Magnetic separation of magneticactivated carbons for water

treatment and reuseChiara Caterina Borghi

Department of Electric, Electronic and Information Engineering,University of Bologna, Bologna, Italy

Yoko AkiyamaDivision of Sustainable Energy and Environmental Engineering,Graduate School of Engineering, Osaka University, Osaka, Japan

Massimo FabbriDepartment of Electric, Electronic and Information Engineering,

University of Bologna, Bologna, Italy

Shigehiro NishijimaDivision of Sustainable Energy and Environmental Engineering,

Graduate School of Engineering, Osaka University, Osaka, Japan, and

Pier Luigi RibaniDepartment of Electric, Electronic and Information Engineering,

University of Bologna, Bologna, Italy

Abstract

Purpose – The aim of this paper is the study of the magnetic separation of pollutants from water bymeans of a magnetic filter. A magnetic activated carbons nanometric powder that combines thewell-known pollutants absorbent capacity of activated carbons with the magnetic properties ofmagnetite (Fe3O4) is used.

Design/methodology/approach – The considered magnetic filter is made of stainless steelspheres, magnetized by an external flux density field provided by permanent magnets. Flux densityand fluid velocity fields are evaluated using volume integral equation method. The modelling of theparticles trajectories inside the filter allows calculating its capture efficiency.

Findings – The results of the model are tested on the experimental data obtained using two differentsetups. A removal of the powder larger than 90 percent is achieved in both cases. The pollutantremoval efficiency is checked on surfactants (water diluted). Their adsorption on magnetic activatedcarbons leads to residual concentration below the limit for the reuse in agriculture (according to theItalian legislation) for all the tested surfactants.

Originality/value – The proposed process combines efficiently a physico-chemical phase of adsorptionand a magnetic phase of filtration due to the particular properties of magnetic activated carbons.

Keywords Filtration, Magnetic activated carbons, Magnetic separation, Magnetostatics, Water reuse,Water treatment

Paper type Research paper

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/0332-1649.htm

The authors are grateful to MS-Engineering Ltd, that provided MAC, and JTEKT Corp. thatprovided the steel spheres.

COMPEL: The International Journalfor Computation and Mathematics inElectrical and Electronic Engineering

Vol. 33 No. 1/2, 2014pp. 445-462

q Emerald Group Publishing Limited0332-1649

DOI 10.1108/COMPEL-03-2013-0088

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1. IntroductionWater saving and reuse are pressing issues to have a sustainable development.Reducing wastewater pollutants flow-rates and concentrations would first of alldecrease the water bodies pollution. Second, if the concentrations are lower than thevalues allowed by law for a reuse in agriculture, the actual intake of water resource isreduced. Surfactants are among the contaminants affecting irrigation water quality.They generate undesired foams, decrease the effectiveness of water aeration andadversely affect plant growth (Duncan et al., 2008; Borghi et al., 2011). Surfactants are themain constituents of detergents and are classified as non ionic, cationic and anionic onthe basis of the carried charge. According to Italian legislation their total concentrationlimits for water reuse in agriculture is 0.5 mg/l (Ministerial Decree 185/2003).

In Borghi et al. (2011) it has been shown that magnetite and hematite powders cansignificantly improve the removal of surfactants by means of magnetic separation.The process considered is made of two phases: first the powder is added tothe surfactant-water solution, with the aim to adsorb the surfactant, and second thesuspension is cleaned passing through a magnetic filter that captures the powder.The efficiency of the process critically depends on both steps and the performancecannot be greatly improved using magnetite or hematite. Magnetite powder is aferrimagnetic and non porous iron oxide and an improvement of the adsorption can onlybe achieved by means of a reduction of the diameter of the adsorbent, due to the increaseof the specific area. However, the reduction of the diameter worsens the capture in themagnetic filter thus reducing the efficiency of the separation. Hematite powder, which isa better adsorbent since it is porous, is paramagnetic and much more difficult to capture(Rossier et al., 2012). The optimal process requires a powder with both good absorbanceand magnetic properties.

Activated carbons (AC) are excellent and versatile adsorbents which are used inmany areas to remove organics, inorganics and vapours, in particular for thepurification of air and water (Bansal and Goyal, 2005; Gaspard et al., 2008). Anywaythe lack of magnetic properties makes them removable only by filtration (with sand ormembranes) or sedimentation with disadvantages in terms of time and costs. Magneticactivated carbons (MAC) are a combination of AC with magnetite allowing theexploitation of the advantages of both materials (Do et al., 2011; Jia et al., 2011). Thus,the proposed process uses the AC part of the MAC in order to perform surfactantsadsorption and the magnetite part to magnetically filter them. The MAC used consistof nanometric particles, usually difficult to capture. However, due to hydrophobicity,MAC in water solutions generate micrometric aggregates which can be removed alsowith low magnetic fields.

The magnetic separation of pollutants from water is not a new process (Svoboda, 1987;Nishijima and Takeda, 2006; Hu et al., 2007; Shen et al., 2009; Mishima et al., 2010; Nassar,2010). A magnetic filter or separator exploits the magnetic force acting on a magnetizableparticle (surrounded by non-magnetic fluid) in an externally applied flux density fieldwith a spatial gradient (Abbasov, 2007; Mariani et al., 2009, 2010). The magnetic forcemust be able to capture and withhold particles against the drag force of the surroundingfluid and the effects of Brownian motion. Each particle is magnetized by a field which ismade of three terms: a relatively uniform field produced by sources external to the filter,a field produced by the ferromagnetic filtering elements and the field produced by themagnetic moments of the other particles. The external magnetic field can be used to

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saturate the particle to obtain maximum possible magnetic force. The same field is usedto magnetize the filtering elements which provide the magnetic field gradient.

In Mariani et al. (2009, 2010) and Borghi et al. (2011) a magnetic filter using steelwool as filtering element was analysed. Despite its good capture efficiency, the woolfilter has shown two main problems: first the needed periodic washing was difficult toachieve and second a careful wool fixing was required. In order to solve both theseproblems, in this paper stainless steel spheres are chosen as filtering elements(Abbasov, 2007). This choice allows an easy washing with an ultrasonic bath anda simple assembling of the filter (the spheres fill all the filter volume according to aface-centred cubic (FCC) lattice).

The outline of the article is as follows. In Section 2 the MAC properties are reported.Section 3 describes the two experimental setups investigated. In Section 4 thenumerical model based on the analysis of an elementary cell is developed. Section 5shows the comparison of the model outcomes with the experimental results and theadsorption efficiencies of three different surfactants on MAC.

2. MAC propertiesMAC powder provided by MS-Engineering Ltd is used as adsorbents (www.ms-engineering.co.jp/eng/). This powder consists of AC particles combined with magnetite(Fe3O4) ones. The diameter is about 40-50 nm; it was measured suspending MAC inethanol and using a FOQELS particle size analyzer of Brookhaven InstrumentsCorporation. However, when suspended in water solutions, MAC generate micrometricaggregates due to their hydrophobicity. An ultrasonic washing is applied after MACaddition to the pollutant-water samples in order to break the particles’ aggregates withthe purpose of maximizing the MAC surface available for adsorption. Figure 1 showstwo distributions of the aggregates’ sizes of the MAC suspended in distilled water.They refer to the “as purchased” MAC and to the MAC after the ultrasonic washing.It can be seen that the ultrasonic washing changes the sizes distribution increasing by2-3 percent in mass the particles fraction below about 3mm.

The main characteristics of MAC are listed in Table I. MAC combine the largespecific surface of AC with the magnetic properties of magnetite. The pHpzc (point ofzero charge pH) was evaluated by measuring the electrophoretic mobility. At the pHpzc

the number of positive groups on the powder surface equals the number of negative

Figure 1.Sizes distribution of MACaggregates in water with

and without ultrasonicwashing

0

5

10

15

20

25

30

0 3 6 9 12 15 18 21 24 27 30 33

Diameter [µm]

Freq

uenc

y [%

]

MAC in water as purchased

MAC in water after ultrasonic washing

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ones and, as the pH increases, the number of negative groups increases too (Bansal andGoyal, 2005; Borghi et al., 2011). The magnetization curve of MAC measured byQuantum Design PPMS is shown in Figure 2 (m0 is the magnetic permeability ofvacuum). As expected, due to their magnetite content, MAC show a ferromagneticbehaviour.

3. Magnetic filtration systemsTwo experimental setups significantly different in terms of size, external flux density field,water flow rate and average velocity in the filter, were manufactured and tested in order tohave as much as possible data to compare with the outcomes of the numerical model. In bothmagnetic filtration devices the fluid circulates inside a closed-cycle system pushed by apump. The flow starts from a tank filled with a mixture of distilled water, pure surfactantand powder and returns to the same reservoir after passing through the magnetic filter. Theconnection pipes are made of flexible rubber. The filter is made of stainless steel spheres.Permanent magnets provide the external flux density field in the filter volume. Table IIshows the main parameters of the two systems and the symbol used. The effectivesusceptibility xs,eff of the steel takes into account the spheres demagnetizing factor (Fiorillo,2004; Mariani et al., 2009). The average fluid velocity u0 is calculated on the free watersection (evaluated using the section filling factor). The direction and the intensity of theexternal magnetic flux density fieldB0 are not constant in each cross section of the filter witha prevalence of the component normal to the flow velocity. The applied external magnetic

Content Fe3O4 (% vol) 25-35Average pore diameter (nm) 2.53Pore volume (ml/g) 0.49Specific gravity (ISO 787/10) (g/cm3) 1.7Tamped density (ISO 787/11) (g/cm3) 0.45Specific surface (SA) (m2/g) 773pHpzc 4Representative particle size (nm) 40-50Representative aggregate size (mm) 1-3Magnetism Ferrimagnetic

Table I.Properties of MAC

Figure 2.Magnetizationcurve of MAC

0.0

5.0

10.0

15.0

20.0

25.0

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00Applied flux density [T]

µ 0M

[µT

]

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flux density field is relatively uniform in the filter volume; the values reported in Table IIrefer to the maximum value in the centre and the lowest one on the inlet and outlet sections.

4. Filter capture modellingThe model of the spheres filters is developed in the following, by modelling the FCC latticecreated by the spheres. Modelling one elementary cell allows deducing the filter captureefficiency for the two experimental setups and the scaling up to larger filters also. Themain hypothesis of the model is that each particles’ aggregate is spherical, suspended inthe fluid, and subjected to the magnetic and fluid-dynamic forces. The gravitational forceand the interaction among magnetized particles’ aggregates have been neglected.

The elementary cell is chosen as 1/8 of the FCC cell lattice in order to reduce thecomputational effort in evaluating the flux density and the water velocity fields.Assuming tightly packed spheres with 3 mm diameter, the elementary cell is cubic andhas a side of 2.12 mm. It contains four octants of sphere centred on opposite corners asshown in Figure 3(a). The complementary volume shown in Figure 3(b) is the physicaldomain for the water flow and the particles inside it. A right handed Cartesiancoordinate system Oxyz, with the origin defined in the left-down corner of theelementary cell shown in Figure 3 and the axes parallel to the cell edges, is considered.The inlet section for the water flow is assumed to be in the y ¼ 0 plane. The externalflux density field B0 is assumed to be uniform in the cell and directed along the z-axis.

Experimental setup no. 1 Experimental setup no. 2

Filter dataMaterial SUS440C SUS440CSaturation magnetization (T) 1.1 1.1Spheres number 100 6,900Relative permeability 200 200Effective susceptibility xs,eff 2.9 2.9Diameter, ds (mm) 3 3Volume filling factor (%) 55 55Section filling factor (%) 78 78Cross section Circular, 64 mm2 Rectangular, 37 mm £ 23 mmLength (mm) 40 210Average fluid velocity, u0(m/s) 0.16 1.3Circuit dataSystem volume, V 0.1 l 2.5 lFlow rate, q (cm3/s) 2.24 240Tubes inner diameter (mm) 7 18Fluid velocity inside tubes (cm/s) 5.8 94Filtration time (min) 10-20 10-20Pump Roller RotativeFluid viscosity, h (mPa.s) 1 1Magnet-to-filter gap (mm) 1-2 5-6External magnet dataIngot dimensions 25 mm £ 25 mm £ 12 mm 70 mm £ 70 mm £ 30 mmIngot material 1 Nd-Fe-B ingot 6 Sm-Co ingotsRemanence (T) 0.4 1.05Magnetic circuit Absent C-shapedApplied flux density field, B0 (mT) 50-100 450-500

Table II.Magnetic filtration

systems data

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The flux density field B inside the cell is assumed to be stationary. The water velocityfield u inside the cell is assumed to be stationary and laminar. The effect of filterclogging is not taken into account. The flux density B(x) and the water velocity u(x)fields are defined as point-dependent functions in the pre-processing stage through thevolume integral equation method (Mariani et al., 2010; Morandi et al., 2010). Thismethod leads to calculate the fields sources (in a 3 £ 3 £ 3 array of cells surroundingthe studied one) which are defined inside the discretized spheres. Each sphere isdiscretized with 512 tetrahedrons. Thus, the flux density field B(x) and the watervelocity u(x), when evaluated outside the spheres, i.e. inside the water, do not suffer ofsingularities or discontinuities and are continuous and differentiable functions of thepoint x. This complies well with the numerical integration of particle’s trajectorieswhere the gradients of the fields are needed in order to evaluate the forces. Thedistributions of magnetic flux density on the input, output and middle y-sections andon the middle z-section of the elementary cell are shown in Figure 4, for an externalz-directed uniform field of 100 mT. The maximum values of the magnetic flux densityare obtained near the tangency points among the upper and lower spheres. Thedistributions of water velocity on the lower, upper, middle z-sections and on the middley-section of the elementary cell are shown in Figure 5, for an average y-directed velocityof 0.16 m/s. As expected, the water velocity field is nil on the spheres’ surfaces, inparticular at the tangency points. As shown in Figures 4 and 5 the fields B and u arefully 3D; moreover their distributions on opposite faces of the cell are geometricallysimilar but reversed. The available symmetries (reflections of the components of fluxdensity and water velocity fields in the planes orthogonal to the coordinate axesthrough the vertices) allow reconstructing the fields in a larger domain, if needed.

The trajectory of each particles’ aggregate is assumed to be independent from all theothers. It is obtained by integrating numerically the dynamic motion equations wherethe effects of the surrounding fluid, the magnetic field, the constraints due to the filter

Figure 3.Spheres filterelementary cell

(a) (b)

Notes: (a) Steel; (b) water

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geometry and the thermal fluctuations are taken into account, as follows:

dxp

dt¼ vp

mpdvp

dt¼ Fmag þ Fdrag þ Fadd:m þ F lift þ Fgrad:p þ Fth þ Fcoll

8<: ð1Þ

where xp is the time-dependent position of the particles’ aggregate, vp thetime-dependent velocity of the particles’ aggregate and mp is its mass. Among theconsidered forces, described in the following, the leading ones are the drag force (Fdrag)and the magnetic force (Fmag).

The force due to the interaction with the surrounding fluid is the sum of differentterms, i.e. drag, added mass, Saffman’s lift and pressure gradient (Meng andVan der Geld, 1991; Clift et al., 2005). The drag force is evaluated in the following form:

Figure 4.Magnetic flux density fielddistributions on the input(a) output (b) and middle(c) y-sections and on the

middle (d) z-section of theelementary cell

(a) (b)

(c) (d)

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Fdrag ¼ 2SprwCD

2jvp 2 uðxpÞjðvp 2 uðxpÞÞ ð2Þ

where Sp is the aggregate cross section and rw the water density. CD is the dragcoefficient, depending on the relative Reynolds number, defined asRep ¼ rwjvp 2 ujdp=h, where dp is the aggregates’ diameter and h the waterdynamic viscosity. The Schiller-Nauman CD correlation for smooth spherical particles,which recover the Stokes’ law in the limit of small relative Reynolds number, is used(Clift et al., 2005).

The added mass force, i.e. the force required to accelerate the water surrounding theparticle, is considered in the following form (Meng and Van der Geld, 1991):

Fadd:m ¼ 2Vprw

2

dvp

dt2 vp ·7uðxpÞ

ð3Þ

Figure 5.Water velocity fielddistributions on the lower(a), upper (b), middle (c)z-sections and on themiddle (d) y-section of theelementary cell

(a) (b)

(c) (d)

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where Vp is the aggregate volume, and the first term in the parenthesis is moved in theleft hand side of equation (1) for the numerical integration. The spatial derivatives arediscretised with finite-differences using dp as step size, centred in xp.

The expression for the Saffman’s lift force used in equation (1), which is valid forsmall particle Reynolds number, is taken from (Li and Ahmadi, 1992):

F lift ¼ 2KVp

dp

ðhrwÞ1=2

ðD : DÞ1=4D · ðuðxpÞ2 vpÞ ð4Þ

where K ¼ 2.594 is the constant coefficient of Saffman’s lift force and the deformationtensor D is defined as Dij ¼ (›ui/›xj þ ›uj/›xi)/2 with i, j ¼ 1, 2, 3. (Note that thedeformation tensor is half of the shear rate gamma dot.) The double dot defines thesummation on both indices of the tensor, i.e. D:D ¼ Sij Dji Dij. The pressure gradientforce is considered in the following form (Meng and Van der Geld, 1991):

Fgrad:p ¼ Vpðrwvp ·7uðxpÞ2 h72uðxpÞÞ ð5Þ

The second order derivatives are discretised using a centred-difference approximationwith dp as step size, centred in xp.

The magnetic force Fmag is evaluated taking the scalar product of the magneticmoment of the particles’ aggregate times the spatial gradient of the magnetic fluxdensity field applied to the particle (Mariani et al., 2010), as follows:

Fmag ¼ VpMpðBÞ ·7BðxpÞ ð6Þ

The magnetization Mp of the particles’ aggregates is the function of the applied field Bshown in Figure 2 (note that the magnetization is within the nonlinear range for setupno. 2). In evaluating B, the contribution due to the magnetic moments of all the otherparticles is neglected with respect to the fields generated by the external permanentsmagnets and the steel spheres.

The force Fth related to the thermal fluctuations can be modelled as an isotropicGaussian random process with zero mean and constant variance (www.sharcnet.ca/Software/Fluent12/pdf/th/flth.pdf). In order to simplify the calculation the thermalforce is formally time-integrated and subtracted to the particle momentum. Thus, theparticle velocity is written as a sum of an average term and an isotropic thermalfluctuation, as follows:

vp ¼ kvplþ uth ð7Þ

The standard deviation of the resulting thermal velocity isffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið3kT=mpÞ

p, where k is the

Boltzmann constant and T the room temperature. The components of the thermalfluctuation are evaluated at the beginning of each time step of integration ofequation (1) using pseudo-random numbers (Fishman, 1990). This allows the use of adeterministic fifth order Runge-Kutta method for the integration of equation (1). At theconsidered mass flow rates the thermal kinetic energy 3kT/2 is negligible with respectto the kinetic energy of the particles’ aggregate mp , vp .

2/2. Thus, the randomizingeffects of Brownian motion at room temperature are negligible for the aggregates inthe water stream. However, in the capture regions, which are near the tangency points

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among spheres, the fluid is almost at rest and the thermal fluctuations play a roleagainst the particle retention.

Finally, in order to take into account the collisions between particles and spheres, theconstraints force Fcoll is considered. This force acts only when the distance between theaggregate centre and the nearest sphere surface is lower then half of the aggregate diameterdp. The breaking of the aggregates during collisions is possible, but this is not consideredsince it would require the modelling of the interactions between the hydrophobic andmagnetic forces that stabilize the aggregate. Thus, only elastic collisions are considered.

Figure 6 shows some of the trajectories in the elementary cell as seen from twodifferent viewpoints where one of the octants has been removed for easing thevisualization. The particles’ starting positions are calculated applying equation (1) to azero flux density field cell with a uniform input distribution. The number of trajectoriesconsidered in each run is about 400. It can be seen that the particles tend to move nearthe spheres surfaces. In particular, the tangency point among the spheres is the capturezone where the particles can stop. The trajectory calculation is stopped when theparticle exits the cell or its average velocity vanish. The CPU time required for thesimulation of one cell is about 16 h on CPU i7-2600@3.4 GHz (RAM 3.4 GB) excludingthe pre-processing time for the velocity and flux density fields definition.

The results obtained integrating equation (1) are summarized in Figure 7, where theelementary cell capture efficiency vs the capture parameter V is plotted. The captureefficiency s is defined as the ratio between the numbers of captured and enteringparticles, as follows:

s ¼Nparticles

input 2 Nparticlesoutput

Nparticlesinput

ð8Þ

The same definition applies also to the filter capture efficiency. The parameter V isdefined as the ratio between the estimated magnitudes of the magnetic force and dragforce (in the low velocity limit, i.e. Fdrag , 3p dp h u0) as follows:

Figure 6.Trajectories sample in theelementary cell as seenfrom two differentviewpoints (inlet sectionseen from above on theleft, outlet section seenfrom below on the right)where one of the octantshas been removed foreasing visualization

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V ¼d2pMpsxs;eff B0

36hu0dsð9Þ

where dp and Mps are the diameter and the saturation magnetization of the particles’aggregates, u0 the average fluid velocity, h the fluid dynamic viscosity, B0

the external flux density field, xs,eff the effective susceptibility of the steel spheres andds their diameter. The magnitude of the magnetic force used in equation (9) isFmag , (p dp

3/6)(Mps xs,eff B0/2)/ds. It is obtained assuming that a particle in the capturezone is fully magnetised. The local flux density field in the capture zone is estimated asxs,eff B0. A variation of the particle’ magnetic energy of the order Mps xs,eff B0/2 at adistance equal to the steel spheres diameter is considered.

The choice to use V as the capture parameter is clearly incomplete since there areother competing forces besides the drag and the magnetic ones. Therefore, there aredifferent possible sets of values for the system parameters that correspond to the samevalue of V, but lead to different capture efficiencies. The elementary cellcapture efficiency shown in Figure 7 is obtained averaging the different outcomes forsimilar V for about 100 sets of system parameters. All the parameters involved in thedefinition of V are varied. Also the fluid viscosity is varied, since a suspension has aneffective viscosity larger than the surrounding fluid (Landau and Lifshitz, 2011).Moreover, in certain cases there is evidence in ferrofluids of an increase of the viscositywith magnetic field (Odenbach and Stork, 1998).

In order to calculate the filters efficiencies (sf) from the elementary cell one (sc), eachfilter is assumed to consist of N subsequent layers with equal thickness, each made ofelementary cells, orthogonal to the filter axis. In this way the model is scalable andallows studying also larger devices. For each experimental setup the number of layersis evaluated as the ratio between the filter length and the cell side (18 for setup no. 1and 94 for setup no. 2). Assuming that all the cells are statistically independent, theparticle balance on the filter leads to the following relation between the filter captureefficiency and the cell one:

1 2 sf ¼ ð1 2 scÞN ð10Þ

Figure 7.Filters and elementary cellcapture efficiencies vs the

capture parameter V

0

10

20

30

40

50

60

70

80

90

100

–7.8 –7.6 –7.4 –7.2 –7.0 –6.8 –6.6

Log Ω

Cap

ture

Eff

icie

ncie

s [%

] Setup #1 numerical capture efficiency

Setup #2 numerical capture efficiencyElementary Cell numerical capture efficiency

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The filter capture efficiencies shown in Figure 7 are deduced from the cell one usingequation (10).

Figure 7 shows that the capture efficiency increases by increasing the captureparameter V; considering the definition of V given in equation (9), the increasing of themagnetic force against the drag obviously leads to an increase of the particlesretention. Thus, increasing the external field or the particles magnetization hasapproximately the same effect of reducing the average fluid velocity or viscosity. Theincrease of the particle’s aggregates diameter, which influence both magnetic and dragforce, leads to a more efficient capture. Finally, from equation (10) it can be deducedthat increasing the filter length, i.e. the number of layers, increases the overall captureefficiency. In fact Figure 7 shows that experimental setup no. 2, which is longer thanno. 1, has a higher capture efficiency. Anyway in both cases the thinner fraction of thepowder is weakly captured.

The calculated capture efficiency can be used to evaluate the time evolution of theMAC concentration in the system, as follows. The mass balance of the particles withsimilar diameters, labelled populations, leads to the following equation:

dðCkV Þ ¼ 2Ckqdt þ ð1 2 sf ;kÞCkqdt ð11Þ

where Ck is the particle’s concentration for population k made of MAC particles withsimilar diameter, i.e. each of the particles’ fractions corresponding to the bars inFigure 1, V is the system volume and q is the volume flow rate. sf,k is the filteringefficiency for population k, deduced from Figure 7. Solving equation (11) leads toexponential time decay for each population:

CkðtÞ ¼ Ckð0Þexpð2sf ;kqt=V Þ ð12Þ

where the initial concentration Ck(0) for population k is deduced from the experimentaldistribution shown in Figure 1. Eventually, the total MAC concentration at any giventime is obtained summing up the concentration for all the populations, as follows:

CMACðtÞ ¼k

XCkðtÞ ð13Þ

5. Experimental results and discussion5.1 Filter model validationA turbidity meter is used to evaluate the MAC concentration in the systems, using aturbidity-concentration correlation curve. Figures 8 and 9 show the experimental MACresidual for setups nos 1 and 2, respectively, defined as:

Residual ð%Þ ¼Cr

C0£ 100 ð14Þ

where C0 and Cr are the initial and the residual MAC concentrations, i.e. before andafter the filtration. Figure 8 reports the results obtained for setup no. 1, showing thatthe experimental removal of MAC after 10 min filtration is 93 ^ 6 percent. Theresidual is nearly constant after 5 min of filtration. Figure 9 reports the same results forsetup no. 2. The experimental removal of MAC after 10 min filtration is 98 ^ 2 percent.

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The removal is very fast in the first 2 min of filtration and than slowly decreasing. Inboth cases filtration without external field, i.e. mechanical filtration, leads to worse andspread results; the effect of the magnetic flux density field on the filter’s performancecan be clearly seen since without external field the MAC residual is much larger.The relatively small capture obtained with the mechanical filtration may be due to theresidual magnetization of the spheres, which were reused from previous experiments.

Figures 8 and 9 show the time dependence of the residuals calculated usingequations (13) and (14). The error bars are obtained considering a mass redistribution up

Figure 9.Comparison between the

experimental andnumerical residuals

during the magneticfiltration in setup no. 2

0.01

0.1

1

10

100

0 5 10 15 20

Time [min]

Res

idua

l MA

C [

%]

Mechanical filtration setup #2 experimental resultsMagnetic filtration setup #2 experimental resultsMagnetic filtration setup #2 numerical results

Note: The filled dots show the residual during the mechanicalfiltration in setup no. 2, i.e. without applied field

Figure 8.Comparison between the

experimental andnumerical residuals

during the magneticfiltration in setup no. 1

0.1

1

10

100

0 5 10 15 20

Time [min]

Res

idua

l MA

C [

%]

Mechanical filtration setup #1 experimental results

Magnetic filtration setup #1 experimental results

Magnetic filtration setup #1 numerical results

Note: The filled dots show the residual during the mechanicalfiltration in setup no. 1, i.e. without applied field

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to 4 percent of the powder in the populations of particles with diameter lower than 3mm.This can be justified considering the ultrasonic washing applied after MAC addition tothe pollutant-water samples. Another possibility of redistribution can be the breaking ofthe aggregates during filtration because of collision with the spheres. The overallcomparison for both experimental setups is satisfying but the correspondence is betterfor setup no. 2. This may be due to the larger number of spheres constituting the filter insetup no. 2 with respect to no. 1. In fact in setup no. 1 the possible positioning errors whilerealizing the filter itself, the larger non uniformity of the applied field and the largerfraction of spheres placed on the filter surface are all source of variability on the results(as shown by the larger error bars of Figure 8 with respect to Figure 9).

The experimental results and the numerical ones shown in Figure 9 well agree at thebeginning of the filtration. As shown in Figure 7 the capture efficiency of setup no. 2for all the particles with the diameter larger than about 0.5mm (corresponding to logV ø 2 7.6) is near 100 percent. In this case equation (12) shows that the initial slope ofthe MAC residual depends only from the ratio between flow rate and system volume.For what concern the time behaviour of the filter after 10 min, it can be seen that setupno. 2 shows a weak decrease of the MAC residual that is not present in setup no. 1. Thiscan be explained since the setup no. 2 has larger capture efficiency than no. 1 for thethinner fraction of the powder, as shown in Figure 7.

5.2 Surfactants adsorptionIn order to check the applicability of the proposed process to water treatment, theremoval of different surfactants is tested. Table III reports the name, CAS number andmolecular formula of the tested surfactants; SDS and Triton X-100 were purchased bySigma-Aldrich Group and Kemfluid EQ18 from Biochimica S.p.A.

The initial and final concentrations of the surfactants are measured by reaction withdyes using a Hach-Lange spectrophotometer Odyssey DR 2500. In order to evaluate theconcentration a calibration of the spectrophotometer, based on the reactions of the specificindicator-dyes (Table III) with the surfactants, was carried out before the experiments.Since the main purpose of this research is to evaluate the applicability of magnetic

Surfactant Name/CAS number/molecular formula Indicator dye

Anionic SDS Methylene blue (MB)[Sodium dodecyl sulphate]CAS number 151-21-3Molecular formula NaC12H25SO4

Cationic Kemfluid EQ18 Cetyltrimethylammoniumbromide (CTAB)[Bis-(acyloxyethyl)-hydroxyethyl-methylammonia-

methylsulphate]CAS number 91995-81-2Molecular formula SO4CH3[(C4H7O3)2NC3H8O]

Non ionic Triton X-100 Tetrabromophenolphthaleinethyl ester (TBPE)[polyethylene glycol p-(1,1,3,3-tetramethylbutyl)-phenyl

ether]CAS number 9002-93-1Molecular formula C14H22O (C2H4O)n (n ¼ 9 2 10)

Table III.Tested surfactants andrelative indicator dyes

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separation to a municipal wastewater treatment outflow, different values of the initialconcentrations of surfactant have been chosen to simulate real situations (4, 2 and 1 mg/l).Each test start with the generation of the sample by mixing surfactants with distilled water(autostill WG222S Yamato Scientific). Then, the concentration of surfactant is measuredwith the corresponding spectro-photometric method. The initial sample is partitioned intofive equal jars and MAC are added. Each subsample is first mixed for 30 min with amagnetic stirrer (Masuda SM-60N, speed 2) to allow the adsorption of surfactant on thepowder and then the MAC separation step is carried out using the experimental setup no. 1.Finally, after a 10 min filtration, the concentration of the surfactant remaining in thetreated water is measured through the same spectro-photometric method.

The results are reported in terms of residual defined using equation (14), where C0

and Cr are the initial and the residual surfactant concentrations in the solutions.In Figures 10-12 the residual of each surfactant is plotted as a function of theconcentration of powder used. Figures 10 and 11 show the behaviour of the non ionicsurfactant Triton X-100 and the anionic surfactant SDS, respectively. Regardless of theinitial concentration it is possible to capture about 97 ^ 3 percent of the surfactantswith 0.1 g/l of MAC. Smaller concentrations of surfactants are easier to remove.Figure 12 shows the behaviour of the cationic surfactant Kemfluid EQ18. For all the

Figure 10.Residual of Triton X-100after adsorption on MACand magnetic separation

TRITON X-100Initial concentrations

0

10

20

30

40

50

60

70

80

90

100

0.01 0.1 1

MAC concentration [g/l]

Res

idua

l sur

fact

ant [

%]

1 mg/l

2 mg/l

4 mg/l

0.03 0.05 0.5

Figure 11.Residual of SDS after

adsorption on MAC andmagnetic separation

SDSInitial concentrations

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0.01 0.1 1

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idua

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ant [

%]

1 mg/l

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4 mg/l

0.03 0.05 0.5

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initial concentrations it is possible to capture about 98 ^ 2 percent of the surfactantwith 0.5 g/l of MAC. Smaller concentrations seem more difficult to remove.The reproducibility of the data was checked doing three times all the tests. Theadsorption of all surfactants leads to concentration below the 0.5 mg/l limit for waterreuse in agriculture (according to Italian legislation), using at most 0.5 g/l of MAC.

Adsorption of a solute from a solution is influenced by several factors: the porosity andthe chemical nature of the solid surface, the nature of the components of the solution, theconcentration of the solution, salts and molecules in the aqueous phase that can compete foradsorption sites, the pH of the solution that determines the electric charge of the solidsurface (Bansal and Goyal, 2005). Because of MAC composition the predominantsurfactants adsorbents are the porous AC; they mainly adsorb because of hydrophobicinteraction between the surfactant tail and the MAC surface and by hydrogen bonding(Gonzalez-Garcia et al., 2004; Soria-Sanchez et al., 2010). The results achieved suggest thepredominance of hydrophobic interactions over all. The pH conditions are less importantfor the capture. In fact Triton X-100, due to the short hydrophobic tail and the absence of acharge that can compete for the adsorption, is the surfactant that achieves the best removal.

6. ConclusionsThis paper reports a sustainable process for the treatment of an urban wastewateroutflow aimed to reduce pollutants concentrations near to the back ground levels or,at least, below the limits allowed by law for a reuse in agriculture. The consideredprocess uses MAC to combine the well known absorbent capacity of AC with themagnetic and catalytic properties of magnetite. The process consists of two phases: firstthe MAC powder is added to the pollutant-water solution, with the aim to adsorb thepollutant, and second the suspension is cleaned passing through a steel spheresmagnetic filter that captures the powder. Modelling one elementary cell of the FCC latticecreated by the spheres allowed to deduce the capture efficiency of a filter by scaling up.Two different experimental devices were manufactured to test the model. Theexperimental values obtained on the capture efficiency for the MAC in the filters werewell comparable with the results obtained from numerical modelling and in 10 minfiltration the MAC removal was above 90 percent for both setups. In order to checkthe applicability of the process, the adsorption and separation of different surfactant

Figure 12.Residual of KemfluidEQ18 after adsorption onMAC andmagnetic separation

KEMFLUID EQ18Initial concentrations

0

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0.01 0.1 1

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ant [

%]

0.03 0.05 0.5

1 mg/l

2 mg/l

4 mg/l

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were tested. Starting with concentration in the urban wastewater range, values belowthe 0.5 mg/l limit for water reuse in agriculture (according to Italian legislation) wereachieved using at most 0.5 g/l of MAC.

References

Abbasov, T. (2007), “Theoretical magnetic filtration with magnetized granular beds: basicprinciples and filter performance”, China Particuology, Vol. 5, pp. 71-83.

Bansal, R.C. and Goyal, M. (2005), Activated Carbon Adsorption, CRC Press, Boca Raton, FL.

Borghi, C.C., Fabbri, M., Fiorini, M., Mancini, M. and Ribani, P.L. (2011), “Magnetic removal ofsurfactants from wastewater using micrometric iron oxide powders”, Separation andPurification Technology, Vol. 83, pp. 180-188.

Clift, R., Grace, J.R. and Weber, M.E. (2005), Bubbles, Drops, and Particles, Academic Press,New York, NY, pp. 110-112.

Do, M.H., Phan, N.H., Nguyen, T.D., Pham, T.T.S., Nguyen, V.K., Vu, T.T.T. and Nguyen, T.K.P.(2011), “Activated carbon/Fe3O4 nanoparticle composite: fabrication, methyl orange removaland regeneration by hydrogen peroxide”, Chemosphere, Vol. 85, pp. 1269-1276.

Duncan, R.R., Carrow, R.N. and Michael, T. (2008), Turfgrass and Landscape Irrigation WaterQuality Assessment and Management, CRC Press, Boca Raton, FL, pp. 13-38.

Fiorillo, F. (2004), Measurements and Characterization of Magnetic Materials, Elsevier-AcademicPress, Amsterdam, pp. 9-16.

Fishman, G.S. (1990), “Multiplicative congruential random number generators with modulus2 * *b: an exhaustive analysis for b¼32 and a partial analysis for b¼48”, Mathematics ofComputation, Vol. 189, pp. 331-344.

Gaspard, S., Durimel, A., Chaker Ncibi, M. and Altenor, S. (2008), “Activated carbon inwaste recycling, air and water treatment, and energy storage”, in Goosen, M.F.A., Schaffner,F.C., Laboy-Nieves, E.N. and Abdelhadi, A.H. (Eds), Environmental Management,Sustainable Development and Human Health, CRC Press, Boca Raton, FL, pp. 441-459.

Gonzalez-Garcia, C.M., Gonzalez-Martın, M.L., Gonzalez, J.F., Sabio, E., Ramiro, A. and Ganan, J.(2004), “Nonionic surfactants adsorption onto activated carbon: influence of the polar chainlength”, Powder Technology, Vol. 148, pp. 32-37.

Hu, J., Lo, I.M.C. and Chen, G. (2007), “Comparative study of various magnetic nanoparticles forCr(VI) removal”, Separation and Purification Technology, Vol. 56, pp. 249-256.

Jia, Z., Peng, K., Li, Y. and Zhu, R. (2011), “Preparation and application of novel magneticallyseparable g-Fe2O3/activated carbon sphere adsorbent”, Materials Science and Engineering:B, Vol. 176, pp. 861-865.

Landau, L.D. and Lifshitz, E.M. (2011), Fluid Mechanics, Elsevier, Amsterdam, pp. 73-75.

Li, A. and Ahmadi, G. (1992), “Dispersion and deposition of spherical particles from pointsources in a turbulent channel flow”, Aerosol Science and Technology, Vol. 16, pp. 209-226.

Mariani, G., Fabbri, M., Negrini, F. and Ribani, P.L. (2009), “High-gradient magnetic separationof micro-pollutant from wastewaters”, La Houille Blanche, Vol. 6, pp. 109-117.

Mariani, G., Fabbri, M., Negrini, F. and Ribani, P.L. (2010), “High-gradient magnetic separationof pollutant from wastewaters using permanent magnets”, Separation and PurificationTechnology, Vol. 72, pp. 147-155.

Meng, H. and Van der Geld, C.W.M. (1991), “Particles trajectory computations in steady nonuniform liquid flows”, Liquid Solid Flows: First ASME/JSME Fluids EngineeringConference, Portland, Oregon, pp. 183-193.

Magneticseparation

461

Mishima, F., Akiyama, Y. and Nishijima, S. (2010), “Research and development of magneticpurification system for used wash water of drum”, IEEE Transactions on AppliedSuperconductivity, Vol. 20, pp. 937-940.

Morandi, A., Fabbri, M. and Ribani, P.L. (2010), “A modified formulation of the volume integralequations method for 3D magnetostatics”, IEEE Transactions on Magnetics, Vol. 46,pp. 3848-3859.

Nassar, N.N. (2010), “Rapid removal and recovery of Pb(II) from wastewater by magneticnanoadsorbents”, Journal of Hazardous Materials, Vol. 184, pp. 538-546.

Nishijima, S. and Takeda, S. (2006), “Superconducting high gradient magnetic separation forpurification of wastewater from paper factory”, IEEE Transactions on AppliedSuperconductivity, Vol. 16, pp. 1142-1145.

Odenbach, S. and Stork, H. (1998), “Shear dependence of field-induced contributions to theviscosity of magnetic fluids at low shear rates”, Journal of Magnetism and MagneticMaterials, Vol. 183, pp. 188-194.

Rossier, M., Schreier, M., Krebs, U., Aeschlimann, B., Fuhrer, R., Zeltner, M., Grass, R.N.,Gunther, D. and Stark, W.J. (2012), “Scaling up magnetic filtration and extraction to the tonper hour scale using carbon coated metal nanoparticles”, Separation and PurificationTechnology, Vol. 96, pp. 68-74.

Shen, Y.F., Tang, J., Nie, Z.H., Wang, Y.D., Ren, Y. and Zuo, L. (2009), “Preparation andapplication of magnetic Fe3O4 nanoparticles for wastewater purification”, Separation andPurification Technology, Vol. 68, pp. 312-319.

Soria-Sanchez, M., Maroto-Valiente, A., Guerrero-Ruiz, A. and Nevskaia, D.M. (2010),“Adsorption of non-ionic surfactants on hydrophobic and hydrophilic carbon surfaces”,Journal of Colloid and Interface Science, Vol. 343, pp. 194-199.

Svoboda, J. (1987), Magnetic Methods for the Treatment of Minerals, Elsevier, Amsterdam.

Corresponding authorMassimo Fabbri can be contacted at: massimo.fabbri@unibo.it

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