Journal of Magnetism and Magnetic Materials 125 (1993) 34-38 North-Holland Viscosity, resistivity and surface tension measurements of Fe,O, ferrofluid M.S. Dababneh, N.Y. Ayoub, I. Odeh and N.M. Laham Physics Department, Yarmouk Unirwsc~, It-bid, Jordan Received 10 September 1992; in revised form 11 December 1992 The viscosity n of Fe,O, ferrofluid at volume concentrations in the range t = 0.0-0.013 are measured. The corresponding range of values of q is 1.6-1.8 cp. A linear relationship exists between the relative viscosity and the concentration of the fluid. Measurements of relative resistivity of Fe,O, ferrofluid at various concentrations (E = 0.00526-0.0526) are also reported. The relative resistivity is taken with respect to the resistivity of the highest value of concentration available (e = 0.0526) which is 2.05~ 10h R-m. The results show that the relative resistivity is inversely proportional to the concentration of the fluid. The variation of the resistivity with applied magnetic field is also presented. Measurements of the surface tension of Fe,O, ferrofluid show a continuous increase with increasing concentration and have values ranging from 25.0 to 26.63 dyn/cm in the concentration range E = 0.0-0.0.526. 1. Introduction Great interest has been devoted in the past three decades to magnetic fluids following the successful attempt to produce a stable magnetic fluid by Rosensweig et al. [l]. The interest in ferrofluids is due mainly to its importance in modern chemical technology and its wide industrial applications. Magnetic ferrofluids are ultrastable colloidal systems containing single-domain ferromagnetic or ferrimagnetic particles [2]. The ferrofluids are superparamagnetic (have zero coercivity and zero remanence). These systems can form chains and compact clusters [3,4]. Various theoretical and experimental studies were made on ferrofluids such as studies on its magnetic [5] and optical 161 properties. In the present work we measure the viscosity at various concentrations of Fe,O, ferrofluid. Measurements of the relative resistivity and its variation Correspondence to: Dr M.S. Dababneh. Physics Department, Yarmouk University, Irbid, Jordan. with concentration and with applied magnetic field are also presented. Finally, we present the measurements of the surface tension of Fe,O, ferrofluid and its variation with the concentration of the fluid. 2. Experimental A magnetite (Fe,O,) ferrofluid was prepared in our laboratory using the wet method [7]. The Fe,O, particles were produced by the following successive reactions: 2FeC1, + FeSO, + 8KOH -j 2Fe( OH), + Fe( OH), + 6KCl Fe,O, (particles) + 4H,O + salts. (1) The Fe,O, particles produced were washed with hot water and acetone to remove the salts as far as possible, but we could not get rid of these salts completely. The particles were then dispersed in a carried liquid (isopar M, petroleum distillate) 0304~8853/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights resewed
MS. Dababneh et al. / Various measurements of Fe,O, ferrojluid 35 by the action of a surfactant (oleic acid). Centrifuging the fluid improved its colloidal stability by removing any large aggregates that may have been present. In this paper we are interested in the effects of varying the concentration on various properties of the ferrofluid. In the following, we present two independent methods to determine the concentration (~1 of the ferrofluid. In the first method we use the relation [5] = I,/&, (2) where Z, is the saturation magnetization of the sample and I, = 480 emu/cm3 is the saturation magnetization of the Fe,O, bulk material. In the second method we measure the mass m of a certain volume V, of the sample. If there is a volume V, of the pure material of Fe,O, in the sample then the volume of the carrier fluid would be V, - Vr. Measuring the density of the carrier fluid (p, = 0.769 g/cm31 and knowing [8] the density of the pure Fe,O, (pf = 5.18 g/cm3), then dividing this equation E = V,/V,, we get E - ps - pc PF-PC by V,, and knowing that (31 The results we obtain for E using eqs. (2) and (3) are consistent to better than 1%. The stock fluid we prepared had a concentration E = 0.0526, from which we obtained other concentrations by dilution with the carrier fluid. Direct measurements of the viscosity of Fe,O, ferrofluid at various concentrations were made using a ROIN viscometer. An amount of 400 cm3 of fluid was required to carry out these measurements. Calibration measurements of the viscosity of distilled water at various temperatures and of ethyl alcohol were made. The results were consistent to better than 5% of the tabulated results [S]. The resistivity measurements were performed with a 4 x 4 x 6 cm Perspex cell. The electrodes were copper plates of 4 X 4 cm area. The electrodes were kept parallel to each other at the desired distance by suitable Perspex bridges. The effective area of the plates in contact with the fluid was 14.4 cm2. The resistance of the fluid was measured with a (hp 3456 A) digital multimeter. The relative resistivity was obtained from the ratio of the resistance of the cell at the desired concentration with respect to the resistance of the same cell at the highest concentration available (E = 0.0526). The variation of the resistivity with the applied magnetic field was studied by placing the cell between 10 x 10 cm poles of an electromagnet. The magnetic field was measured by a Hall-probe gaussmeter and was very much uniform throughout the region of study to better than f 1%. Due to the low values of volume fraction studied, demagnetization effects were ignored. The surface tension of the ferrofluid was measured using a glass capillary tube of radius R = 0.5 mm placed vertically in a magnetite ferrofluid reservoir. The surface tension y was deduced from the relation p&r y = 2 cos 9 where p is the density of the fluid, g is the gravitational acceleration, h is the height of the fluid in the capillary with respect to the surface of the fluid in the reservoir, and 13 is the contact angle of the fluid with the capillary tube. A travelling telescope was used to measure h as to estimate the angle 8, which was close to zero. This method for measuring the surface tension was calibrated using distilled water and alcohol. The results were consistent to better than 2% with the standard tabulated results [8]. 3. Results and discussion The following results were obtained from measurements at room temperature (N 20 C). 3.1. Viscosity In fig. 1 we present the relation between (7 - nj/n,, versus the concentration E, where Q and 77 are the measured viscosity of the carrier fluid (4)
3h M.S. Dabubneh et ul. / Vurious measurements of Fe,(I, fhwfhi t l (E = 0) and the ferrofluid, respectively. Although only three points are presented in the graph due to the lack of the ferrofluid and the carrier liquid, the relation is clearly linear. The slope of the curve is 9.6, which means that E from which we deduce the following relation q/n,, = 1 + 9.66. (5) For low-concentration, uncoated spherical particles, Einstein derived a theoretical model for determining the viscosity of the fluid given by [9]?j/?-/{j = 1 + &. (6) For higher concentrations, a two-constants expression was suggested by Rosensweig [9], given by 1 q/no = (1 -Ue _Q) (7) which for small concentrations becomes 7/n,, = 1 + UE + be +.. (8) Neglecting terms higher than E will reduce eq. (8) into eq. (6) with the coefficient a = 5/2; this factor is only correct when considering the effect Fig. I. Relation between viscosity and concentration of Fe30, ferrofluid. v is the viscosity at specific concentration, T,, is the viscosity of the carrier fluid and t is the concentration. Fig. 2. Variation of relative rrsistivity with the inverse ol the concentration. of viscous forces on spherical uncoated particles and it will be larger otherwise [9]. In the system we are studying the particles are quite awkward in shape and are coated with a surfactant which obviously will increase the viscous forces between the carrier fluid and the surface of the particles and in turn will increase the value of the coefficient u as found in eq. (5) to be 9.6. 3.2. Hesistil it! Figure 2 presents the variation of the resistivity with the inverse of concentration of the magnetic ferrofluid. Since the same cell with a distance of 5 mm between the electrodes is used for all concentrations, we measure the relative resistivity with respect to the highest concentration available (E = 0.0526). As can be seen in fig. 2, the resistivity is inversely proportional to the concentration in the region of study. The variation of the relative resistivity with applied magnetic field at E = 0.00789 is shown in fig. 3. The results show a continuous decrease in resistivity with the applied magnetic field up to 190 G, after which it remains constant. Similar behaviour for other concentrations and distances between the electrodes has been observed [IO]. We believe that the conduction in the ferrofluid is due to ions formed from the residuals of the salts produced in the chemical reaction (1). We therefore expect that, on the average. each
M.S. Dababneh et al. / Various measurements of Fe,O, ferrofluid 37 fine particle will trap a few molecules of the salts on its surface which, when dissolved in the carrier fluid, will dissociate into ions. The collisions of these ions with other molecules and particles are responsible for the resistivity of the fluid. Let us assume, on the average, f salt molecules are trapped with each Fe,O, particle of the ferrofluid. Since we are dealing with small concentration (E < 0.05261, we can approximately assume, from the point of view of electrical conduction, that our system is a dilute electrolyte system. Hence, by Einstein-Stokes [ll] formula the resistivity, p, of the fluid is given by 6V+,1 p= fne (9) where 77 is the viscosity of the fluid, R, is the radius of the salt molecules, N is the number of fine particles per unit volume of the fluid, and e is the electric charge of the ion. Multiply and divide eq. (9) by (r/6>03, where D is the average diameter of the fine particles, we get f5vr, = f [(T/(j)D3N]e2 kt/6)d31 = n2qr,d3 f 6e2 (10) where we use the fact that E = a/6 D3N. Substituting eq. (5) into eq. (101, we obtain,=,,+c E where the constants C, and C, are given by c, = 9.6~r q,r,d fe2 > c,=.rr2nr,d3 fe2 At the highest available concentration, corresponding resistivity P,,, is given by Dividing eq. (11) resistivity pr &=P=&+Kz Pm E (11) E,, the (12) by eq. (12), we get the relative (13) z ; 0.980 3 2 0.975 Fig. 3. Variation of relative resistivity with the applied magnetic field for a sample of E = 0.00789. where the constants K, and K, are given by K, = cnc1 EnlC2 K,= E,C1 + c, E,C, + c,. It is clear from eq. (13) that the relative resistivity is inversely proportional to the concentration of the fluid which explains the main features of fig. 2. In fig. 3 we present the variation of the resistivity of the fluid at concentration E = 0.00789. It is clear that up to about 3.4% decrease in resistivity has been observed when the magnetic field is increased up to 190 G. We can explain this behavior as follows. As mentioned above, the conduction in the ferrofluid is due to the ions of the residual salts trapped with the particles during preparation. Some of these ions have to percolate through the surfactant molecules and some through the clusters and aggregates that are partially present in the system. On application of the magnetic field, these clusters and aggregates try to open up and align themselves in the direction of the field, which is turn eases up the percolation of the conducting ions and hence increases the conduc-
concentration. We have also observed a decrease in the resistivity when a magnetic field is being applied in the direction of the electric field in the fluid. However, this behavior is observed for limited magnetic field values. Finally, the measured surface tension showed that this property of the ferrofluid is increasing with t - starting with a minimum value (25 dyn/cm) which corresponds to the surface tension of the carrier fluid (E = 0). Acknowledgements so1 002 0s cos 35 c Fig. 4. Measured surface tension y in dyn/cm versus concen- tration of the Fe,O, tivity of the system, resistivity. 3.3. Surface tensiorz ferrofluid. consequently decreasing its We present in fig. 4 the variation of the surface tension with the concentration of the Fe,O, ferrofluid. The results show a continuous increase in surface tension with increasing concentration. The variation of surface tension y with the concentration E is estimated by an empirical formula y = 2s + 1056., (14) which is obtained by fitting the present data. 4. Conclusion Viscosity measurements of Fe,O, ferrofluid have been made for four different concentrations including the carrier fluid (E = 0.0). We have observed a linear relationship between the relative viscosity and the concentration of the fluid. Direct measurements of the resistivity showed that it varies linearly with the reciprocal of the concentration of the fluid, which means that the conductivity of the fluid increases linearly with We would like to acknowledge the financial support of the Higher Council for Scicncc and Technology and Yarmouk University. We wish to thank MS Tina Nicklin for typing this articlc. N.Y.A. wishes to acknowledge the use of ICTP. Trieste library facilities. References [II [?I [31 [41 [Sl [61 R.E. Rosenaweig. J.W. Nester and R.R. Timmina. Am In\t. Chem. Symp. Ser. 5 (1965) 101. R.W. ( hantrell. A. Bradbury. J. Popplewell and S.W. Charles. J. Appl. Phys..?13 ( IYXZ) 2717. (.F. Hayes and S.R. Hwang. J. Colloid Interface Sci. (111 (1077) 443. GA. Jones, IEEE Trans. Magn. 23 t 19X8) 1050. R.W. Chantrell. N.Y. Ayoub and J. Popplewell. J. Magn. Magn. Mater. 53 (1085) 19% N.Y. Ayoub, R.Y. Abdrlal. R.W. Chantrell. J. Popplewell and K. O Grady. J. Magn. Magn. Mater. 7Y (19x9) Xl: N.Y. Ayoub. B. Abu-Ai\heh. M. Dababaneh. N. Laham and J. Popplewell. IEEE Trans. Magn. 25 (19x9) 3860: and reference5 therein. P. Davies, J. Popplewell and J.P. Llewellyn. IEEE Trans. Magn. 22 (1986) 1131; J. Popplewell. P. Davies. A. Brad- bul); and R.W. Chantrell. IEEE Trans. Magn. 27 (19x6) 112X and references therein. I71 S.E. Khalafalla and G.W. Reimer\. IEEE Trans. Mapn. MAGI6 (1980) 17X. Nl Handbook of Chemistry and Physics. 57th rd. (C lcveland. OH, CRC Pre5s. 1977). [ )I R.E. Rosensweig. Ferrohydrodynamics (C amhridge Liniversity Pre\x. Cambridge. 19x5) p. 6.1. [lo] MS. Dababneh, N.Y. Ayoub. I. Odeh and N.M. Lah;lm, to he published. [I I] J.R. Reitz, F.J. Milford and R.W. Christy. Foundations of Electromagnetic Theory. 3rd ed. (Addison-Wecleq. Reading. MA. 1979).