Description and performance of a fully automatic device for the study of thesedimentation of magnetic suspensionsG. R. Iglesias, M. T. López-López, A. V. Delgado, and J. D. G. Durán Citation: Review of Scientific Instruments 82, 073906 (2011); doi: 10.1063/1.3609228 View online: http://dx.doi.org/10.1063/1.3609228 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/82/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Development and validation of a 10kHz–1MHz magnetic susceptometer with constant excitation field J. Appl. Phys. 111, 07E349 (2012); 10.1063/1.3680200 Magnetorheology and sedimentation behavior of an aqueous suspension of surface modified carbonyl ironparticles J. Appl. Phys. 107, 09B507 (2010); 10.1063/1.3358613 Magnetorheological carbonyl iron particles doubly wrapped with polymer and carbon nanotube J. Appl. Phys. 105, 07E703 (2009); 10.1063/1.3058674 A study of patterning and annealing effects on the performance of magnetic planar inductor J. Vac. Sci. Technol. B 26, 1407 (2008); 10.1116/1.2958245 Sedimentation and redispersion phenomena in iron-based magnetorheological fluids J. Rheol. 50, 543 (2006); 10.1122/1.2206716

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REVIEW OF SCIENTIFIC INSTRUMENTS 82, 073906 (2011)

Description and performance of a fully automatic device for the studyof the sedimentation of magnetic suspensions

G. R. Iglesias,1 M. T. López-López,2 A. V. Delgado,2 and J. D. G. Durán2,a)

1Institute of Physical Chemistry, University of Graz, 8010 Graz, Austria2Department of Applied Physics, School of Science University of Granada, 18071 Granada, Spain

(Received 3 March 2011; accepted 16 June 2011; published online 19 July 2011)

In this paper we describe an experimental setup for the automatic determination of the sedimentationbehavior of magnetic suspensions (i.e., disperse systems consisting on ferro- or ferri-magnetic parti-cles in a suitable fluid) of arbitrary volume fraction of solids. The device is based on the evaluationof the inductance of a thin coil surrounding the test tube containing the sample. The inductance L isevaluated from the measurement of the resonant frequency of a parallel LC circuit constructed withthe coil and a capacitor of known capacitance. The coil can be moved vertically along the tube atspecified steps and time intervals, and from the knowledge of L as a function of the vertical positionand time, one can get an image of the particle concentration profiles at given instants of time. Theperformance of the device is tested against suspensions of spherical iron particles in the micrometersize range dispersed in silicone oil, with various initial concentrations of solids. The sedimentationprofiles are then compared with the predictions of existing models for the settling of disperse systemsof non-interacting particles. © 2011 American Institute of Physics. [doi:10.1063/1.3609228]

INTRODUCTION

Because of both their present and potential technologicalapplications1–6 and their remarkable physical properties,7–9

there is a considerable interest in improving our knowledgeand understanding of suspensions of magnetizable (ferro-or ferri-magnetic) particles in a carrier fluid. If the particlesize is in the few nanometer range, the system is knownas a ferrofluid: because of their small particle size, theparticles are monodomain, and often supeparamagnetic. Ifthe magnetic particles are larger (in the micrometer range),the system is named magnetorheological suspension ormagnetorheological fluid (MRF). Although such particles aremultidomain, an externally applied magnetic field, even iflow (B ≥ 10 mT in air) can induce large magnetic momentsin them. The magnetically polarized particles will in turninteract via magnetic dipolar interactions leading to the for-mation of particle chains in the direction of the field. Thesechains mechanically reinforce the fluid and transform it fromNewtonian to viscoelastic, with strong, field-dependent yieldstress; this is the magnetorheological (MR) effect.

Considering the relatively large particle sizes involvedin an MRF, the high density of the usually employed ironpowders (about 7.5 g/cm3), and the necessity of using a notvery viscous carrier fluid (if a wide MR response must beachieved), sedimentation of the particles is a major concern.The packing of the particles at the bottom of the containermay become very compact if the MRF is left standing for evenmoderate time periods. It is thus essential, for the character-ization of these systems, to have suitable procedures to testtheir rate of sedimentation and to evaluate and control howthis process occurs.

a)Author to whom correspondence should be addressed. Electronic mail:jdgarcia@ugr.es. FAX: +34-958 24 32 14.

The opacity of the MR suspensions for the concentra-tions of solids typically employed prevents the use of opti-cal methods for sedimentation follow-up. For these reasons,some instruments and procedures were developed, with theaim of measuring the sedimentation rate of MRFs. Interest-ing examples are the designs of Gorodkin et al.,10 later im-proved by Chen and Chen,11 by using a permalloy inductorthat allowed to double the range of linearity of the effectivesignal obtained. These authors calculated the sedimentationconstant of a commercial MRF by the inductance method, andthe same principle was applied in previous works of this andother laboratories.12–17

Our proposal in this paper is to present a simple, self-contained, and cost-effective apparatus suitable for the studyof the sedimentation processes in magnetic suspensions ofany nature and virtually any concentration in solids. The ap-paratus is based on the use of a sensing coil that sweeps thecontainer vertically at specified time intervals. The coil (withlength much smaller than the container height) encloses ateach position a small volume of the magnetic suspension,where the local volume fraction of solids is φ. The induc-tance L of the coil will hence change with position and time,so that measuring L will provide information on the local vol-ume fraction of magnetic particles.10–17

In addition to describing the device (that we will callmagnetoscan hereafter) and its methodology of use, we willshow its performance by recording the settling profiles of ironsuspensions of several volume fractions, dispersed in siliconoils.

Description of the magnetoscan

Figure 1 shows the mechanical realization of the device.A stepper motor of 1.8o/step was selected to drive a free ver-tical screw. A supporting plate is fixed in a nut and it can

0034-6748/2011/82(7)/073906/6/$30.00 © 2011 American Institute of Physics82, 073906-1

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073906-2 Iglesias et al. Rev. Sci. Instrum. 82, 073906 (2011)

move up/down driven by the motor. The direction and rateof motion of the scanning sensing coil can be previously de-termined by the operator, and controlled through the parallelport of the computer. As observed, the key element is the sens-ing coil, and the associated dependence between its induc-tance L and the volume fraction φ of magnetizable particles itencloses.

The scanning coils tested are 5 mm long, with 75 turns ofcopper wire 0.2 mm2 in cross section (AWG 24; 0.51 mm indiameter). The dependence between the values of L and φ hasbeen discussed in Refs. 13 and 14, and, in summary it is basedon the determinations of the resonant frequency f of a parallelcircuit formed by L and a conveniently chosen capacitor(capacity C = 10 nF in the presented design). Briefly, if f (t,z)is the resonant frequency of the coil at position z and time t(z = 0 is the bottom surface of the test tube), then the volumefraction of solids at that time and position can be obtainedfrom

f (t, z) =√

1 − φ(t, z)

1 + 2φ(t, z). (1)

An interesting quantity is the relative frequency fr,given by the ratio between the frequency f0 at any positionfor t = 0 (when the particles are homogeneously distributedin the suspension with volume fraction φ0) and the local,instantaneous frequency (1),

fr (t, z) ≡ f0

f (t, z)

√[1 + 2φ(t, z)](1 − φ0)

[(1 + 2φ0)][1 − φ(t, z)]. (2)

From this, φ(t,z) can be obtained, that is a knowledge of thevolume fraction of solids at every position and time is madepossible. This is a direct evaluation of the sedimentationrate, and it is performed in real time by the control and dataacquisition software.

As above mentioned (Fig. 1), a stepper motor connectedto the parallel port of a computer moves the coil up and downalong the sample, at a user-selected rate. The left panel ofFig. 2 details the complete electronic circuit designed for thispurpose. The sensing coil, L, is associated with a capacitor,C, in a parallel LC circuit, in turn connected to an oscillatingcircuit which is composed of five resistors R1–R5, two capac-itors C2 and C3, and one integrated circuit (LM311) work-ing as a voltage comparator. This produces a square wave(2.5 V) at a frequency equal to the resonant frequency ofthe LC parallel, and it was around 500 kHz for the presentdesign.

To read and store the frequency of the oscillating circuitwe use a 12F683 microprocessor pre-programmed as a fre-quency counter with a standard serial output connected to theserial port of the computer via the RS-232 protocol. The maincontrol of the device was carried out by dedicated softwarewritten in VISUAL BASIC R©. Figure 2 shows an example ofthe appearance of the user’s control window. The user can se-lect the display of total experiment time, number of runs, scanrate, waiting time between successive measurements, cycles,initial and final positions.

FIG. 1. (Color online) Mechanical realization of the device.

Experimental

The magnetic particles were HQ carbonyl iron fromBASF (Germany). Figure 3 is a SEM picture that exempli-fies the spherical appearance of the particles and their sizedistribution. Measurements performed on over 150 particlesin pictures like the one shown yielded an average diameter(± standard deviation) of 900 ± 300 nm. The silicone oil wasfrom Aldrich (USA) with a nominal viscosity of 10 mPa s.

The magnetic suspensions were prepared by simply dis-persing the required amount of solids in the carrier liquid,adding the iron slowly under uniform stirring. The sedimen-tation profile determinations were performed by placing thesuspension to be studied in test tubes 50 mm long, and15 mm outer diameter, filled with 6 mL of MRF. The experi-mental conditions are set and data recording is started. In thetypical experimental setup described above, the scanned ver-tical distance was 30 mm, the scan starting 10 mm below thefluid surface and finishing 10 mm above of the tube bottom.Data were recorded at 1.5 mm height steps; the sensing coilwas maintained 1 s at each position, and one further secondwas needed to reach the next position. Once a scan was fin-ished, a waiting time of 3 s was allowed before starting a newone. Hence the typical total time for one complete measure-ment, with 15 cycles, took about 460 s.

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073906-3 Iglesias et al. Rev. Sci. Instrum. 82, 073906 (2011)

FIG. 2. (Color online) (Left) Electronic circuit of the instrument. (Right) An example of the control window in VISUAL BASIC.

RESULTS AND DISCUSSION

Sedimentation profiles

The device and procedures were tested in different MRFscontaining iron concentrations 3, 5, 10, 15, 20, and 25% (vol-ume fractions) in silicone oil of 10 mPa s viscosity. As men-tioned, unless special precautions are taken, the sedimentationof iron in such a low viscosity fluid is a very fast process thatends up with all the solids deposited on the bottom of the con-tainer within minutes. Figure 4 shows the results for the mostdilute systems (3% volume fraction): each curve is a snap-shot of the particle concentration along the test tube. We notethat at the bottom of the tube the volume fraction is some-what higher than 3%, an indication of the fact that the actualtime is >0 when the coil reaches the bottom upon complet-ing the first scan. The device also allows analyzing the rate ofsedimentation by checking the rate of change of iron volumefraction, φ, at a fixed position z, as described in Refs. 10–14,although the representation proposed in Fig. 4 is perhaps the

FIG. 3. Scanning electron microscope picture of the iron particles used in thefluid formulations for testing the magnetoscan. The bar length is 2000 nm.

most illustrative way to acquire information about the rate ofsediment formation in the systems.

Figure 5 illustrates the change of φ with time at three dif-ferent positions above the tube bottom, z = 10 mm, 25 mm,and 40 mm. This type of plot also provides a very clear viewof how the sedimentation proceeds: note how the evolutionfrom a well dispersed suspension with homogeneous volumefraction of iron towards a sedimented system with virtuallyno particles in the upper section of the tube takes about 1 min.We can also observe that at the bottom (z = 10 mm) the vol-ume fraction increases during the first 2 min, and afterwardsit decreases. The reason for this behavior is the formation ofsediments in the bottom of the test tube; during the first 2 minthe accumulation of particles in loose sediments provokes theincrease of particle concentration at z = 10 mm. As time in-creases above 2 min the sediments become more compact,decreasing their height and thus progressively leaving free ofparticles in the tube at a position z = 10. Overall, the sedi-mentation proceeds very differently for different positions inthe test tube.

FIG. 4. (Color online) Volume fraction (φ) profile of iron particles suspendedin a 10 mPa s silicone oil (z is the distance to the bottom of the container) atthe specified time after preparation. The time taken to test the whole z rangewas 30 s in all cases. Initial volume fraction: φ0 = 3%.

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073906-4 Iglesias et al. Rev. Sci. Instrum. 82, 073906 (2011)

FIG. 5. (Color online) Volume fraction of iron as a function of sedimentationtime for three positions in the test tube. The data correspond to the systemsdescribed in Fig. 4.

Moderate and high particle concentrations

The variety of settling behaviors appears more evident inmore concentrated samples, as shown in Fig. 6, correspondingto MRFs with initial φ0 = 5% and 10%. The behavior of the

sedimentation process for φ0 = 5% and 10% appears similarto that found in Fig. 4 for 3% volume fraction, except thatthe time required to achieve significant sedimentation is nowlonger.

This is not true for concentrations of 15% and above(Fig. 7). The settling process is now rather different, evenqualitatively: as time passes, the volume fraction at the toplevel decreases, but at the latest steps of the process the maxi-mum volume fraction is not located at the first few millimetresin the bottom of the test tube, but rather somewhere betweenz = 25 mm and z = 30 mm. This is probably an indication ofthe hindering effect that the high particle concentration hason the sedimentation of the upper fraction of the fluid: theincrease in concentration produced by particles coming fromthe upper volume is compensated by the decrease associatedto sediments directed toward the bottom. In addition, thecurves above 15% display another interesting feature, namely,the volume fraction never reaches the zero value at the top,where, although small, it remains finite. It can be argued thatthis is another manifestation of the hindered sedimentation.

In order to clarify this possibility, the settling behaviorof these MRFs can be compared to that of non-magneticparticles, a field where considerable research has been per-formed, both experimentally and in theory and simulations.Reasons for such similarities come from the fact that the av-erage size of our iron particles is large enough for them to be

FIG. 6. (Color online) Left: plots of the volume fraction profiles for different times in settling suspensions of iron with initial volume fractions φ0 = 5% and10%. Right: time evolution of the volume fraction at three positions of the test tube.

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073906-5 Iglesias et al. Rev. Sci. Instrum. 82, 073906 (2011)

FIG. 7. (Color online) Same as Fig. 6, but for initial volume fractions φ0 = 15%, 20%, and 25%.

multidomain, from the magnetic point of view. This meansthat, in the absence of applied fields, the particles have neg-ligible magnetization, and they will not experience magneticinteractions between each other.

Theoretical reference for the present results can be foundin, for instance, the excellent review by Berres et al.,18 whereinformation on different batch sedimentation models is pro-vided. The most complex situation occurs when the sediment-ing suspension is polydisperse in size and has a high concen-tration of solids. The simplest treatment, elaborated by, forinstance, Batchelor19 gives the following expression for thevelocity of a particle in a suspension of volume fraction φ in

terms of the Stokes sedimentation velocity v∞ of a sphere ina infinitely diluted suspension:

v(φ) = v∞(1 − nφ) (3)

although the most frequently used version was obtained byRichardson and Zaki,20

v(φ) = v∞(1 − φ)n, (4)

where the value of the exponent n (in fact considered as afitting parameter) is typically in the range 4.5-5.5. Either ofthese equations is indicative of a reduction of the settlingvelocity as the particle concentration rises, because of the

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073906-6 Iglesias et al. Rev. Sci. Instrum. 82, 073906 (2011)

increase in the effective viscosity and density of the surround-ing medium. Equation (4) is still valid in the case of monodis-perse suspensions even in they are highly concentrated insolids, but it does not take properly into account the existenceof a return flow of fluid associated to the downward sedi-mentation of the particles. An approximate generalization wasfound by Masliyah,21 and Lockett and Bassoon,22 for whichthe case of a polydisperse suspension where different parti-cles differ only in size but not in density (as it is the case inthe present experiments) reads

vi (φ1, φ2, ..., φN ) = v∞1(1 − φ)n−1

× [δi − (δ1φ1 + δ2φ2 + ... + δN φN )] .

(5)

It is assumed that the particle size distribution containsN different particle diameters, with

δi =(

di

d1

)2

. (6)

Knowledge of the velocities vi is obviously essential, asthe sedimentation is controlled by the flux density functionsfi = φi vi .23, 24 If, for simplicity, we consider just a bidispersesuspension, then the arguments first given by Smith25 canbe used for reaching a semi-quantitative description of thesedimentation:18 the upper part of the suspension will be de-pleted in the concentration of the fastest-settling fraction (thelarger particles). As a consequence, the smaller particles willsettle more rapidly in that region than in the original suspen-sion, with the two species homogeneously distributed. Nev-ertheless, a material balance indicates that the concentrationof the slower-settling (smaller) particles is increased in thetop zone (the Smith effect). A sort of “nose” is in fact foundin numerical simulations of the concentration profiles of thesmaller particles in a bidisperse sedimenting suspension.26

Such concentration increases of the slow-settling size frac-tions in the upper levels are the most likely explanation of thekinked-shape of concentration profiles in the case of the mostconcentrated iron suspensions (Fig. 7). The overall agreementof our results with existing models indicates that the proposedexperimental procedure and device are useful in the evalua-tion of the settling behavior of magnetic fluids.

CONCLUSIONS

In this work we have described the construction and con-trol of a device for the evaluation of the particle concentration

profiles of magnetic suspensions, as a function of time. It isthus a direct way for characterizing the settling, and from thisobtaining information about the stability of the suspensions.The method is based on the determination of the inductanceof a short sensing coil surrounding the suspension, and whichis made to scan along a test tube containing the sample. Thedevice is tested by measuring the volume fraction profiles ofiron suspensions in silicone oil, and the results are comparedto predictions of sedimentation velocities of polydisperse sus-pensions of non-interacting particles.

ACKNOWLEDGMENTS

Financial support from Project Nos. P08-FQM-3993 andP09-FQM-4787 (Junta de Andalucía, Spain), Project No.FIS2009-07321 (MICINN, Spain), is gratefully acknowl-edged. One of the authors (M.T.L.-L.) also acknowledges fi-nancial support by the University of Granada (Spain).

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