Reversible, field induced agglomeration in magnetic colloids

Reversible, Field Induced Agglomeration in Magnetic Colloids 1 EDWARD ALLEN PETERSON Department of Physics, U. S. Air Force Academy, Colorado Springs, Colorado 80840

AND DAVID ALLEN KRUEGER Department of Physics, Colorado State University, Fort Collins, Colorado 80523

Received September 7, 1976; accepted January 13, 1977 Reversible agglomeration of magnetic particles (20-300-.~ diameter) in a colloidal suspension has been induced by applying various magnetic fields: nonuniform static fields and uniform ae or dc fields of magnitudes from 2.5 to 230 Oe. A sensitive Colpitts oscillator circuit monitored the spatial and temporal variations in magnetization in a vertical ll-cm column of magnetic fluid. The results are consistent with the hypothesis that spherical agglomerates of 10T-109particles are formed and settle gravitationally. The agglomeration was most pronounced in a commercially available water-base, 200-G ferrofluid; 20% of the particles formed agglomerates of _>107 particles and settled out in 1 hr in a 230-Oe uniform ac or de field. This effect was present to a lesser extent in other fluids (200-G ester base, 3% of the particles agglomerate in 1 hr; 200-G hydrocarbon base, ~-~0.05% in 2 hr). Electron micrograph studies indicate that all sizes of particles participate in the agglomeration. Centrifuge experiments show that the agglomerates are not limited by close packing upon settling to the bottom of the tube. The Colpitts oscillator should be useful in determining the stability of magnetic fluids used in applications such as magnetic ink printers, metal separation, etc. It may also be useful in experimental investigation of agglomeration hypotheses because the extent of the agglomeration can be conveniently controlled via the application of magnetic fields. I. INTRODUCTION

can create substantial inhomogeneities ill the fluid which grow in time. These inhomogeneities, of course, modify the magnetic b o d y force and can lead to reduced performance in a variety of applications (14). Even though there are published reports on the manufacture of magnetic colloids (15, 16), the details of the manufacture of the commercially available fluids are proprietary. This gives added importance to a simple, relatively rapid technique for determining the stability of these fluids prior to their useage for extended time periods. Because the size of the agglomerates and the fraction of the fluid which participates in the agglomeration increases with increasing magnetic field, it is possible that these fluids and this technique offer unique possibilities for more detailed studies of agglomeration phe-

Ferrofluids (1, 2) are commercially available colloidal suspensions of magnetite particles in a carrier fluid such as water or kerosene. Their applications and much of their intrinsic interest are based on the existence of a controllable magnetic b o d y force. I n most work on these fluids, the colloidal suspension is assumed to be spatially uniform and stable against agglomeration (3-13). We have studied ferrofluids with three types of carrier fluids (water, kerosene, ester) which are uniform and quite stable with no applied magnetic field. We find that the application of relatively small fields 1 Based in part on a dissertation presented by E. A. Peterson to Colorado State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy. 24

Journal of Colloid and lnlerface Science, Vol. 62, No. 1, October i5, 1977 ISSN 0021-9797

Copyright © 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.

FIELD INDUCED AGGLOMERATION

nomena. It should be mentioned, however, that due to the long settling times involved, our technique is not sensitive to agglomerates of less than roughly 107 particles for typical fluids. In the following sections we discuss the experimental arrangement, the results and interpretation of our agglomeration experiments, some related experiments to determine particle sizes (electron micrographs), magnetization properties of the fluid (vibrating sample magnetometer), and maximum packing of magnetite particles (centrifuge), and our summary and conclusions. Gaussian units are used throughout and the ferrofluids are characterized by their nominal values of 4~r times the saturation magnetization (4~rM~). II. E X P E R I M E N T A L

25

TRAVELING VERNIER SCALE

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-PLUG

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II

FREQUENCY] COUNTER

ARRANGEMENT

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The ferrofluid sample holder is an 11-cm glass tube with 0.6-cm inner diameter. The experiment has two stages, (a) exposure to gravitational settling, uniform fields (using a long solenoid), and/or gradient fields (using a permanent magnet) and (b) measurement of the concentration of magnetic particles as a function of the distance along the tube. A schematic of our measurement system is shown in Fig. 1. The resonant frequency, f, of the Colpitts oscillator depends upon the inductance of the sensing coil which in turn depends upon the material filling the coil. Our circuit was designed with f = f0 ~ 106 Hz with no sample in the sensing coil. A linear relationship between the normalized frequency change zXf/fo = (fo -- f ) / f o and the magnetization, M1500, at 1500-Oe applied field has been experimentally established by vibrating samplemagnetometer and oscillator circuit measurements on ferrofluid samples. We find A f i f o = 9.1 X 10.4 Ml~0Cwhere M is in gauss. These samples have an order of magnitude range in particle concentration achieved by successive dilutions of a 600-G water-base ferrofluid. Therefore, the shift in the resonant frequency of the Colpitts oscillator upon insertion of the fluid, &f = fo -- f, is a measure of the concentration of magnetic particles near the sensing coil. The

FERROFLUID COLUMN PLUG

Fla. 1. Schematic of the experimental a r r a n g e m e n t (sensing coil is stationary, ferrofluid column moves vertica]ly).

spatial resolution is characterized by experiments showing that zXf is sensitive to the fluid within 0.37 cm of the center of the sense coil. 2 A typical data set is obtained by moving the sample column vertically through the sensing coil in small increments to establish a baseline concentration profile. The sample column is then removed, exposed to the appropriate magnetic environment for a given time interval, and then reinserted in the sensing coil for another concentration profile measurement. As long as the tube is not jostled, these profiles are stable over quite long times (hours or even days) in the absence of an applied magnetic field so that the time to make the measurements (~minutes) is not critical. The latter was established by noting that profile measure2 By moving a thin ferrite disk t h r o u g h the sense coil, we find A f is proportional to the distance of the ferrite disk from the center of the coil. T h e A f at 0.37 cm from the coil center is 25% of the zXf at the coil center.

Journal of Colloid and Interface Science, Vol. 62, No. 1, October 15, 1977

26

P E T E R S O N AND K R U E G E R aT~

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FIO. 2. Concentration profiles after exposure to a 230-Oe uniform vertical field for (1) 0 min, (2) 5 min, (3) 10 min (4) 15 rain (5) 25 min, and (6) 30 min.

ments made up to an hour after removal from the applied field and profile measurements made immediately after removal from the applied fields differ by less than the linewidths in the figures presented. Overall measurement accuracy and repeatability is better than one part in 103 for the frequency data.

external field of 230 Oe for various cumulative times. (The 2~f/fo measurements were made down to 0.001 but the results were truncated in the figures.) That is, the fluid was exposed to 230 Oe for 5 min, the field turned off, the A fifo profile measured, the field turned on for an additional 5 min, etc. The migration of magnetic particles to the bottom of the tube is quite evident. Assuming this migration is due to the gravitational settling of large agglomerates, we have plotted the temporal change of the vertical position for points with constant /',fifo values (shown as sections ~, 7, and e in Fig. 2). There is approximately a linear distance vs time dependence with terminal velocities varying from 0.0035 to 0.0048 cm/sec (a to e) supporting the interpretation of gravitational settling. In Fig. 3 we plot the distance vs time curves for point -y from experiments using tubes of length 7, 11, and 15 cm. The fact that the same slope fits all three curves is consistent with a gravitational settling model 12

9 111. R E S U L T S A N D I N T E R P R E T A T I O N

In this section we will discuss (a) results for uniform applied fields, (b) the evidence for reversibility of the agglomeration with little spatial dispersal upon breakup, (c) the evidence that all size particles participate in the agglomeration, (d) results for nonuniform and ac uniform fields, and (e) the results for fluids other than the 200-G water-base fluids. (a) In almost all experiments discussed below we have obtained an initially uniform &fifo profile (except for the instrumental rounding at the top and bottom) by allowing the fluid to settle gravitationally for 2 weeks or more and then decanting our sample. Except for the last part of this section, all the results are for 200-G water-base fluid. In Fig. 2 we see the effects of placing the vertical column of fluid in a uniform vertical

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Journal of Colloid and Interface Science, Vol. 62, No. 1, October 15, 1977

FIELD INDUCED AGGLOi~iERATION

27

I00 0.0

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Fie.. 4. Dependence of the settling velocity on the magnetic field strength. where there is negligible net accretion during the settling. The nonzero time intercept is evidence for a formation time for the agglomerates. Repeating these experiments for other applied fields gives the terminal velocity (of point ~/) as shown in Fig. 4. If a threshold field exists, it must be below 2 . 5 0 e for the sample. The upper limit of VT has not been investigated, but it is possible that a limiting value of VT will be reached when the applied field is large enough to cause magnetic saturation. Using these data an estimate of the number of magnetite particles/agglomerate, n, can be made. Assume a spherical agglomerate composed of close-packed magnetite particles of diameter d (--~140 A), each with a surfactant layer l (~--30 ~), and a Stokes drag with a nominal 7-cP viscosity, ~/,3

6rr~ VwR = rag,

i

i

~ iiiit

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[1]

where R and m are the agglomerate radius and effective mass and g = 980 c m / s e & Next we assume that the effective mass is due solely to the magnetite in the agglomerate (i.e., we assume that the surfactant density is about the same as the carrier fluid density) so m = npTrd3/6 where a is the effective density of magnetite ( ~ 4 g/cm 3, corrected for buoyancy). Assuming a close-packed arrangement of spheres of diameter d + 2l gives a packing 3Note that the Reynolds number = pVTR/~I is roughly 10-4.

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Fro. 5. Percent of ferrofluid involved in agglomeration as a function of field strength. fraction of 0.74 and R = ½(d-}- 2/)(n/0.74) II3.

[2]

Combining Eqs. [1-] and [2] gives n = [18~VT(d + 21)]3n[O.74)I/3d3,og] -3/2.

[3]

For an applied field of 230 Oe, we have VT = 0.0042 cm/sec which gives n~--109 and R----- 1.2 X 10-~ cm. For a 2.5-Oe field we have n ~ 3 X 107. Assuming that the particles are ellipsoidal with a surface described by x2/a2+ y2/b2 + z2/c ~ = 1 rather than spheres requires replacing R by (abe) I/~ and replacing ~/by @ in Eq. [-1]. X m a y be obtained from results given by Lamb (17). For particles falling along the z axis we find for 0.04<_ a/c_< 1 and 0.04 < b/c < 1 that 0.955 < X < 1.71. For 0.12c < a = b < c we find 0.955 < X < 1.17. Equation [3] is modified by replacing ~/by ~X. Thus our estimate for the number of particles, n, varies as V/2. Since X is close to one for a fairly large range of shapes, our values for ~/ are not especially sensitive to our assumption of a spherical shape. For more elongated shapes, X will be larger than 1.7 and our values of n assuming spheres will be an underestimate. The fraction of the magnetite particles which form agglomerates large enough for us to detect can be obtained by comparing &fifo values at some intermediate depth in the fluid (e.g., 5 cm in Fig. 2) before and after application of the

Journal of Colloid and Interface Science,

Vol.

62,

No.

i,

October

15,

1977

28

PETERSON AND KRUEGER 1.085

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Flo. 6. In situ frequency change vs time for 200-G water-base fluid. Frequency with no sample present 1.100 X l06 Hz. A uniform 230-Oe vertical field was turned on at A and turned off at D. Frequency at A = 1 065 950 Hz, at F = 1 065 000 Hz. field. Figure 5 shows the magnetic field dependence of this fraction. For fields between 10 and 345 Oe, this dependence is H °.5. This simple result is not understood. (b) We now turn to the evidence for the reversibility of the agglomeration. Two lines of evidence lead us to conclude that these large (--~109) agglomerates break up into smaller units (<107) within a minute or so after removing the magnetic field. First, the profiles in Fig. 2 were not observed to change after removal of the field, but because of the time to measure a profile, this only puts an upper limit of i to 2 min for the breakup time. Second, in an effort to measure agglomeration time more directly, the oscillation circuit sensing coil was placed inside a vertical solenoid with the ferrofluid sample in place. The sensing coil was at the bottom of the sample column. Repeated application and removal of the magnetic field by turning the solenoid current on and off results in exponential-like rises and

decays not attributable to circuit response. A typical set is shown in Figs. 6 and 7. The major portion of the frequency change (A-B) when the field is applied is due to a saturation effect whereby a large number of particles are aligned in the applied field and thus are unaffected by the sensing field which is less than 0 . 5 0 e . The tail on this initial curve (B-C) can be interpreted as the agglomerate formation region wherein interactions among particles during agglomeration cause them to be further aligned so as to be less responsive to the sensing field. The downward sloping region (C-D) indicates additional particles settling into the region from further up the column. When the field is turned off, the major portion of the curve (D-E) is due to the particles relaxing from alignment with the applied field. The tail (E-F) is interpreted as the regime in which the dipole-dipole interactions among the particles are no longer effective and m a y be considered as a measure of the agglomerate breakup time. The frequency difference between A and F is a measure of the increase in particle concentration in the region during this field exposure. Note that the frequency difference C - D is less than the difference A - F because the particles are less responsive to the sensing field. For data such as those shown in Fig. 7 the agglomerate formation time constant, if, is about 40 sec and the breakup time constant, tb, is about 10 sec. I t should be emphasized that

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Journal of Colloid and Interface Science, Vol. 62, No. 1, October iS, 1977

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FIELD

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these times, t, and lb, are for the 109 particle agglomerates to break into agglomerates of less than 107 particles. We are unable to measure how much smaller than 107 particles the fragments are. From the intercept in Fig. 3 we can also estimate the time to initially form a 109 particle agglomerate as about 2-3 rain. The difference between this formation time and tile 40-sec re-formation time may be that, due to incomplete breakup, the fragments are larger than were available in the initial formation. Even though the agglomerates break up upon removal of the magnetic field, we have observed that a concentration profile, say the 30-rain curve in Fig. 2, is changed by less than 1% when left undisturbed in no magnetic field for a period of weeks. This can be understood by noting that the time for a 200-.~ diameter particle to diffuse 10 cm is on the order of years. However, a vigorous shaking or gentle inversion of the column (less than five inversion pairs) will restore the ferrofluid column to a uniform profile (within 2% top to bottom variation). This uniform distribution will then be maintained for at least a week, regardless of the sample's previous history of exposures to uniform fields.

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AGGLOMERATION

29

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Fie. 9. Concentrationprofilesfor (A) initial zero field conditions, (B) a 5-hr exposure to a 230-Oe uniform horizontal field, and (C) a subsequent 1-hr exposure to a 230-Oeuniform vertical field. (c) Evidence that all sizes of particles participate in the agglomeration comes from electron micrographs and vibrating sample magnetometer measurements on samples taken from the column before being exposed to a field and from the top and bottom of a column after exposure to a field. The size distributions from electron micrographs were the same to within experimental error. The magnetization vs applied field curves were also very nearly the same (differences less than 5%) with a possible shift toward larger size particles at the bottom of the column than at the top after field exposure. The existence of this shift is very uncertain though, since it is of the same magnitude as the experimental error. (d) Experiments were performed on the 200-G water-base ferrofluid with a variety of other magnetic fields. The results are consistent with the agglomeration hypothesis. They also show how the local magnetization can be changed by application of a field gradient. Figure 8 shows the effect of a uniform, vertical, 60-Hz, 230-Oe rms field applied by placing the sample in an Alfred Electronics Model BS231AE solenoid which has a region about 18 cm long and 3 cm in diameter over which the field is uniform within about 1%.

Journal of Colloid and Interface Science, Vol. 62, No. 1, October 15, 1977

30

PETERSON AND KRUEGER 0,--- . . . . . .

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Figure 9 shows the effect of a uniform, horizontal, 230-Oe field applied by suspending the sample vertically between the 20-cmdiameter pole faces of a Varian 4200 System N M R - E P R magnet. Both Figs. 8 and 9 show that the frequency (_<60 Hz) and orientation of the magnetic field do not affect the fraction of the particles which agglomerates. However, the concentration profiles at the bottom of the tube are different. Figures 10 and 11 show the effects of placing the column of fluid above and below the outer edge of a permanent magnet. The maximum field gradient was about 500 Oe/cm with the maximum field about 1500 G. These were produced by an Alnico V rod magnet 8 in. long and 2 in. in diameter. One expects that the magnetic force/volume, (M.V)H (18) would attract the magnetic particles to the pole faces, and this does happen, as we see from the figures. It should be noted in the previous experiments with uniform applied fields of 230 and 2.50e that the changes in the concentration profiles were essentially complete within 1 and 10 hr, respectively. On the other hand, with gradient fields, changes were still occurring after thousands of hours. The sequence of measurements in Fig. 11 deserves further comment. With the magnet above the fluid

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Af / fo FIG. 11. Concentration profiles after exposure to a 500-Oe/cm gradient field from above for (A) 0 hr, (B) 1 hr, (C) 245 hr, (D) 2100 hr, and (E) 5000 hr.

column, the first effect we see is an increase in the concentration of magnetic particles at the bottom of the column. This is followed by a subsequent buildup at the top of the column and a decrease at the bottom of the column. These measurements are not understood but a very tentative argument follows. Part of the buildup at tile bottom may be an artifact of our measuring technique because, as in all experiments, we removed the permanent magnet before making the profile measurements to eliminate the direct effect of the permanent magnet on the Colpitts oscillator frequency. Part of the buildup on the bottom may occur while we are removing the permanent magnet by the falling of a super large agglomerate(s) (roughly 1.5 X l0 -2 cm in diameter) 4 which is formed and held at the top by the magnet3 As the. ferrofluid becomes concentrated and more viscous at the top of the column, the large agglomerates do not fall 4 This size comes from using ,7 = 0.07 P and VT = 10 cm/60 sec in Eqs. [2-1 and [-3]. This VT is consistent with the data in Fig. 4. In fact the straight line in Fig. 4 for H > 40 Oe goes through the point H = 1500 Oe and VT = 10 cm/60 sec. 6 Note that for M "~ 200 G/47r and OH/Oz = 500 Oe/cm, we have ( M - V ) H roughly twice the gravitational force density on the magnetic particles.

dourna~ of Colloid and Interface Science, Vol. 62, No. 1, October 15,

1977

FIELD INDUCED AGGLOMERATION to the bottom so the peak at the bottom disappears. (e) Several of the previously mentioned experiments were performed using other fluids such as 200-G ester base and 200-G hydrocarbon base. The concentration profiles were qualitatively similar to those for the 200-G water-base fluid. Agglomeration was present but to considerably lesser extent. The fraction of particles participating in the agglomeration can be estimated in two ways. The comparison of A fifo values at an intermediate depth in the fluid is the best way if the effect is large. For the ester-base fluid, the fraction of particles agglomerating in 1 hr is 3%. For very small effects such as in the 200-G hydrocarbon base, we can make a rough estimate by comparing the added area in the peak region with the total area under the Af/fo vs depth curve. For the hydrocarbon-base fluid we estimate only 0.05% of the particles participate. This method is somewhat uncertain because of instrumental rounding of the curves. Figure 12 illustrates that quite large effects are observed even for the hydrocarbon fluid when exposed to a gradient field over long periods of time.

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Fie. 12. Hydrocarbon-base ferrofluid concentration profiles after exposure to a 500-Oe/cm gradient field from below for (A) 0 hr, (B) 100 hr, (C) 370 hr, (D)

850 hr, and (E) 1900 hr (the change at the top of the column is due to evaporative losses).

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Fro. 13. Particle size distributions for water-base (O) and hydrocarbon-base or ester-base ( • ) ferrofluids as determined from electron micrographs.

IV. R E L A T E D E X P E R I M E N T S

Electron micrographs were used to determine the size distribution of magnetic particles in the ferrofluid. The particles were assumed to be spherical and the equivalent circle method was used to assign particle diameters. Figure 13 shows the results for the 200-G water-, hydrocarbon-, and ester-base fluids. The larger sizes in the water-base fluid provide at least a partial explanation for its much stronger tendency to agglomerate. A vibrating sample magnetometer was used to determine magnetization vs applied field for the three 200-G fluids as shown in Fig. 14. The saturation magnetizations were 14.4, 13.5, and 13.5 G for the water-, hydrocarbon-, and esterbase fluids, respectively. Figure 15 shows the effect of the gravitational field alone over long time periods. Comparison with previous experiments shows that the concentration peak after 2500 hr of gravitational settling is not as extensive as that after a 1 hr exposure to a 230-Oe field. Note also that the upper portion of the profile is sloping whereas, in effects due to magnetic fields, the upper profile has a vertical portion. To set some limits on the concentration effects possible, we conducted centrifuge ex-

Journal of Colloid and Interface Science, Vol. 62, No. 1, October t5, 1977

32

PETERSON AND KRUEGER 1.0 \

z o 0.8

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N ILu

_J 1.1_ = ofY

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FIG. 14. Normalized magnetization curves obtained from vibrating sample magnetometer data for (A) water-base, (B) hydrocarbon-base, and (C) ester-base ferrofluids. periments. Curves showing the cumulative effect of centrifuging a 200-G water-base Ferrofluid sample for ½-hr intervals at successively higher g forces are presented in Fig. 16. Centrifuging at 8000g for ½ hr produced concentration peaks at the bottom of the tube 1.9 and 3.3 times greater than the original values for 200-G hydrocarbon- and water-base fluids, respectively. The extent of these concentrations is significantly larger than any concentrations observed using magnetic fields indicating that the magnetic cases were not limited by hard sphere packing.

.: ~ .......

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FIo. 16. Concentration profiles due to centrifuginga 200-G water-baseferrofluidfor cumulativecentrifuging: (A) initial profile, (B) 16g for ½ hr, (C) 70g for ½hr, (D) 300g for ½hr, (E) 2200g for ½ hr, and (F) 8000g for ½hr. The bottom 2.5 cm was removed from a ferrofluid sample which had previously been exposed to a uniform 230-0e vertical field for over 2 hr. This removes all the particles which had originally participated in agglomeration and settled to the bottom of the sample tube. The new sample was then allowed to stabilize for 24 hr with no field applied. Upon exposure to the uniform, vertical 230-Oe field for 2 hr, additional agglomeration was observed, but less than 5% of the residual ferrofluid appears to be involved. This gives a technique to obtain a fluid which is more resistant to agglomeration.

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V. SUMMARY AND CONCLUSION

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Fro. 15. Concentration profiles due to gravitational settling for (A) 0 days, (B) 42 days, (C) 104 days, and (D) 232 days.

To summarize, agglomerates appear to form within 2 rain of exposure to a magnetic field. For a water-base ferrofluid in a 230-Oe field, the agglomerates are approximately 20 #m in diameter if assumed to be spherical, consist of approximately 109 particles, and involve approximately 20~0 of the particles in the settling or concentration effect. The extent of the agglomeration is field dependent. The agglomerates break up within seconds after the field is removed. The agglomeration and gravitational settling appear to be completely reversible with gentle agitation after the field is removed. In. the agglomeration process the driving force is the magnetic dipole-dipole interaction among the magnetite particles.

Journal of Colloid and Interface Science, Vol. 62, No. I, O c t o b e r 15, 1977

FIELD INDUCED AGGLOMERATION Evidence for this is the absence of large agglomerates with no applied field and the significant difference in the agglomeration for water-base ferrofluids as compared to the esterbase and hydrocarbon-base ferrofluids. The dipolar interaction in the water-base fluid is much larger than in the other two fluids because of the presence of much larger magnetite particles. We have found that all sizes of magnetite particles are included in the large agglomerates. Considerable theoretical effort is necessary to make a quantitative connection between the dipolar force and agglomeration. Some work has been done but only for small numbers of particles in linear or chain-like configurations (19, 20). Theoretical work is in progress on modeling the large agglomerates which we have observed. While no reports of observations of any gravitational settling as a consequence of agglomeration are available, both Bibik in the USSR and Martinet in France have presented magneto-optical evidence for agglomeration in magnetic liquids. Bibik's studies have been conducted with dilute magnetic liquids prepared in his laboratories (22, 23). His magnetic liquids are approximately 0.1 to 0.01 as concentrated as our ferrofluids and thus direct comparisons are tenuous at best. Bibik has investigated the decrease in transparency of several magnetic liquids when a uniform magnetic field is applied. He uses this technique as a measure of the colloidal stability when various electrolytes are added to the colloid. Martinet (24), however, has used commercial ferrofluids as well as his own magnetic liquids. He has used 10 to 100/~m slices of magnetic liquids polymerized as in a gel during magnetic field exposures to show that the magnetic susceptibility and the optical birefringence and dichroisrn become anisotropic. Both Bibik and Martinet attribute their observations to a filamentary agglomeration or correlation among particles in a direction parallel to the magnetic field. Martinet has further observed that the agglomeration effect is present in a

33

water-base ferrofluid in "weak" magnetic fields (10's of gauss) while no agglomeration was present in a hydrocarbon-base ferrofluid even in "strong" magnetic fields (a few kilogauss). The water-base results are in qualitative agreement with our findings although we cannot ascertain the shape of the agglomerates. Martinet probably did not observe agglomeration in the hydrocarbon-base ferrofluids as we did because his field exposure times were not long enough. From all this work it is clear that agglomeration occurs in m a n y magnetic fuids under a variety of conditions and results in significant changes in the magnetic properties of the fluid. Thus the possibility of agglomeration should be considered in any application where the magnetic liquids will remain at rest in a magnetic field. I t is expected that fluid agitation will reduce agglomeration but no quantitative estimate of the necessary shear forces is available. Note added in proof. Recently the optical investigations of agglomerates by Hayes (25, 26) and Hayes and Hwang (27) have come to our attention. Using an optical microscope they have observed the formation of agglomerates in a fluid very similar to our 200-G water base fluid. VI. ACKNOWLEDGMENTS E. A. P. would like to acknowledge valuable discussions with A1 Tveten concerning various aspects of the experiments. Financial support for E.A.P. was given by the Air Force Institute of Technology and the U. S. Air Force Academy. The Office of Naval Research also supported this work through Contracts N00014-67-A0299-0020 and N00014-76-C-0250. REFERENCES 1. ROSENS\¥E1G, R. E.~ ]'NTESTOR,J. W., AND TIMM1NS, R. S., in "Mater. Assoc. Direct Energy Convers.

Proc. Sym., 1965 [AIChE-I. Chem. E. Symposium Series, nS.] p. 5. 2. KAISER, R., AND ROSENSWEIG, R. E., NASA

CR-1407, 1969. 3. KAISER, R., AND MISKOLCZY, G., I E E E Trans. Magn. Mag-6, 694 (1970). 4. MosI~ow]Tz,R., Res/Develop 2S, 58 (1974). 5. RESLER, E. L., JR., AND ROSENSWEIG, R. E., A I A A J. 2, 1418 (1964). 6. Rosxz~swEio,R. E., A I A A ar. 4, 1751 (1966).

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7. ROSENSWEIG,R. E., MISKOLCZY,G., AND EZEKIEL, F. D., Mach. Des. 40, 145 (1968). 8. WOLFE, R., AND NOI~TH,J. C., Appl. Phys. Lett. 25,

122 (1974). 9. ZELAZO,R. E., ANDMELCHER,J. R., J. Fluid Mech. 39, 1 (1969). 10. CARY, B. B., JR., AND FENLON, F. H., J. Acoust. Soc. Amer. 45, 1210 (1969). 11. MCTAGUE, J. P., J. Chem. Phys. 51, 133 (1969). 12. JENKINS, J. T., Arch. Rational Mech. Anal. 46, 42

(1972). 13. CuRTIs, R. A., Phys. Fhdds 14, 2096 (1971). 14. PERRY, M., Ph.D. Thesis, Colorado State University, Fort Collins, Colorado, 1976. ]5. REIMERS, G. W., AND KHALAFALLA, S. E., U. S. Bur. Mines, Tech. Prog. Rep. 59, 1972. 16. KAISER, R., AND MISKOLCZY,G., Y. A ppL Phys. 41, 1064 (1970).

17. LAMB, H., "Hydrodynamics," 6th ed., p. 604. Dover, New York, 1932. 18. BROWN, W. F., JR., Amer. J. Phys. 19, 290 (1951). 19. DEGENNES, P. G., AND Pmcus, P. A., Phys. Konclens. Mater. 11, 189 (1970). 20. JORDAN, P. C., Mol. Phys. 25, 961 (1973). 21. HA~PAVAT, G., IEEE Trans. Magn. Mag-10, 919 (1974). 22. BIBlE, E. E., Kolloid. Zh. 35, 1141 (1973). 23. BIBIK, E. E., LAVgOV, I. S., AND MERKUStIEV, O. M., Kolloid. Zh. 28, 631 (1966). 24. MARTINET,A., Rheol. Acta 13, 260 (1974). 25. HAYES, C. F., J. Colloid Inlerface Sci. 52, 239 (1975). 26. HAYES, C. F., Mol. Cryst. Liq. Cryst. (to be published). 27. HAYES, C. F., AND HWANO, S. R., J. Colloid Interface Sci. (to be published).

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