the were pulses. characterised The duty cycle by three is the parameters: percentage theof timemagnitude in which of the the current, step function frequency is positive, and duty and cycle not zero.of the Those pulses three. The parametersduty cycle is were the percentage controlled ofwith time a PCin which using athe LabVIEW step function (National is positive Instruments, and not Austin, zero. TX,Those USA) three application parameters that were was controlled written for withthis purpose.a PC using The a LabVIEW current in ( theNational electromagnet Instruments, was indicatedAustin, TX, by USA) the power application supply that and was was written read in forthe this application. purpose. The current in the electromagnet was indicated by the power supply and was read in theTo application. transform the from the piezoelectric sensor to a readable voltage signal, a chargeTo amplifiertransform (504D, the electric Kistler, charge Winterthur, from Switzerland)the piezoelectric was used.sensor It wasto a operatedreadable in voltage the ‘long’ signal, mode, a chargein which amplifier the charge (504D, amplifier Kistler performed, Winterthur, as an Switzerland integrator.) Thewas time used constant. It was operated of the amplifier in the in‘long’ this mode,mode wasin which found the to becharge suffi cientlyamplifier long performed for the quasi-static as an integrator. measurements The time in theconstant study. of The the signal amplifier from inthe this charge mode amplifier was found was to also be sufficiently read in the LabVIEWlong for the application, quasi-static which measurements used a total in amount the study of. threeThe signalchannels. from The the data charge acquisition amplifier was was performed also read with in a the rate LabVIEW of 1000 samples application/s, using, which a PCI use deviced a total (NI amountPCI-6035E, of three National channels Instruments,. The data Austin, acquisition TX, USA). was performed with a rate of 1000 samples/s, using a PCI device (NI PCI-6035E, National Instruments, Austin, TX, USA). 2.3. The In-House Pressure Sensor 2.3. TheThe In pressure-House Pressure that the Sensor particles apply on a surface can be measured with a pressure sensor [26,27]. However,The pressure studies that in which the particles sidewall apply pressure on a wassurface measured can be inmeasured a time-varying with a pressure magnetic sen fieldsor were [26,27] not. However,found. A solutionstudies in to which eliminate sidewall the influence pressure ofwas the measured magnetic in field a time on the-varying measurement magnetic is field presented were notin Referencefound. A solution [15], but to it eliminate may not bethe suitable influence for of the the dynamic magnetic measurements field on the measurement of pressure. is In presented addition into Reference the magnetic [15] field, but restriction,it may not abe geometrical suitable for restriction the dynamic exists measurements as well: the thicknessof pressure. of theIn addition pressure tosensor the magnetic must not field exceed restriction, a few millimetres. a geometrical Otherwise, restriction the exists distance as well: between the thethickness electromagnet of the pressure and the sensorparticles must would not beexceed large, a and few the millimetres. magnetic field Otherwise, would not the be distance sufficiently between strong the near electromagnet the wall. Because and theof thoseparticles considerations, would be large, an in-house and the pressuremagnetic sensor field would was developed; not be sufficiently it is thin, strong and not near significantly the wall. Becauseaffected byof thethose magnetic considerations, field, as discussed an in-house below pressure in Section sensor 2.4 .was developed; it is thin, and not significantlyThe active affected part ofby the the sensor magnetic is a diaphragmfield, as discusse that stretchedd below in when Section a relative 2.4. pressure is applied to it; theThe diaphragm active part made of the from sensor piezoelectric is a diaphragm polyvinylidene that stretched fluoride when (PVDF) a relative film pressure of 28 µm is(1-1003702-7, applied to it;Measurement the diaphragm Specialties made from Inc., piezoelectric Berwyn, PA, polyvinylidene USA). Wired ringed-shape fluoride (PVDF) copper film tape of 28 was μm glued (1-1003702 on each- 7,side Measurement of the PVDF Specialties using a conductive Inc., Berwyn, adhesive PA, USA (see). W Figureired 3ringeda). It- isshape noteworthy copper tape that was the thicknessglued on eachshown side in of the the figure PVDF is using out of a proportion,conductive adhesive so it can be(see noticed Figure easily3a). It inis noteworthy the scheme. that The the wired thickness PVDF shown in the figure is out of proportion, so it can be noticed easily in the scheme. The wired PVDF Fluids 2020, 5, 98 5 of 15

FluidsFluids 20202020,, 55,, xx 55 ofof 1515 unit was glued with epoxy to a solid back, which was the sensor housing. A hole of 10 mm diameter PVDF unit was glued with epoxy to a solid back, which was the sensor housing. A hole of 10 mm wasPVDF made unit in was the glued middle with of theepoxy housing to a solid such back, that thewhich PVDF was could the sensor be deformed housing. when A hole pressure of 10 wasmm diameter was made in the middle of the housing such that the PVDF could be deformed when applied.diameter The was sensor made had in theto be middle protected of the completely housing from such water that the leaks. PVDF Therefore, could bethe deformed window where when pressure was applied. The sensor had to be protected completely from water leaks. Therefore, the thepressure sensor was was applied. inserted The was sensor covered had with to be nylon. protected Prior completely to that, silicone from greasewater wasleaks. smeared Therefore, on thethe window where the sensor was inserted was covered with nylon. Prior to that, silicone grease was PVDFwindow to preventwhere the an airsensor gap was between inserted the PVDFwas covered and nylon. with nylon. Prior to that, silicone grease was smearedsmeared onon thethe PVDFPVDF toto preventprevent anan airair gapgap betweenbetween thethe PVDF and nylon.

FigureFigure 3. 3.The The in-house iin--house pressure pressure sensor. sensor. (a )(( Illustrationaa)) IllustrationIllustration of the ofof the wiredthe wiredwired polyvinylidene polyvinylidene fluoride fluoride PVDF PVDF unit; (unitb) drawing;; ((b)) drawingrawing of the ofof sensor thethe sensorsensor and the andand housing. thethe housing.housing. The sensor was calibrated in the experimental chamber using increasing hydrostatic pressure. The sensor was calibrated in the experimental chamber using increasing hydrostatic pressure. Initially, the chamber was filled with water to the same height as in the experiment. Subsequently, Initially,Initially, thethe chamberchamber waswas filledfilled withwith waterwater toto thethe samesame heightheight asas inin thethe experiment.experiment. Subsequently,Subsequently, the pressure in the chamber was increased to a desired level, each time from the same initial pressure. thethe pressurepressure inin thethe chamberchamber waswas increasedincreased toto aa desireddesired level,level, eeach time from the same initial pressure. The duration until the pressure reached the desired level was approximately 1.5 s. The pressure increase The duration until the pressure reached the desired level was approximately 1..5 ss.. The pressure was measured with a pressure calibrator (Presscal Pressure Calibrator PC105, Beamex, Pietarsaari, increaseincrease was measured with a pressure calibrator (Presscal Pressure Calibrator PC105, Beamex,, Finland), and compared with the signal difference from the charge amplifier. The calibration was Pietarsaari, Finland),), an and compared with the signal difference from the charge amplifier. The performed after every replacement of the nylon cover. A typical calibration curve is presented calibrationcalibration was performed after every replacement of the nylon cover. A typical calibration curve is in Figure4. presented in Figure 4. ] ] a a P P k [ k

[

e e r r u u s s s s e e r r P P

Figure 4. Calibration results with linear fitting. Figure 4. Calibration results with linear fitting. 2.4. Measurement Errors 2.4. Measurementrement Errors The sensor exhibits three types of measurement errors. The significant one is the calibration error, The sensor exhibits three types of measurement errors. The significant one is the calibration definedThe as sensor a linearity-repeatability exhibits three types error. of measurement It is the maximum errors. absolute The significant error between one is the the calibration calibration error, defined as a linearity-repeatability error. It is the maximum absolute error between the measurementserror, defined and as the a linearity linear curve.-repeatability The largest error. calibration It is the error maximum is 0.1 kPa , absolute which is 3% errorof the between full-scale the calibrationcalibration measurementsmeasurements andand thethe linearlinear curve.curve. TheThe largestlargest calibrationcalibration errorerror isis 0..1 kPa,, whichwhich isis 3% of thethe fullfull--scalescale output.output. TheThe secondsecond ererrorror isis thethe influenceinfluence ofof thethe magneticmagnetic field.field. ToTo evaluateevaluate thisthis error,error, a magnetic pulse was applied on the sensor while the hydrostatic pressure was maintained constantconstant.. Fluids 2020, 5, 98 6 of 15 output. The second error is the influence of the magnetic field. To evaluate this error, a magnetic pulse was applied on the sensor while the hydrostatic pressure was maintained constant. The largest influence of the magnetic field on the sensor was equivalent to a pressure of 0.06 kPa. The third error is drifting, meaning that the measured signal from the charge amplifier was drifting slowly to saturation, even when the pressure was constant. The drifting was measured over a long duration while no additional pressure was applied on the sensor, and it was linear in general. The error was calculated as the drift per measurement time in the experiment, and the largest value was equivalent to a pressure of 0.05 kPa.

2.5. Preparation of Particle Suspension The particles used in the current experiment were iron carbonyl powder, of diameters 8 µm and 1 µm (US5004, US Research Nanomaterials, Inc.), as in Reference [7]. The particles were weighted to the desired amount in 50 mL test tubes. Each test tube with particles was filled with 4 mL of phosphate-buffered saline solution and subsequently mixed to create a suspension. The suspension was drawn with a syringe, and was subsequently ready to be injected into the experimental chamber. The syringes used were 10 mL ones, with a 1.20 mm 38 mm needle. × 2.6. Experimental Method The experiment was performed with different amounts of suspended particles (25, 50, 75, 100, 200 2 mg). The experimental procedure was as follows: the suspensions were injected into the ± experimental chamber from a distance of 1–2 cm from the centre of the pressure sensor; during the injection, the electromagnetic field was maintained steady using a 20 A current to attract the particles in the required location. Subsequently, 1 Hz pulses were applied using a positive step function of 20 A; The first 20 pulses were with 50% duty cycle, and then the duty cycle was gradually reduced by 10% every 3 pulses. Before every injection, the experimental chamber was cleaned to remove the old particles. During the preparation of the particles to injection, some particles were not drawn or stuck in the syringe, and therefore were lost and not injected. For consistency, all the results of the experiment were referred to by the initial amount of particles that were weighted instead of the injected amount of the particles.

3. Results and Discussions The general behaviour of the particles was investigated using video records of the experiment, which is separated into three stages. The first stage is when the particles are in the presence of a steady magnetic field. The behaviour of the particles in this stage is compared with particles from previous works. The second and third stages are when the field is turned off and on, similar to a pulsating field. Along with the qualitative investigation, the pressure that the particles apply on the sidewall was measured during the pulses. The measurements were used to investigate the influence of three parameters on the sidewall pressure: the amount of the particles, duty cycle, and size of the particles.

3.1. Behaviour of Particles in Steady Magnetic Field When the particles in the experiment were subjected to a magnetic field, they no longer behaved as a suspension of powder. Instead, the particles created long structures, which will be referred to as chains (see Figure5a). This behaviour is unlike to that reported by Ganguly [ 18–20], in which chains were not created in the core region (marked as C in Figure5c). The absence of the chains in References [18–20] is due to the small size of the coated particles used (10 nm). The chain structures were observed in the results of Balakin [21] for particles with an average size of 100 µm (see Figure5b). ∼ The chains that occur are due to the dominant particle–particle interaction. This interaction is both magnetic and mechanical: the particles are attracted to each other owing to magnetic force; in addition, the particles induce mechanical friction when they are in contact with other particles. The friction Fluids 2020, 5, 98 7 of 15 could explain how the chains are held horizontally, despite the gravity/buoyancy force. The chains in the current study do not break because the shear stress is not sufficiently strong, owing to the Fluids 2020, 5, x 7 of 15 absence of flow [28,29]. The relation between the particle–particle attraction and the friction force can bethe explained absence of by flow the static[28,29] friction. The relation model, between based on the Amontons–Coulomb particle–particle attraction friction and low: the friction force can be explained by the static friction model, based on Amontons – Coulomb friction low: F = µs N (1) f ,max · , = ∙ (1) Here, µs is the friction coefficient for the particles, and N is the normal force between the particles. Here, is the friction coefficient for the particles, and is the normal force between the The normal force depends on the magnetic attraction of the particles, and it is stronger when closer to particles. The normal force depends on the magnetic attraction of the particles, and it is stronger when the sidewall. closer to the sidewall.

FigureFigure 5.5. ObservationObservation ofof bulkbulk ofof particles.particles. ((aa)—Particles) – Particles inin thethe presentpresent work.work. ((bb)—Experiment) – Experiment fromfrom ReferenceReference [[18]18].. ((cc)—Experiment) – Experiment fromfrom ReferenceReference [[21]21]..

3.2.3.2. BehaviourBehaviour ofof ParticlesParticles inin aa PulsatingPulsating ElectromagneticElectromagnetic FieldField TheThe partpart inin whichwhich thethe magneticmagnetic fieldfield waswas turnedturned ooffff waswas notnot includedincluded inin previousprevious studies;studies; inin thethe currentcurrent study,study, itit occursoccurs betweenbetween pulses.pulses. InIn thethe absenceabsence ofof aa magneticmagnetic field,field, thethe particlesparticles areare expectedexpected toto detachdetach fromfrom thethe wallwall andand settle.settle. TheThe finalfinal positionposition ofof threethree settledsettled bulksbulks ofof particlesparticles withwith didiffefferentrent amountsamounts isis presented presented in in Figure Figure6, 0.56, 0s.5after s after the fieldthe field was turnedwas turned off, immediately off, immediately before itbefore was turnedit was onturned again. on It again. appears It appears that part that of each part bulkof each did bulk notsettle did not and settle remained and remained attached toattached the wall. to Thethe wall. part thatThe didpart not that settle did not is referred settle is toreferred as “stable to as mass,” “stable and mass, the” partand thatthe part settled that as settled “unstable as “unstable mass.” mass.” TheThe stablestable massmass diddid notnot settlesettle becausebecause itit waswas heldheld byby thethe residualresidual magneticmagnetic fieldfield ofof bothboth thethe corecore ofof thethe electromagnetelectromagnet andand thethe particles;particles; measurementsmeasurements ofof thethe magneticmagnetic field,field, presentedpresented in FigureFigure2 2bb,, showsshows thatthat thethe electromagnetelectromagnet has remanence of 0.0040.004T T;; as as can can be be seen seen in in Figure Figure6 ,6 settling, settling particles particles werewere maintainedmaintained inin structuresstructures eveneven whenwhen theythey werewere farfar fromfrom thethe electromagnetelectromagnet duedue toto theirtheir ownown hysteresis.hysteresis. BecauseBecause ofof thethe hysteresis,hysteresis, thethe particlesparticles inin thethe stablestable massmass werewere stillstill attractedattracted toto thethe corecore ofof thethe electromagnetelectromagnet and and to to each each other, other, even even while while the the current current was was turned turned off. Theoff. sizeThe ofsize the of stable the stable mass dependsmass depends on the on location the location where thewhere magnetic the magnetic force is tooforce weak is too and weak the friction and the could friction not could hold any not more hold particles.any more Becauseparticles the. Because stable the mass stable depends mass depends completely completely on the hysteresis, on the hysteresis, it doesnot it does depend not depend on the initialon the amount initial amount of the particles. of the particles. Hence, theHence, stable the mass stable should mass beshould the same be the for same all the for amounts, all the amount as longs, asas thelong initial as the injected initial injected amount amount is greater is thangreater that than of thethat stable of the mass. stable This mass. statement This statement was tested was intested the experimentin the experiment when thewhen duty the cycle duty of cycle the electromagneticof the electromagnetic field was field gradually was gradually reduced reduced from 50% fromto 10%50%. Theto 10% results. The are results discussed are discussed in detailhereinafter. in detail hereinafter. Figure 6 shows that the greater the amount of the particles, the farther that the unstable mass settles; this observation is attributable to the cluster behaviour of the unstable mass in a viscous medium. The normalised gravity/buoyancy force, per amount of particles, is equal for all the amounts. However, the larger amounts create larger clusters, on which the normalised drag force is Fluids 2020, 5, 98 8 of 15

Figure6 shows that the greater the amount of the particles, the farther that the unstable mass settles; this observation is attributable to the cluster behaviour of the unstable mass in a viscous medium. The normalised gravity/buoyancy force, per amount of particles, is equal for all the amounts. FluidsFluids 20 202020, 5, ,5 x, x 8 8of of 15 15 However, the larger amounts create larger clusters, on which the normalised drag force is weaker. weaker.Therefore,weaker. Therefore, Therefore, in the balance i nin the the betweenbalance balance between thebetween gravity the the/buoyancy gravity/buoyancy gravity/buoyancy force and force force drag and force,and drag drag the force, dragforce, the force the drag drag becomes force force becomeslessbecomes dominant less less dominant dominant in larger clusters.in in larger larger Hence,clusters. clusters. the Hence, Hence, larger the the unstable larger larger massunstable unstable settles mass mass faster. settl settleses faster. faster.

FigureFigureFigure 6. 6. 6. BulkBulk Bulk of ofof particles particlesparticles of ofof three threethree amounts, amounts, amounts, after after after the the the field field field is is is turned turned turned off o offff for for 0.5 0.5 s s. .s .

WhenWhen the the electromagnetic electromagnetic field fieldfield was was turned turned on onon again, again, the the unstable unstable mass mass was was attracted attracted to toto the the electromagnet.electromagnet. The The bulks bulks of of 50 5050 mg mgmg andand 100 100 mgmg mg,, after,after after theythey they werewere were collectedcollected collected again, again, are are presented presented in in FigureFigure 77 .7. The.The The shapeshape shape ofof of thethe the bulkbulk bulk afterafter after thethe the attractionattraction attraction waswas was notnot not symmetrical,symmetrical, symmetrical, andand and thethe the particlesparticles particles tendedtended tended toto to aggregateaggregate below below the the stable stable mass. mass. This ThisThis is isis reasonable reasonablereasonable because becausebecause at atat a a alower lower position position the the magnetic magnetic force force comprisescomprises a alarger larger ve vertical verticalrtical component. component. When WhenWhen the thethe amount amountamount ofof of the thethe particlesparticles particles was waswas higher, higher,higher, more more particles particles aggregatedaggregated at at at the the the lower lower lower position, position, position, and and and therefore therefore therefore did did not did applynot not apply apply pressure pressure pressure on the on onrequired the the required required location. location. location. Hence, Hence,theHence, sidewall the the sidewall sidewall pressure pressure pressure is assumed is is assumed assumed to have to to an have have asymptote, an an asymptote, asymptote, limiting limiting limiting the possible the the possib possib pressurelele pressure pressure for the for givenfor the the givenelectromagneticgiven electromagnetic electromagnetic field. Thatfield. field. assumption That That assumption assumption was tested was was tested withtested results with with results fromresults subsequentfrom from subsequent subsequent experiments. experiments. experiments.

Figure 7. Shapes of two bulks after they were attracted again. FigureFigure 7. 7. Shape Shapes sof of two two bulks bulks after after they they were were attracted attracted again again. . 3.3. Pressure Measurements 3.3.3.3. Pressure Pressure Measurements Measurements The sidewall pressure applied by the particles was measured during the experiment. Five different amountsTheThe ofsidewall sidewall8 µm particles pressure pressure were applied applied used to by investigateby the the particles particles the influence was was measured measured of the amount during during on the the the experiment.sidewall experiment. pressure, F Fiveive differentduringdifferent pulses amounts amounts of 50% of ofduty 8 8 μμm cycle.m particlesparticles The influence were were used used of the to to dutyinvestigate investigate cycle was the the investigated influence influence of withof the the aamount seriesamount of on pulseson the the sidewallwithsidewall reduced pressure, pressure, duty. during Finally,during pulses pulses the influence of of 50% 50% of dutyduty the cycle. particle cycle. The The size influence influence on the sidewall of of the the duty duty pressure cycle cycle was was was investigated investigated investigated withbywith comparing a aseries series of of thepulses pulses results with with of reduced thereduced8 µm duty. duty.particles Finally, Finally, with the the similar influence influence results of of the the of particle1 particleµm particles. size size on on the Thethe sidewall sidewall typical pressurepressure was was investigated investigated by by comparing comparing the the results results of of the the 88 μμmm particlesparticles with with similar similar results results of of 11 μμmm particles.particles. T Thehe typical typical measured measured sidewall sidewall pressure pressure durin duringg one one pulse pulse of of 50%50% dutyduty cycle cycle is is presentedpresented in in Figure Figure 8 8 for for five five amounts amounts of of 88 μμmm particles.particles. Each Each value value of of the the sidewall sidewall pressure pressure is is relativerelative to to the the value value at at the the beginning beginning of of the the pulse. pulse. For For all all the the amounts, amounts, but but mostly mostly in in 25 25, ,5050, , andand 7575 mgmg casescases, the, the sidewall sidewall pressure pressure when when the the electromagnetic electromagnetic field field is is turned turned on on can can exhibit exhibit a aresponse response toto a astep step function function rather rather than than a nan impulse impulse function. function. Hence, Hence, it it can can be be concluded concluded that that the the effect effect of of the the Fluids 2020, 5, x 9 of 15

particles’ impact is neglected compared to the magnetic force. One reason for the weak impact effect is that the particles were not attracted as a bulk, i.e., as one unit, with one large mass. Instead, they

Fluidswere2020 attracted, 5, 98 as groups that contain a small amount of particles. That is because particles closer9 of 15to the core experienced a stronger magnetic field and therefore attracted faster than farther particles. In addition, the particles were affected by the drag force from the interaction with the fluid, reducing measuredtheir speed sidewall the therefore pressure their during impact. one pulse of 50% duty cycle is presented in Figure8 for five amounts of 8 µm particles. Each value of the sidewall pressure is relative to the value at the beginning ofFluids the 20 pulse.20, 5, x For all the amounts, but mostly in 25, 50, and 75 mg cases, the sidewall pressure when9 of 15 the electromagnetic field is turned on can exhibit a response to a step function rather than an impulse function.particles’ Hence,impact itis can neglected be concluded compared that to the the e ffmagneticect of the force. particles’ One impactreason for is neglected the weak comparedimpact effect to theis th magneticat the particles force. Onewere reason not attracted for the weakas a bulk, impact i.e., eff asect one is thatunit the, with particles one large were mass not. attracted Instead, asthey a bulk,were i.e.,attracted as one as unit, groups with that one largecontain mass. a small Instead, amount they of were particles attracted. That as is groups because that particles contain closer a small to amountthe core of experienced particles. That a stronger is because magnetic particles field closer and therefore to the core attracted experienced faster a than stronger farther magnetic particles. field In andaddition, therefore the attractedparticles fasterwere thanaffected farther by the particles. drag force In addition, from the the interaction particles were with a fftheected fluid by, thereducing drag forcetheir fromspeed the the interaction therefore the withir theimpact. fluid, reducing their speed the therefore their impact.

Figure 8. Pressure results during one pulse for different amounts.

It also appears in Figure 8 that the maximal pressure in 25, 50, and 75 mg cases was achieved after ~0.1 s, which is also the peak time of the electromagnetic field (the time between the beginning and the first peak). In these cases, all or most of the particles were collected near the transducer before the peak time of the electromagnetic field. In the cases of 100 and 200 mg, the sidewall pressure continued to increase after the rise of 0.1 s until the electromagnetic field was turned off. The reason for that can be seen in Figure 9 for the 100 mg case. A significant amount of particles were still collected to the transducer after 0.1 s, while some of the particles were not collected during the Figure 8. Pressure results during one pulse for different amounts. whole magnetic pulse.Figure Thes 8.e Pressure measurements results during of the one pressure pulse for during different one amounts. pulse support a previous analysisIt also in appearsthat larger in Figureamounts8 that of theparticles maximal settle pressure farther in away.25, 50 , and 75 mg cases was achieved after 25, 50 75 mg 0.1 ForsIt, also which the appears amounts is also in the of Figure peak100 and8 time that 200 of the the maximalmg electromagnetic, a longer pressure time in fieldin which (the the time, and electromagnetic between cases the beginning field was isachieved turned and ∼ ~0.1 s theonafter firstis required peak)., which Into thesecollect is also cases, more the all peakparticles or most time and of of the the achieve particleselectromagnetic steady were pressure collected field (.t heFigure near time the 10 between transducer shows thethe beforebeginning recorded the peakpressuresand the time first offor thepeak) two electromagnetic .pulses; In these the cases first field., all is or In1 most theHz cases pulseof the of particleswith100 and50% were200 dutymg collected ,cycle, the sidewall andnear thethe pressure secondtransducer continuedis 0 before.5 Hz 100 200 mg towiththe increase peak 75% time afterduty of thecycle; the rise electromagnetic hence, of 0.1 fors until the two thefield cases electromagnetic. In thethe electromagnetic cases of field wasand turn turned-off time off, .the was The sidewall the reason same. pressure for In that this 0.1 s canfigure,continued be seenthe time,to in increase Figure the horizontal9 after for the the rise100axis, ofmg is normalisedcase. until A significant the by electromagneticthe time amount period of particlesfieldof the was pulse. wereturned It stillappears off. collected The tha reasont the to 100 mg thepressurefor transducerthat canresulted be after seen from0.1 in thes Figure, while 0.5 9Hz some for pulse the of the increase particlesd case until were. A / notsignificant = collected0.75, and amount during reached of the particlesa wholemaximum magneticwere value still 0.1 s pulse.highercollected These by aboutto measurements the transducer15% than ofthat after the resulted pressure, fromwhile during the some one1 Hz ofpulse thepulse. support particles The reason a previous were for not that analysis collected is the in attraction during that larger the of amountsmorewhole particles magnetic of particles when pulse. settle the Thes 0 farther. 5 eHz measurements pulse away. was used. of the The pressure pressure during did not one reach pulse a constant support valuea previous since notanalysis all th ein available that larger particles amounts were of particlescollected settle until farther = 1.5 away. s. For the amounts of 100 and 200 mg, a longer time in which the electromagnetic field is turned on is required to collect more particles and achieve steady pressure. Figure 10 shows the recorded pressures for two pulses; the first is 1 Hz pulse with 50% duty cycle, and the second is 0.5 Hz with 75% duty cycle; hence, for the two cases the electromagnetic turn-off time was the same. In this figure, the time, the horizontal axis, is normalised by the time period of the pulse. It appears that the pressure resulted from the 0.5 Hz pulse increased until / = 0.75, and reached a maximum value higher by about 15% than that resulted from the 1 Hz pulse. The reason for that is the attraction of more particles when the 0. 5 Hz pulse was used. The pressure did not reach a constant value since not all the available particles were collected until = 1.5 s.

Figure 9. The evolution of a bulk of 100 mg during pulse of 50% duty cycle.

For the amounts of 100 and 200 mg, a longer time in which the electromagnetic field is turned on is required to collect more particles and achieve steady pressure. Figure 10 shows the recorded

Fluids 2020, 5, 98 10 of 15 pressures for two pulses; the first is 1 Hz pulse with 50% duty cycle, and the second is 0.5 Hz with 75% duty cycle; hence, for the two cases the electromagnetic turn-off time was the same. In this figure, the time, the horizontal axis, is normalised by the time period of the pulse. It appears that the pressure Fluids 2020, 5, x t T = 10 of 15 resultedFluids 2020 from, 5, x the 0.5 Hz pulse increased until / 0.75, and reached a maximum value higher10 of by 15 about 15% than that resulted from the 1 Hz pulse. The reason for that is the attraction of more particles Figure 9. The evolution of a bulk of 100 mg during pulse of 50% duty cycle. when the 0.5 HzFigurepulse 9. was The used. evolution The of pressure a bulk of did 100 not mg reach during a constant pulse of value 50% sinceduty cycle not all. the available particles were collected until t = 1.5 s.

FigureFigure 10. 10. PressurePressure results results during during two two shapes shapes of of pulses pulses for for the the amount amount of of 200 200 mg mg of of particles. particles. Figure 10. Pressure results during two shapes of pulses for the amount of 200 mg of particles. ToTo enable enable a acomparison comparison between between the the sidewall sidewall pressure pressure measurements measurements of different of different amounts, amounts, the To enable a comparison between the sidewall pressure measurements of different amounts, the resultsthe results in this in section this section are referred are referred to the maximum to the maximum pressure pressure difference di atfference the pulses. at the It is pulses. the difference It is the results in this section are referred to the maximum pressure difference at the pulses. It is the difference betweendifference the between maximum the pressure maximum at pressurethe pulse, at and the pulse,the pressure and the at pressure the beginning at the beginning of the pulse. of theTypical pulse. between the maximum pressure at the pulse, and the pressure at the beginning of the pulse. Typical resultsTypical of results the sidewall of the sidewallpressure pressure are presented are presented in Figure in 11, Figure for five11, formeasurements five measurements of 200 ofmg200. Themg . results of the sidewall pressure are presented in Figure 11, for five measurements of 200 mg. The horizontalThe horizontal axis is axis the is chronological the chronological number number of the of the pulse, pulse, the the left left axis axis is is the the maximum maximum pressure pressure horizontal axis is the chronological number of the pulse, the left axis is the maximum pressure differencedifference in in each each pulse, pulse, and and the the right right axis axis is is the the duty duty in in the the pulse. pulse. Between Between the the first first and and the the twentieth twentieth difference in each pulse, and the right axis is the duty in the pulse. Between the first and the twentieth pulses,pulses, which which is is the the last last pulse pulse of of the 50%50%duty, duty, the the sidewall sidewall pressure pressure converges. converges. That That is becauseis because at theat pulses, which is the last pulse of the 50% duty, the sidewall pressure converges. That is because at thefirst first pulses pulses the the bulk bulk is dependentis depende onnt on the the position position and and rate rat ofe theof the injection. injection. Subsequently, Subsequently, when when the the first pulses the bulk is dependent on the position and rate of the injection. Subsequently, when thepulses pulses were were continued, continu theed, particlesthe particles arranged arranged themselves themselves in a repeatable in a repeatable form. Theform. forms The areforms referred are the pulses were continued, the particles arranged themselves in a repeatable form. The forms are referredto as “undeveloped to as “undeveloped forms” and forms “developed” and forms,”“developed analogous forms, to”undeveloped analogous to and undeveloped developed flow and in referred to as “undeveloped forms” and “developed forms,” analogous to undeveloped and developedpiping. Additionally, flow in pip dispersioning. Additio occurrednally, between dispersion the occurred pressures, between even in the the pulses pressures, of developed even in forms. the developed flow in piping. Additionally, dispersion occurred between the pressures, even in the pulsesIt is assumed of developed to have forms. occurred It is because assumed of to the have actual occurred amount because of the particlesof the actual that wasamount successfully of the pulses of developed forms. It is assumed to have occurred because of the actual amount of the particlesinjected, that which was was successfully slightly di injectedfferent at, which each time.was slightly different at each time. particles that was successfully injected, which was slightly different at each time.

FigureFigure 11. 11. MaximumMaximum pressure pressure difference difference at ateach each pulse, pulse, for for five five measurements measurements of of200 200 mg mg. Figure 11. Maximum pressure difference at each pulse, for five measurements of 200 mg. Because of the development of the forms during the pulses, the sidewall pressure at the 20th Because of the development of the forms during the pulses, the sidewall pressure at the 20th pulse is considered as the most accurate sidewall pressure that the injected amount of particles pulse is considered as the most accurate sidewall pressure that the injected amount of particles applies. The results of the sidewall pressure at the 20th pulse are summarized in Figure 12a, for all applies. The results of the sidewall pressure at the 20th pulse are summarized in Figure 12a, for all five amounts of 8 μm. The results include the minimum, maximum, and average pressure at the five amounts of 8 μm. The results include the minimum, maximum, and average pressure at the pulse, for each amount. A correlation was fitted with the average sidewall pressures: pulse, for each amount. A correlation was fitted with the average sidewall pressures: Fluids 2020, 5, 98 11 of 15

. Because of the development of the forms during the pulses, the sidewall pressure at the 20th pulse is considered as the most accurate sidewall pressure that the injected amount of particles applies. The results of the sidewall pressure at the 20th pulse are summarized in Figure 12a, for all five amounts of 8 µm. The results include the minimum, maximum, and average pressure at the pulse, for each Fluidsamount. 2020, 5 A, x correlation was fitted with the average sidewall pressures: 11 of 15

P = 1.61 arctan(0.015 ξ) (2) = 1.61 ∙·arctan(0.015·∙ ) (2) Here,Here, ξ isis thethe amountamount of of the the particles, particles, and and it it varies varies in in the the range range 25–200 25 − mg.200 Themg. agreement The agreement of the ofcorrelation the correlation to the to results the re issults presented is presented in Figure in Figure 12b. The 12b horizontal. The horizontal axis is axis the is nominal the nominal amount amount of the ofparticles, the particles, and the and vertical the vertical axis is axis the averageis the average sidewall sidewall pressure pressure at the 20th at the pulse 20th for pulse a given for amount.a given amount.The fitting The suggests fitting suggests that asymptotic that asymptotic sidewall sidewall pressure pressure exists, although exists, although that pressure that pressure was not achievedwas not achievedexperimentally. experimentally. By the correlation, By the correlation, the maximum the maximum sidewall pressuresidewall ispressure2.5 kPa. is ~2.5 kPa. ∼

2.5 2.5

Minimal pressure (a) (b) Average pressure 2 Maximal pressure 2 ] ] a a

P 1.5 P 1.5 k k [ [

e e r r u u s s s s

e 1 e 1 r r P P Average pressure at the 20th pulse, 0.5 0.5 for 8 m P=1.61arctan(0.015 ) [kPa] ±0.3 [kPa]

0 0 25 50 75 100 200 0 50 100 150 200 250 Nominal amount [mg] Nominal amount [mg]

Figure 12. Results of the maximum pressure difference at the 20th pulse, for different amounts. Figure 12. Results of the maximum pressure difference at the 20th pulse, for different amounts. (a) – (a)—Min, Average and Max of each set of measurements. (b)—The average of each set of measurements, Min, Average and Max of each set of measurements. (b) – The average of each set of measurements, with a correlation. with a correlation. The experimental results of the sidewall pressure are compared with a simplified model, which was The experimental results of the sidewall pressure are compared with a simplified model, which also used in Reference [7]: was also used in Reference [7]: Fm,z = V ρ M(B) B (3) · · ·∇ , = ∙ ∙ () ∙ ∇ (3) Fm,z P = (4) A, = (4) Here, Fm,z is the magnetic force on the aggregation, perpendicular to the sidewall, V is the volume of theHere spherical, , is aggregation, the magneticρ is force the apparent on the aggregation density, and, M peisrpendicular the magnetization to the sidewall of the aggregation., is the volumeIn the current of the study,spherical the aggregation, values of the above is the parameters apparent aredensity,B = 0.2 andT , B =is 28theT magnetization/m, M = 0.1 A ofm the2/g ∇ · aggregationand ρ = 2.6. gIn/ cmthe3 current. As can study be seen, the in values Figure of7, the the above aggregation parameters cannot are be described= 0.2 T, as∇ a= sphere,28 T/m as, assumed= 0.1 A in∙ m Reference/g and [7].= Considering2.6 g/cm . As an areacan beA of seen a spherical in Figure aggregation 7, the aggregation would yield cannot errors be of describedmore than as an a order.sphere Instead,, as assumed the area in ReferenceA of the aggregations [7]. Considering was evaluatedan area usingof a spherical photo analysis aggregation under wouldan assumption yield errors of aof hemispherical more than an aggregation. order. Instead, The the values area for of the the amounts aggregations of 75 mgwasand evaluated200 mg usiwereng interpolated photo analysis/extrapolated. under an assumption A comparison of between a hemispher the estimatedical aggregation (Equations. The (3) value ands (4))for and the amountsthe experimental of 75 mg sidewall and 200 pressure mg were is presented interpolated/extrapolated. in Figure 13 and shows A comparison good enough between agreement the estimatedbetween them.(Equation A reasons (3) and for the (4)) di andfference the experimental between the measuredsidewall pressure and evaluated is presented sidewall in pressureFigure 13 is andthe behaviourshows good of enough the particles agreement [15]. Due between to the the formationm. A reason of long for and the disperseddifference chains between of particlesthe measured under andthe influenceevaluated of sidewall the magnetic pressure field is andthe behaviour drag force, of not the all particles the particles [15]. experienceDue to the theformation same magnetic of long andfield dispersed and its gradient. chains of particles under the influence of the magnetic field and drag force, not all the particles experience the same magnetic field and its gradient. FluidsFluids2020 2020, 5, ,5 98, x 1212 of of 15 15 ] a P k [

e r u s s e r P

FigureFigure 13. 13.Comparison Comparison betweenbetween the the modelled modelled and and experimental experimental pressure. pressure.

ToTo investigate investigate the the influence influence of the of duty the duty cycle cycle on the on sidewall the sidewall pressure, pressure, the duty the cycle duty was cycle reduced was graduallyreduced gradually from 50% fromto 10% 50%during to 10% the pulsesduring 20–32. the pulses The reduced20 − 32 duty. The cyclereduced implies duty the cycle increased implies durationthe increased of the duration field being of turnedthe field o ffbeing. As theturned duty off. cycle As wasthe duty reduced, cycle the was unstable reduced, masses the unstable settled lowermasses and settled could lower not beand collected could not again be collected when the again field when was turnedthe field on. was As turned a consequence on. As a consequence of the loss ofof the theparticles, loss of the the particles, measured the sidewallmeasured pressure sidewall was pressure reduced. was The reduced. results The of theresults sidewall of the pressure sidewall measurementspressure measurements during the during reduction the inreduction the duty in cycle the areduty presented cycle are in presented Figure 14 infor F theigure 5 amounts14 for the of 5 8amountsµm particles. of 8 Theμm horizontalparticles. The axis horizontal is the chronological axis is the chronological number of the number pulse (as of inthe Figure pulse 11(as), in and Figure the vertical11), and axis the is vertical the maximum axis is the pressure maximum difference pressure in thedifference pulse; the in beginningthe pulse; the is with beginning the 19th is pulsewith the to focus19th onpulse the to pulses focus in on which the pulses the duty in which cycle was the reduced;duty cycle each was black reduced; marker each refers black to anothermarker amountrefers to ofanother particles amount and includes of particles the multiple and includes repetitions the multiple for theamount. repetition Thes for colored the amount and marked. The colored trend lines and showmarked how trend the average lines show sidewall how pressure the average of each sidewall amount pressurechanges with of each the reduction amount changes of the duty with cycle. the Itreduction appears thatof the three duty pulses cycle. for It appears each duty that cycle three may pulses be insu forffi eachcient duty to achieve cycle may the developedbe insufficient form to andachieve repeatable the developed sidewall form pressure; and repeatable therefore, thesidewall discussed pressure results; therefore, are only the of dutydiscussed cycle reductionresults are fromonly50% of du(thety cycle developed reduction form) from to 40% 50%. A significant(the developed decrease form) in to the 40% measured. A significant pressure decrease occurred in only the atmeasured the 22nd pressure pulse, instead occurred of atonly the at 21st the pulse.22nd pulse, The reason instead is of that at the the 21st 22nd pulse. pulse The is the reason first is one that that the occurs22nd pulse0.6 s afteris the the first field one wasthat turnedoccurs o0ff.6; therefore,s after the before field was that turned pulse, aoff; critical therefore, mass before settled that far away.pulse, Thea critical decrease mass in thesettled sidewall far away. pressure The duringdecrease the in 22nd the pulsesidewall was pressure higher for during larger the initial 22nd amounts pulse was of particles,higher for supporting larger initial the previous amounts discussion of particles in, that supporting larger unstable the previous masses discussion settle faster. in It that was larger also discussedunstable masses that the settle stable faster. mass It shouldwas also be discussed the same that regardless the stable of mass the initial should amount be the ofsame the regardless particles. Whileof the theinitial duty amount cycle wasof the reduced particles. to 10%While, most the duty of the cycle particles was reduced were settled to 10% and, most not attracted of the particles again. Hence,were settled the particles and not at attracted the final pulseagain. canHence, be regarded the particles as the at “stable the final mass.” pulse It can appears be regarded that the as final the sidewall“stable mass. pressure” It atappears the 32nd that pulse the final is almost sidewall the same pressure for all at the the amounts 32nd pulse of particles. is almost Hence, the same it can for beall concludedthe amounts that of the particles. stable massHence, is indeedit can be not concluded dependent that on the the stable initial mass amount is indeed of the not particles. dependent on the initialFor di amountfferent applications, of the particles. smaller particles might be required. Cardiac pacing, for example, requires particles smaller than 3 µm, instead of 8 µm as were used for the feasibility of the application [7]. The sidewall pressure applied by three amounts of 1 µm particles was measured in a similar procedure as that of the 8 µm particles. The results of the sidewall pressure of the 1 µm and 8 µm particles during the 20th pulse are compared in Figure 15. The sidewall pressure that the 1 µm particles applied was lower than that of the 8 µm particles, but with a difference of less than 5%, for the three amounts. It is possible that such difference is only attributable to the fine-tuning of the different parts of the system. Therefore, the influence of particle size on pressure is not clear for the particles studied. Further research with smaller particles is required to determine the influence of particle size on the sidewall pressure. Fluids 2020, 5, x 13 of 15 ] a P k [

e s l u p

e h t

t a

e c n e r e f f i d

e r u s s e Fluids 2020, 5, 98 r 13 of 15 Fluids 2020, 5, x P 13 of 15

] a

Figure 14. MaximumP pressure at the pulses while reducing the duty cycle. k [

e s l u p For different applications, smaller particles might be required. Cardiac pacing, for example, e h t

requires particles smallert than 3 μm , instead of 8 μm as were used for the feasibility of the a

e

application [7]. The sidewallc pressure applied by three amounts of 1 μm particles was measured in n e r

a similar procedure as thate of the 8 μm particles. The results of the sidewall pressure of the 1 μm f f i d and 8 μm particles during the 20th pulse are compared in Figure 15. The sidewall pressure that the e r u

1 μm particles applied wass lower than that of the 8 μm particles, but with a difference of less than s e r

5%, for the three amounts.P It is possible that such difference is only attributable to the fine-tuning of the different parts of the system. Therefore, the influence of particle size on pressure is not clear for the particles studied. Further research with smaller particles is required to determine the influence of particle size on the sidewall pressure. Figure 14. Maximum pressure at the pulses while reducing the duty cycle. Figure 14. Maximum pressure at the pulses while reducing the duty cycle.

For different applications, smaller particles might be required. Cardiac pacing, for example, requires particles smaller than 3 μm , instead of 8 μm as were used for the feasibility of the application [7]. The sidewall pressure applied by three amounts of 1 μm particles was measured in ] a

P 8 μm 1 μm

a similar procedure as thatk of the particles. The results of the sidewall pressure of the [

e and 8 μm particles duringr the 20th pulse are compared in Figure 15. The sidewall pressure that the u s s

1 μm particles applied wase lower than that of the 8 μm particles, but with a difference of less than r 5%, for the three amounts. P It is possible that such difference is only attributable to the fine-tuning of the different parts of the system. Therefore, the influence of particle size on pressure is not clear for the particles studied. Further research with smaller particles is required to determine the influence of particle size on the sidewall pressure.

FigureFigure 15. 15.Comparison Comparison betweenbetween the the pressure pressure results results of of 1 1 and and 8 8µ μmm particles. particles.

4.4. ConclusionsConclusions ] a P

In this work, a pulsatingk magnetic field was used to attract ferromagnetic particles toward the [

In this work, a pulsating magnetic field was used to attract ferromagnetic particles toward the e sidewall of a water chamber.r The behaviour of the particles was investigated, and the pressure they u

sidewall of a water chamber.s The behaviour of the particles was investigated, and the pressure they s apply on the wall was measured.e apply on the wall was measured.r P WhenWhen the the magnetic magnetic field field was was turned turned o off,ff, a a certain certain part part of of the the particles particles (the (the stable stable mass) mass) remained remained attachedattached to to the the chamber chamber sidewall sidewall due due to to magnetic magnetic hysteresis. hysteresis. TheThe stablestable massmass waswas significant significant to to the the immediateimmediate sidewall sidewall pressure pressure that that was was applied applied when when the the field field was was turned turned on on at at each each pulse, pulse, and and to to the the sidewallsidewall pressure pressure at at pulses pulses with with low low duty duty cycle. cycle. The The results results of of the the experiments experiments confirmed confirmed that that for for the the specified configuration, the size of the stable mass did not depend on the initial amount of the particles. The remaining particles that detached from the sidewall (the unstable mass) settled toward the bottom of the chamber.Figure 15. Larger Comparison unstable between masses the settled pressure faster results and of farther1 and 8 awayμm particles. from the stable mass, because of the cluster behaviour of the bulk of the particles. When the duty cycle of the magnetic pulses was4. Conclusions reduced, some particles migrated far away and could not be attracted again when the magnetic field was turned on. As a result, the sidewall pressure during the following pulses was decreased. In this work, a pulsating magnetic field was used to attract ferromagnetic particles toward the The relation between the amount of the particles and the sidewall pressure was investigated sidewall of a water chamber. The behaviour of the particles was investigated, and the pressure they experimentally with measurements of the pressure. According to the measurement results, apply on the wall was measured. an approximate asymptotic dependence between the sidewall pressure and the mass of the particles When the magnetic field was turned off, a certain part of the particles (the stable mass) remained was proposed for the specified particles and magnetic pulses. The proposed experimental correlation attached to the chamber sidewall due to magnetic hysteresis. The stable mass was significant to the allows for an effective evaluation of the sidewall pressure values in similar experiments. immediate sidewall pressure that was applied when the field was turned on at each pulse, and to the sidewall pressure at pulses with low duty cycle. The results of the experiments confirmed that for the Fluids 2020, 5, 98 14 of 15

The experimental results were compared with simplified estimations. The comparison shows their satisfactory agreement for the assessment of maximum allowable sidewall pressure in similar experiments.

Author Contributions: Conceptualization, A.A. and A.L.; methodology, A.A. and O.W.; software, O.W.; validation, O.W., A.L. and B.M.; formal analysis, O.W.; investigation, O.W.; resources, A.L. and A.A; data curation, O.W.; writing—original draft preparation, O.W.; writing—review and editing, O.W., A.L., B.M. and A.A.; visualization, O.W.; supervision, A.L., B.M. and A.A.; project administration, A.L.; funding acquisition, A.L. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: The authors thank Yoram Etzion from Ben-Gurion University of the Negev for the contribution of the electromagnet and particles and to Rafi Shikler from Ben-Gurion University of the Negev for the contribution of the PVDF film and the help for the sensor development. Conflicts of Interest: The authors declare no conflict of interest.

References

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