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On the measurement of magnetophoretic mobilities
Colloids and Strrfacer, 7 (1963) 136-146 Elsevier Science Publishers 3.V.. Amsterdam
ON THE MEASUREMENT
LAURtER
L. SCHRAhlM
Syncrude Canada Ltd.. (Canada) (Received
28 October
-
135
Printed in The Netherlands
OF MAGNETOPHORETIC
MOBILITIES
and BRUCE W. CLARK
Research
Department.
1982; accepted
RO.
Ilox 5790.
Edmonton,
in final form 17 February
Atbcrta
TGC dIG3
1983)
ABSTRACT’ A method and apparatus have been dcvclrped which provide a means for Ihc mcasurement of parlicle or droplet motions induced in a Ruid medium induced hy an applied magnolic field. Such motions nrc observed for particles which have a magnetic rusceptibiliLy; hence they am capable of phoretic (magntltophorcttc) motion. ~bSCrKI~ioJ~S of magnctile surpenduns indicalc thnt in dtlition to lha parlick magnclization, the megnclophoretic mal~ility is deprndcnt upon particle concentration, solution conditions, and the time cxpnsed ha soluLion (a@ine). The method is spplical~lc tu the detcrminalion or optimal sduLion coaditiom fm the magnetic rrmovd or rccovcry of mahy dispersed phnscs.
t NTIZODUCTION
Magnetic scparalion l~roccssus have long llcan usecl to scparatc netic
materials
from
a wiclo rang0 of feed materials.
With
strongly mag-
the dcvclopment
of
(IIGMS) tccl~nology, magnetic separation is now commonly used tr>isolntu weakly magnetic and/or vcr$ small parliclcs from the *uspending media. Applications of HGMS range from removing undesirable tnngfwtic particlcs from wast4zwatcr or coal, clay and other mineral processing streams to recovering desirable magnetic particles such as iron ore anrJ titanium minerals. The many applications of HGMS have been rcvicwcd elscwherc [l--3]. With the ability to influence tfw motion of very fine high
aadicnt
magnetic
separation
llarticlos, rolloiclal systems tecomc nmcnablc to HGhlS technology. White this technology is finding widespread applications, it requires careful optimization of mechanical and process l,aramctew Co ensure that the magnetic forces are
able to ovt:rcomc frictional, gravitational, and interparticle forces [ 2,3). In E1GMS a cannister is typically filled with a filamentary ferromagnetic matrix material and placed in a magnetic field. The cannister is then operated as a flow-through separator. High magnetic field gradients generated near the matrix filament surfaces exert strong forces which attract magnetic part.iclas to the surfaces where they can bc held. The fundamcntnl element to efficient operation lies in the relative rates of capture and escape of particles. While much work has been done on aspects of the various geometries, magnetic field
0166-6622/83/$03.00
0 1983
Elsevier Science Publishers
B.V.
.
136
strengths, matrix materials and matrix configuration, little is known about the mobitities of the particles in the suspending fluid. A number of studios of particle trajectories near a magnetized fiber have
been made to establish collision cross sections and the mechanism by which particles are deposited on the fibers [ 4-71. Such studies have tended to concentrate on the flow p&terns of pti-iclcs in, for example, a gas stream (41 or
pure water [S]. These methods suffer from a number of drawbacks in that t..le results are dependent upon the configuration of the particular apparatus and there is some difficulty in choosing the variables to be measured. ha addition, little if any account is taken of the effects of solution conditions and pzrticte interactions, To avoid some of them problems a method has been dcvctopcd which allows for the direct observation of part.icle and droplet magnctophoret-ic mobilities under a constant applied magnetic field gracticaat.The method provides a simple means for rapidly evaluating the effects of particle (droplet) nature, concentration and solution conditions, The results are immediately npplicablc to the optimization of process conditions as well as providing fundamental information which reftects the nature of the intcrfrwe. Tf fl?OHY
A pnrliclc suspended in a mcrlium to which a magnetic fictd is applied wilt be subjrx%xl to n magnelic force. In one dimension Ihis rorcc may hc espressect (see for example [ 2,8 1) ns Pbl
= V(Mp - lwhy)p(dD/dx)
(1)
end is positive as written for paramagnetic and ferromagnetic partictcs. Ilew I’ is the particle volume, Alp onrt fiifil nrc the particle and medium m;lgtwtiz* tions respcctiv4y, p is tbc particle density, and d8/ds is the magnetic field gradient at the locntion of the particle. fn gcncrat the particles wili either reduce or enhance thu mngnctiu field in their vicinily - the latter for pnmmngnctic nnct ferromagnetic particles. Due to this effort, n given particle wilt cxtwrience n touot .9ffeulivo field gradient which is different from the cxtcwnlly iti~>I>lid field gracilcnt by an amotmt A. The mngniturtc of this cffcct will dcpcnd upon the parUclc concentration nnrt fbc applied field gradient and may he cxprcsscd as A = ~(c)(dn/dx)
(2)
where NC) is some function of the particle concentration, ic force on a particle may be written as PA1 = V(Afp - RInf )P(dU/dx)(f
+ T(c))
c* The total magnet(3)
A t>iuC!le moving uncter the infhcn~c of magnetic forces will cspcricncc additional drag forces which oppose the motion. The viscous drag force eserted on a spherical particle can be csprcsscd as a function of the particle velocity r&t-ive to the medium (v) by Stokes’ law as
137 (4)
Fs = Gaqau q is the medium viscosity and a is the particle radius. Making use of the condition that
where
(5)
cFi=o
i
and rearranging we obtain from Eqs. (3) and (4) MdB/dx)=
W~P-MM)P~~+
(6)
f(c)ll(6nrlo)
the term v/(dB/dx) is the oxperimcntally accessible magnetophoretic mobility which we denote pnt. We will assume Mnl to be insignificant for ferromagnetic particles suspended in an aqueous medium. Here
St&
varw
‘A’
DETAIL
See
Fig. 1. Illustration scale).
of the magnctophoretic
CETAIL
mobility
‘A’
apparatus.
(Drawn
approximately
to
133 EXPdRIMENTAt
A sample of magnetite (Ferric-Ferrous Oxide, purified, black, Fisher wti used as received. A stock suspension of 0.200% (w/w) was pro pareci wit:1 deionized water_ From the stock suspension a series of suspensions of approximat&y 0.06% magnetite was prepared and adjusted to soluaion pH values in the range 6-11 with NaOH. After stable pH levels were obtained a series of suspension of concentrat-ions O,Ol~U.O60% (w/w) were prepared
Scientific)
which were diluted
propriata pH.
where necessary
with deionized
water adjusted
to the ap
Apparatus The experimental configuration for the mametophoretic mobility apparatus is shown in Fig. 1. The system consists of a modi&d Zeta Meter microelec-
Reterence
Points
for
Field
Strength
Measurements Fig. 2. (a) hjagnctic pole arrangement slrenglh mrasuremcnb 85 a function corresponds to point “a”.
and (b) rcfcrence points in one pcdc face for field of distance betv~een the magnet pohzs. The cell axis
139 trophoresis apparatus (Zeta Meter Inc., New York). This apparatus includes a vieting microscope fitted with an ocular reticule, a clear plexi$ass cell with etched reference lines, and an essentially darkfield illumination system, Other microscope and cell systems can be used in the came way. The poles of an electromagnet are arrangedat each end of the cell and aligned so as to produce a magnetic field gradient along the cell axis. In Fig. 2a the magnet pole dimensions are shown which compare with the cell dimensions of 13.8 cm (I) X 4 cm fw) X 1.6 cm (h) (excluding the reservoirs).The electromagnet was provided with DC power at 12 V and 3 A. A differential gaussmeter (Model 2000, Radio Frequency Labs, Boonton, NJ.) was used to measure thr(appHed magnetic field strength and field gradient as a function of distance along the cell axis and along positions parallel to the cell axis originat.ingfrom pole face reference positions shown in Fig. 2b. In
this figure Ihe cell axis corresponds t.o position “a”.
Mstance
From
Left Pole
(cm)
Fig. 3. Graph of rnagnelic field strenglh variation along the cell axis (-) and atong a line parallel to the cell axis (A) originating at the points shown in Fig. 2b as “a” and ‘Bc*‘, recpectiueay.
140
Procedure The apparatus described may be used to measure either electrophoretic or magnetophoretic m~bjlities. Electxophoretic measurements were made with normal precautSons using a direct voltage over distance method [9]_ The velocity of particles moving under the influence of a magnetic field aione were determined in an analogous manner by timing the travel of 40-50 particles over a distance of 160 m. Particles were tracked along the same plane as for dectrophoretic measurements at a distance of 9 cm from the “left” magnetic pole {see discussion below). The choice of 9 cm from one polo is somewhat arbitrary and arises out of the geometry of this particular experimental arrangcment. The use of a videotape recording system allowed for acquisition of the needed data in a short period of t.ime, enabling thermal overturn to be avoided. All measurements were performed at 25 f 2°C.
3
6
12
9
Distance From Left Pole
11 .5
km)
Fig. 4. Graph of magnetic field strength variation along the cell axis (*) and along lines paralld to the cell axis originating at the points shown in Pig. 2b as “a,” “b” (a) and “d” 10).
141 RESULTS
AND
DISCUSStON
The same viewing posilion (0.147 diameters from the wall) was employed for both types of mobility measurements. This choice is somewhat, arbitrary in
the magnetic case for which there is no clecbro-osmotic walls. The variation in magnetic field strengSh between
flow aiong the cell the poles is given in
Figs. 3 and 4 for positions parallel to the cell axis starting from the reference
points shown in Fig. 2b. At the viewing position used for mobility determinations, the applied field strength was 21.3 mT. The variation in magnetic field gradient is shown in Fig. 5 whew again curves a, b and d correspond to measurements made along paths parallel to the cell axis originating at the points s11ow11 in Fig. 2b. The magnetic field gradient at the viewing position was 2.7 mT cm-‘. As discussed above, the magnctophorctic mobility is evaluated as the observed velocity divided by the local applied magnetic field gradient. In the present case the average 6 pm diameter particles occasionally formed into ca. 20
16 2
I
I
Distance
From
12
9
6
3
Left
Polo
1
.5
(cm)
Fig. 5. Graph of magnetic field gradicmt variation along the celi axis (*) and along lines parallel to the cell axis originating at the pair ts shown in Fig. 2b as “a,*’ “b” (u) and “d”
(A’)’
142
40-60 pm length chains when magnetized. This did not appear to influence the disiribution of particle velocities and all aggregates were tracked quaMy. We observed a strong influence of sample age which did not appear to be strongly pH dependent on the magnetophoretic mobilities. This phenomenon will by discussed below. Because of the importance of ageing effects, data from a consistent sample age (69 d 2 days beyond initial dispersion in aqu*Dus solution) arc reported.
0
WE.6.
prtlsions.
I
I
I
0.2
I
6.4
I
I
0.6
Concentration 19/U Varhtiun
in nraenabphoretie
The solid
c~ruc
is that
motility with concentration described by Eq+ (8).
DC magnetite
in pI1 G sus-
The conccntr;rtion dependence of the magnetophoret-ic mobility is shown in Pig, 6 for suspensions at, pH 6. The marked concentration dcpendcnce shown ill this FihWre is not surprising in view of the ability of fcrromagnctic mabxial to ~nl~~n~c an applied magnetic field. Due to the complex nature of the field
enhancement, mobilitics are reported only as a function of the applied field. The particle magnetization (Mp) is obtained from the magnetophorctic mobi,iE ity at infinite dilutiolti (p~,~ = 0.12 cm2 S-* T-‘) 3s 1.6 A rnS kg--‘. In this cnsc the particles are at only t\vo percent of their saturation magnetization of &out EMA tn2 kg- I [ 10). The magnctophorctic mobility is seen to increase with rllagarrtitc conccntr3tion according to nn equation of the form f(c) = csp (??lC) - 1
(71
143
Est. error i
Fig:. 7. Variation magnetite.
of magnctophorctic
where m = 5.1 1 g-l.
mobility
with solution
pH for 0.4 g/l cuspcnsions
of
Equation (a) then becomes
PM = VMpp t?xp (NIC)/(GffrW) .
(8)
This equation is plotted in Fig. 6. The influoncc of soWion pfI on the magnctophorctic mobility of magnetite. particles is shown in Fig. 7. The corresponding variation in elcctrophoretic mobility of the particles is shown in Fig. 8. For magnetite suspensions, hydroxyl ions are potential detcrmir
I
L
I
9
7
11
PH
Fnr = VI& fit
-
filbl )dd~/~)(l
= Z3(c~/kT)‘[,(rra)
where
+ [(p+
+ f(c,
- fR)
+ p-)ckT/(l2rrqE~)]
191
~c~lwwf4(h’o~
(101
z = elcctroly te valence, p+, p_ = frictional consiants of dissolved ions, = comphx funotions of K fl from Overbmk [ 151, and fhf4 viscosity. r7 = solution While this equation, if included in the force balance, should successfully accoimt for any relaxation effects, it is found not to Ix significant for tllc prcsrtnt cnsc. Calculating zeta potentials from the electrophoretic data and solving Eq. (10) leads to a predicted reduction in magnctophorrttic mobility of at mast 2% over the pli range G-11; whereas, in fact, a reduction of 3096 was observed. 7%~ low predickd reduction arises from the fact that the ionic strength was not held constant. Thus the most highly charged particles (at pH 11) were in the highest ionic strength background (KLI - 260 due to pH adjustment). -
146
It is suggested that in the absence of additional drag forces, solution pH may have some influence on the particle magnetization, Mp. As noted above, the magnetophoret.ic mobilities were observed t.o increase with the time magnetic ~.articles were in contact with aqueous solution. The increase in mobility appears to result from particle rearrangements which increase the overall magnet ization of the particle aggregates. These observations are in agreement with those of Bate [ 101 for slightly larger (ca. 40 yrn diam.) sized multi-domain magnet.ite particle aggregates. Bate found that when the aggregates were dispersed in solution, the particles became susceptible to rearrangements which yielded an increased magnetic remanence. It is possible that solution pH has a bearing on such rearrangements due to the reaction of hydroxyl ions in which the outer surface of the particles are charged. CONCLWSlON
The procedure described in this study has several advantages which distinguish it from other techniques in common use. It is now possible to conveniently and rapidly evaluate the influence of solution conditions, particle or droplet nature and concentration on rnobilities in a magnetic field. The magnctophoretic mobility data provide fundamentat information as well as a means for optimization of magnetic separation processes by adjusting suspcnsion conditions. In determining magnctophorctic mobilitics, care must bc taken to specify the experimental conditions (concentration, pH, etc,) since particle interactions play a more significant, albeit less understood, role in determining this property than for examptc the electrophoretic mobility. ACKNOWLEDGEMENT
The authors arc grateful to Syncrude Canada Ltd, for permission to publish this paper.
REFERENCES I H.H. Kolm, IEEE Trans. hlagn., Meg-l 1 (197s) 1567. 2 J.A. Obetteuffer, IEEE Trans. hlagn., hYsg+lO (1974) 223. 3 J.A. Obertcuffer and 1. Wcchslcr, in Fine Particlcr Prowssing, Int. Sympos. Proe., 2 (1980), ~9. 1178-1216. 4 R,P. Treat and W.P. Lawsor., J. App!. Phys., SO (1979) 3596. 5 H. Hoffman, M. Neudel, H. Schewe and J. Rcfflc, Appl. Phys.. 24 (1981) 229. 6 K. Hay&i and S. Uchiyama, IEEE Trans. Magn., Mag-16 (1980) 827. 7 W.H. McNecse, P.C. Wankat and P.J. Fricdtaender, IEEE Trans. Magn.. hlag-16 (1980) 643. 8 EC. Stoner, Magnetism and Matter, Mcthuen, London, 1934,675 pp. 9 Zeta h¶eter Inc., Zeta Meter Manual, 3rd. ed.. Zeta Meter Inc.. New York. 1976, 139 pp. 10 0. Bate, in D.J. Craik (Ed.), Magnetic Oxides, Part 2, Wiley, New York, 1976, pp, 689-742.
11 R.A. Robinson and R.H. Stokes, Electrolyte Sohttionr, 2nd ed., Butterworthr, tondon, 1959, p. 333ff. 12 P. Kruus, Liquids and Solutionc, Dekker, New York, 1977, p. 141ff. 13 R.J. Hunter, Zeta Potential in Colloid Science, Academic Rrets, New York, 1981, pp. s9-124. 14 J_Th,8. Cherbeek and P.H. Wersema, fn M. Bier (Ed.), EieeLrophoresTsTheory, Methods and Applimatlons, Vol. II, Academic Press, New York, 1967, pp. l-52. IS J.‘I%.CL Overbeek, in H. Mark and E.J.\Y. Verwey (EEL), Advances in Colloid Science, VoL III. Intcrscience, New York, 1950. pp. 97-135.
ON THE MEASUREMENT
LAURtER
L. SCHRAhlM
Syncrude Canada Ltd.. (Canada) (Received
28 October
-
135
Printed in The Netherlands
OF MAGNETOPHORETIC
MOBILITIES
and BRUCE W. CLARK
Research
Department.
1982; accepted
RO.
Ilox 5790.
Edmonton,
in final form 17 February
Atbcrta
TGC dIG3
1983)
ABSTRACT’ A method and apparatus have been dcvclrped which provide a means for Ihc mcasurement of parlicle or droplet motions induced in a Ruid medium induced hy an applied magnolic field. Such motions nrc observed for particles which have a magnetic rusceptibiliLy; hence they am capable of phoretic (magntltophorcttc) motion. ~bSCrKI~ioJ~S of magnctile surpenduns indicalc thnt in dtlition to lha parlick magnclization, the megnclophoretic mal~ility is deprndcnt upon particle concentration, solution conditions, and the time cxpnsed ha soluLion (a@ine). The method is spplical~lc tu the detcrminalion or optimal sduLion coaditiom fm the magnetic rrmovd or rccovcry of mahy dispersed phnscs.
t NTIZODUCTION
Magnetic scparalion l~roccssus have long llcan usecl to scparatc netic
materials
from
a wiclo rang0 of feed materials.
With
strongly mag-
the dcvclopment
of
(IIGMS) tccl~nology, magnetic separation is now commonly used tr>isolntu weakly magnetic and/or vcr$ small parliclcs from the *uspending media. Applications of HGMS range from removing undesirable tnngfwtic particlcs from wast4zwatcr or coal, clay and other mineral processing streams to recovering desirable magnetic particles such as iron ore anrJ titanium minerals. The many applications of HGMS have been rcvicwcd elscwherc [l--3]. With the ability to influence tfw motion of very fine high
aadicnt
magnetic
separation
llarticlos, rolloiclal systems tecomc nmcnablc to HGhlS technology. White this technology is finding widespread applications, it requires careful optimization of mechanical and process l,aramctew Co ensure that the magnetic forces are
able to ovt:rcomc frictional, gravitational, and interparticle forces [ 2,3). In E1GMS a cannister is typically filled with a filamentary ferromagnetic matrix material and placed in a magnetic field. The cannister is then operated as a flow-through separator. High magnetic field gradients generated near the matrix filament surfaces exert strong forces which attract magnetic part.iclas to the surfaces where they can bc held. The fundamcntnl element to efficient operation lies in the relative rates of capture and escape of particles. While much work has been done on aspects of the various geometries, magnetic field
0166-6622/83/$03.00
0 1983
Elsevier Science Publishers
B.V.
.
136
strengths, matrix materials and matrix configuration, little is known about the mobitities of the particles in the suspending fluid. A number of studios of particle trajectories near a magnetized fiber have
been made to establish collision cross sections and the mechanism by which particles are deposited on the fibers [ 4-71. Such studies have tended to concentrate on the flow p&terns of pti-iclcs in, for example, a gas stream (41 or
pure water [S]. These methods suffer from a number of drawbacks in that t..le results are dependent upon the configuration of the particular apparatus and there is some difficulty in choosing the variables to be measured. ha addition, little if any account is taken of the effects of solution conditions and pzrticte interactions, To avoid some of them problems a method has been dcvctopcd which allows for the direct observation of part.icle and droplet magnctophoret-ic mobilities under a constant applied magnetic field gracticaat.The method provides a simple means for rapidly evaluating the effects of particle (droplet) nature, concentration and solution conditions, The results are immediately npplicablc to the optimization of process conditions as well as providing fundamental information which reftects the nature of the intcrfrwe. Tf fl?OHY
A pnrliclc suspended in a mcrlium to which a magnetic fictd is applied wilt be subjrx%xl to n magnelic force. In one dimension Ihis rorcc may hc espressect (see for example [ 2,8 1) ns Pbl
= V(Mp - lwhy)p(dD/dx)
(1)
end is positive as written for paramagnetic and ferromagnetic partictcs. Ilew I’ is the particle volume, Alp onrt fiifil nrc the particle and medium m;lgtwtiz* tions respcctiv4y, p is tbc particle density, and d8/ds is the magnetic field gradient at the locntion of the particle. fn gcncrat the particles wili either reduce or enhance thu mngnctiu field in their vicinily - the latter for pnmmngnctic nnct ferromagnetic particles. Due to this effort, n given particle wilt cxtwrience n touot .9ffeulivo field gradient which is different from the cxtcwnlly iti~>I>lid field gracilcnt by an amotmt A. The mngniturtc of this cffcct will dcpcnd upon the parUclc concentration nnrt fbc applied field gradient and may he cxprcsscd as A = ~(c)(dn/dx)
(2)
where NC) is some function of the particle concentration, ic force on a particle may be written as PA1 = V(Afp - RInf )P(dU/dx)(f
+ T(c))
c* The total magnet(3)
A t>iuC!le moving uncter the infhcn~c of magnetic forces will cspcricncc additional drag forces which oppose the motion. The viscous drag force eserted on a spherical particle can be csprcsscd as a function of the particle velocity r&t-ive to the medium (v) by Stokes’ law as
137 (4)
Fs = Gaqau q is the medium viscosity and a is the particle radius. Making use of the condition that
where
(5)
cFi=o
i
and rearranging we obtain from Eqs. (3) and (4) MdB/dx)=
W~P-MM)P~~+
(6)
f(c)ll(6nrlo)
the term v/(dB/dx) is the oxperimcntally accessible magnetophoretic mobility which we denote pnt. We will assume Mnl to be insignificant for ferromagnetic particles suspended in an aqueous medium. Here
St&
varw
‘A’
DETAIL
See
Fig. 1. Illustration scale).
of the magnctophoretic
CETAIL
mobility
‘A’
apparatus.
(Drawn
approximately
to
133 EXPdRIMENTAt
A sample of magnetite (Ferric-Ferrous Oxide, purified, black, Fisher wti used as received. A stock suspension of 0.200% (w/w) was pro pareci wit:1 deionized water_ From the stock suspension a series of suspensions of approximat&y 0.06% magnetite was prepared and adjusted to soluaion pH values in the range 6-11 with NaOH. After stable pH levels were obtained a series of suspension of concentrat-ions O,Ol~U.O60% (w/w) were prepared
Scientific)
which were diluted
propriata pH.
where necessary
with deionized
water adjusted
to the ap
Apparatus The experimental configuration for the mametophoretic mobility apparatus is shown in Fig. 1. The system consists of a modi&d Zeta Meter microelec-
Reterence
Points
for
Field
Strength
Measurements Fig. 2. (a) hjagnctic pole arrangement slrenglh mrasuremcnb 85 a function corresponds to point “a”.
and (b) rcfcrence points in one pcdc face for field of distance betv~een the magnet pohzs. The cell axis
139 trophoresis apparatus (Zeta Meter Inc., New York). This apparatus includes a vieting microscope fitted with an ocular reticule, a clear plexi$ass cell with etched reference lines, and an essentially darkfield illumination system, Other microscope and cell systems can be used in the came way. The poles of an electromagnet are arrangedat each end of the cell and aligned so as to produce a magnetic field gradient along the cell axis. In Fig. 2a the magnet pole dimensions are shown which compare with the cell dimensions of 13.8 cm (I) X 4 cm fw) X 1.6 cm (h) (excluding the reservoirs).The electromagnet was provided with DC power at 12 V and 3 A. A differential gaussmeter (Model 2000, Radio Frequency Labs, Boonton, NJ.) was used to measure thr(appHed magnetic field strength and field gradient as a function of distance along the cell axis and along positions parallel to the cell axis originat.ingfrom pole face reference positions shown in Fig. 2b. In
this figure Ihe cell axis corresponds t.o position “a”.
Mstance
From
Left Pole
(cm)
Fig. 3. Graph of rnagnelic field strenglh variation along the cell axis (-) and atong a line parallel to the cell axis (A) originating at the points shown in Fig. 2b as “a” and ‘Bc*‘, recpectiueay.
140
Procedure The apparatus described may be used to measure either electrophoretic or magnetophoretic m~bjlities. Electxophoretic measurements were made with normal precautSons using a direct voltage over distance method [9]_ The velocity of particles moving under the influence of a magnetic field aione were determined in an analogous manner by timing the travel of 40-50 particles over a distance of 160 m. Particles were tracked along the same plane as for dectrophoretic measurements at a distance of 9 cm from the “left” magnetic pole {see discussion below). The choice of 9 cm from one polo is somewhat arbitrary and arises out of the geometry of this particular experimental arrangcment. The use of a videotape recording system allowed for acquisition of the needed data in a short period of t.ime, enabling thermal overturn to be avoided. All measurements were performed at 25 f 2°C.
3
6
12
9
Distance From Left Pole
11 .5
km)
Fig. 4. Graph of magnetic field strength variation along the cell axis (*) and along lines paralld to the cell axis originating at the points shown in Pig. 2b as “a,” “b” (a) and “d” 10).
141 RESULTS
AND
DISCUSStON
The same viewing posilion (0.147 diameters from the wall) was employed for both types of mobility measurements. This choice is somewhat, arbitrary in
the magnetic case for which there is no clecbro-osmotic walls. The variation in magnetic field strengSh between
flow aiong the cell the poles is given in
Figs. 3 and 4 for positions parallel to the cell axis starting from the reference
points shown in Fig. 2b. At the viewing position used for mobility determinations, the applied field strength was 21.3 mT. The variation in magnetic field gradient is shown in Fig. 5 whew again curves a, b and d correspond to measurements made along paths parallel to the cell axis originating at the points s11ow11 in Fig. 2b. The magnetic field gradient at the viewing position was 2.7 mT cm-‘. As discussed above, the magnctophorctic mobility is evaluated as the observed velocity divided by the local applied magnetic field gradient. In the present case the average 6 pm diameter particles occasionally formed into ca. 20
16 2
I
I
Distance
From
12
9
6
3
Left
Polo
1
.5
(cm)
Fig. 5. Graph of magnetic field gradicmt variation along the celi axis (*) and along lines parallel to the cell axis originating at the pair ts shown in Fig. 2b as “a,*’ “b” (u) and “d”
(A’)’
142
40-60 pm length chains when magnetized. This did not appear to influence the disiribution of particle velocities and all aggregates were tracked quaMy. We observed a strong influence of sample age which did not appear to be strongly pH dependent on the magnetophoretic mobilities. This phenomenon will by discussed below. Because of the importance of ageing effects, data from a consistent sample age (69 d 2 days beyond initial dispersion in aqu*Dus solution) arc reported.
0
WE.6.
prtlsions.
I
I
I
0.2
I
6.4
I
I
0.6
Concentration 19/U Varhtiun
in nraenabphoretie
The solid
c~ruc
is that
motility with concentration described by Eq+ (8).
DC magnetite
in pI1 G sus-
The conccntr;rtion dependence of the magnetophoret-ic mobility is shown in Pig, 6 for suspensions at, pH 6. The marked concentration dcpendcnce shown ill this FihWre is not surprising in view of the ability of fcrromagnctic mabxial to ~nl~~n~c an applied magnetic field. Due to the complex nature of the field
enhancement, mobilitics are reported only as a function of the applied field. The particle magnetization (Mp) is obtained from the magnetophorctic mobi,iE ity at infinite dilutiolti (p~,~ = 0.12 cm2 S-* T-‘) 3s 1.6 A rnS kg--‘. In this cnsc the particles are at only t\vo percent of their saturation magnetization of &out EMA tn2 kg- I [ 10). The magnctophorctic mobility is seen to increase with rllagarrtitc conccntr3tion according to nn equation of the form f(c) = csp (??lC) - 1
(71
143
Est. error i
Fig:. 7. Variation magnetite.
of magnctophorctic
where m = 5.1 1 g-l.
mobility
with solution
pH for 0.4 g/l cuspcnsions
of
Equation (a) then becomes
PM = VMpp t?xp (NIC)/(GffrW) .
(8)
This equation is plotted in Fig. 6. The influoncc of soWion pfI on the magnctophorctic mobility of magnetite. particles is shown in Fig. 7. The corresponding variation in elcctrophoretic mobility of the particles is shown in Fig. 8. For magnetite suspensions, hydroxyl ions are potential detcrmir
I
L
I
9
7
11
PH
Fnr = VI& fit
-
filbl )dd~/~)(l
= Z3(c~/kT)‘[,(rra)
where
+ [(p+
+ f(c,
- fR)
+ p-)ckT/(l2rrqE~)]
191
~c~lwwf4(h’o~
(101
z = elcctroly te valence, p+, p_ = frictional consiants of dissolved ions, = comphx funotions of K fl from Overbmk [ 151, and fhf4 viscosity. r7 = solution While this equation, if included in the force balance, should successfully accoimt for any relaxation effects, it is found not to Ix significant for tllc prcsrtnt cnsc. Calculating zeta potentials from the electrophoretic data and solving Eq. (10) leads to a predicted reduction in magnctophorrttic mobility of at mast 2% over the pli range G-11; whereas, in fact, a reduction of 3096 was observed. 7%~ low predickd reduction arises from the fact that the ionic strength was not held constant. Thus the most highly charged particles (at pH 11) were in the highest ionic strength background (KLI - 260 due to pH adjustment). -
146
It is suggested that in the absence of additional drag forces, solution pH may have some influence on the particle magnetization, Mp. As noted above, the magnetophoret.ic mobilities were observed t.o increase with the time magnetic ~.articles were in contact with aqueous solution. The increase in mobility appears to result from particle rearrangements which increase the overall magnet ization of the particle aggregates. These observations are in agreement with those of Bate [ 101 for slightly larger (ca. 40 yrn diam.) sized multi-domain magnet.ite particle aggregates. Bate found that when the aggregates were dispersed in solution, the particles became susceptible to rearrangements which yielded an increased magnetic remanence. It is possible that solution pH has a bearing on such rearrangements due to the reaction of hydroxyl ions in which the outer surface of the particles are charged. CONCLWSlON
The procedure described in this study has several advantages which distinguish it from other techniques in common use. It is now possible to conveniently and rapidly evaluate the influence of solution conditions, particle or droplet nature and concentration on rnobilities in a magnetic field. The magnctophoretic mobility data provide fundamentat information as well as a means for optimization of magnetic separation processes by adjusting suspcnsion conditions. In determining magnctophorctic mobilitics, care must bc taken to specify the experimental conditions (concentration, pH, etc,) since particle interactions play a more significant, albeit less understood, role in determining this property than for examptc the electrophoretic mobility. ACKNOWLEDGEMENT
The authors arc grateful to Syncrude Canada Ltd, for permission to publish this paper.
REFERENCES I H.H. Kolm, IEEE Trans. hlagn., Meg-l 1 (197s) 1567. 2 J.A. Obetteuffer, IEEE Trans. hlagn., hYsg+lO (1974) 223. 3 J.A. Obertcuffer and 1. Wcchslcr, in Fine Particlcr Prowssing, Int. Sympos. Proe., 2 (1980), ~9. 1178-1216. 4 R,P. Treat and W.P. Lawsor., J. App!. Phys., SO (1979) 3596. 5 H. Hoffman, M. Neudel, H. Schewe and J. Rcfflc, Appl. Phys.. 24 (1981) 229. 6 K. Hay&i and S. Uchiyama, IEEE Trans. Magn., Mag-16 (1980) 827. 7 W.H. McNecse, P.C. Wankat and P.J. Fricdtaender, IEEE Trans. Magn.. hlag-16 (1980) 643. 8 EC. Stoner, Magnetism and Matter, Mcthuen, London, 1934,675 pp. 9 Zeta h¶eter Inc., Zeta Meter Manual, 3rd. ed.. Zeta Meter Inc.. New York. 1976, 139 pp. 10 0. Bate, in D.J. Craik (Ed.), Magnetic Oxides, Part 2, Wiley, New York, 1976, pp, 689-742.
11 R.A. Robinson and R.H. Stokes, Electrolyte Sohttionr, 2nd ed., Butterworthr, tondon, 1959, p. 333ff. 12 P. Kruus, Liquids and Solutionc, Dekker, New York, 1977, p. 141ff. 13 R.J. Hunter, Zeta Potential in Colloid Science, Academic Rrets, New York, 1981, pp. s9-124. 14 J_Th,8. Cherbeek and P.H. Wersema, fn M. Bier (Ed.), EieeLrophoresTsTheory, Methods and Applimatlons, Vol. II, Academic Press, New York, 1967, pp. l-52. IS J.‘I%.CL Overbeek, in H. Mark and E.J.\Y. Verwey (EEL), Advances in Colloid Science, VoL III. Intcrscience, New York, 1950. pp. 97-135.