Mechanism of Action of Colloidal Solid Dispersions

Mechanism of Action of Colloidal Solid Dispersions F. Chiñas-Castillo e-mail: [email protected] Instituto Tecnologico de Oaxaca, Wilfrido Massieu s/n, Oaxaca, Oax., México H. A. Spikes Mechanical Engineering Department, Tribology Section, Imperial College, London, SW7 2BX, U.K. 1 In the past there has been considerable interest in the possibility of using liquid lubricants containing dispersed, solid particles in the 1–50 micron size range to reduce friction and wear. These particles are used in greases and some industrial oils. Researchers are now directing their attention to the behavior of much smaller colloidal particles in the range of 5 nm to 200 nm diameter. Such systems are formally known as ‘‘colloidal sols’’ and have been claimed to influence friction and wear. Further reasons for studying such colloidal particles is that they are present in soot-contaminated engine lubricating oils, as wear debris and as partially-soluble additives. Thus, the objective of the work derived in this paper was to investigate the mechanism of action of colloidal solid particles in the range of 5 to 200 nm diameter in lubricating oils. Of particular interest was the effect of slide-roll ratio on particle entrainment and the influence of the ratio of particle diameter to elastohydrodynamic lubricant film thickness on particles’ behavior. This study has shown that in thin film contacts, colloid nanoparticles penetrate EHD contacts mainly by a mechanism of mechanical entrapment. It is found also that in rolling contacts at slow speeds, colloids formed a boundary film of at least 1 or 2 times the particle size. This film influence friction and wear. However, this film is lost at high speed and the film thickness reverts to the colloid-free fluid. The results of this study have enabled a mechanism of lubricating action by colloid sols to be derived. @DOI: 10.1115/1.1537752# Introduction Nowadays many lubricating oils contain solid particles added either deliberately, to improve their lubricating characteristics, or present by accident as is the case of debris contaminants. A large number of papers have reported experimental and theoretical studies on the behavior of particles larger than 1 mm in dispersions in high pressure lubricated contacts @1– 4#. In all the cases, the mean particle size studied has been greater than the prevailing EHD film thickness. Optical studies have shown that, under pure rolling and low speeds ~;0.002 m/s!, large individual particles are trapped between the lubricated, rolling surfaces where they deform plastically and form a thin film adhered to the surfaces. However, this film is removed with increasing speeds @2,4#. At high-speeds, the particles are swept around the contact and few, if any, are entrained. It has been found that these particles show a different behavior in mixed sliding-rolling contacts compared to pure rolling. Under such conditions, large particles were found to accumulate at the inlet and to be entrapped as in pure rolling up to a slide/roll ratio of around 0.7, depending strongly on the particle concentration and size. At higher slide/roll ratios however, the particles accumulated in the inlet, restricting the lubricant supply and causing starvation in the contact and surface damage @4#. In practical applications there exist a number of systems where tiny solid little particles, with size much smaller than 1 mm, are present in lubricating oils. Practically important examples of these systems, termed as ‘‘colloidal sols,’’ are sooty oils where tiny carbon particles are dispersed in an engine oil, and overbased detergent additives, which are based on dispersed solid particles of calcium or magnesium carbonate. Early studies indicate that commercial colloidal dispersions of MoS2 , graphite and ptfe, reduce friction and provide fuel energy saving in automotive engines and gears @5#. In recent years there has also been considerable interest in the application of a range of other colloidallydispersed additives, such as borates and MoS2 . Contributed by the Tribology Division for publication in the ASME JOURNAL OF TRIBOLOGY. Manuscript received by the Tribology Division February 26, 2002; revised manuscript received August 6, 2002. Associate Editor: M. M. Khonsari. 552 Õ Vol. 125, JULY 2003 One of the first systematic attempts to study the tribological properties of metallic nanoparticles in colloidal aqueous dispersions is described by Mishina et al. in @6#. These sols consisting of particles between 30–100 nm were evaluated in a pure sliding contact using different surface materials. Mishina’s experiments indicate that the influence of colloid particles on friction and wear depends strongly on the material. Over the last few years, Xue et al. @7# and Dong’s team @8# have carried out studies on a wide range of different colloid solid nanoparticles in the range of 5–100 nm using a pin-on-disk and fourball tribo-tester. Results of these studies indicate that colloidal nanoparticles show good friction and wear reduction characteristics at concentrations below 2% wt.. However in some cases colloid nanoparticles exhibit a deleterious effect enhancing either friction or wear @6#. Recently the authors of this paper presented a systematic study to explore the behavior of these tiny particles in lubricated contacts and the extent and conditions under which colloidal particles pass through lubricated contacts, and infer how this behavior affect the tribological performance of base lubricants. They observed and measured the build-up of sol particles in contacts using ultra-thin interferometry. It has been found that colloidal nanoparticles do go through rolling contacts to form patchy films at low speeds, contributing to lubricant film thickness, but this film enhancement disappears in high-speed contacts @9#. They also showed that there is a significant difference in the behavior of colloid particles in mixed rolling/sliding conditions. In such contacts, the colloid formed a boundary film at very low speeds, as in pure rolling, but this disappeared with increasing slide-roll ratio @10#. Now, the current paper presents the rules governing the entry and behavior of colloid sol particles in both pure rolling and mixed rolling/sliding lubricated contacts. 2 Materials and Colloid Preparation This paper reports the results obtained from experimental tests performed on three colloidal sol systems. The main characteristics of these systems are listed in Table 1. Hexadecane was chosen as dispersing media and was purified by passage through a column of activated alumina and silica gel prior to use. The colloids were prepared by chemical reduction of Copyright © 2003 by ASME Downloaded From: http://asmedigitalcollection.asme.org/ on 12/11/2013 Terms of Use: http://asme.org/terms Transactions of the ASME Table 1 Main characteristics of the systems under study Particle Dispersing Medium Size ~nm! Gold Gold Silver hexadecane hexadecane hexadecane 20 5 6 metal salts and synthesized in aqueous media; then the particles were transferred to the hydrocarbon phase. Characterization of the colloids was made using a transmission electron microscope ~TEM!; photo-correlation spectroscopy ~PCS! was used to confirm the size of the particles in the hexadecane. 2.1 Preparation of Colloids a. Ag-Oleate. The preparation of this oleate-capped Ag colloid ~coated with a thin layer of oleate! was described previously in paper @9#. It comprises tiny 6 nm Ag spherical particles. b. Au-Oleate. The synthesis of an oleate-capped gold colloid sol is described in reference @10#. It consists of 20 nm solid spherical Au particles. c. Au-Amine. An amine-capped gold colloid sol of 5 nm diameter particle size was stabilized using a primary amine and synthesized according to reference @11#. Dodecylamine (C12H25NH2 ), chloroauric acid (HAuCl4 3H2 O), sodium borohydride 99 percent (NaBH4 ), tetraoctylammonium bromide 98 percent (N (C8 H17) 4 Br) were all obtained from Aldrich Chemical Co. These chemicals were used as received. A yellow solution of 0.284 mmol of chloroauric acid was prepared in 25 mL of distilled water. Next, 0.667 mmol of tetraoctylammonium bromide was dissolved into 25 mL of toluene. This solution was added with rapid stirring to the aqueous solution. This mixture was vigorously stirred until all the orange color was removed from the aqueous phase. Next, 3.1 mmol of dodecylamine in 25 mL of toluene was added with stirring to the twophase mixture. Finally, 4.36 mmol of sodium borohydride solution in 25 mL of distilled water was added to the mixture while stirring. After that, the aqueous phase was discarded and the organic phase reduced in volume to 5 mL by rotary evaporation. Then, 150 mL of n-hexadecane was added to the colloid sol in toluene and mixed with stirring to obtain a uniform dispersion of a deepdark red purple and then the small amount of toluene was evaporated under reduced pressure. 3 Experimental Techniques 3.1 EHD Film Thickness Measurements. Film-forming properties of colloid sols were measured by ultra-thin film interferometry in a high-pressure, ball-on-flat rig @12#. In this, a contact is formed by a highly-polished, steel ball ~AISI 52100, 19 mm diameter! and a chromium and silica-coated glass disc. The rig is coupled with DC servomotor that can drive ball and disc independently, inducing sliding/rolling motion. The composite roughness of the contacting surfaces was 11 nm. The film thickness test rig set up can be found in @9#. All tests were carried out at a controlled temperature of 25°C60.5. In each test, a new steel ball was used and all the relevant rig parts were thoroughly cleaned with analytical grade toluene and acetone. The ball and disc were carefully cleaned by immersion in boiling toluene followed by rinsing with acetone. In this study, a load of 20 N was applied to produce a maximum Hertzian pressure of 0.52 GPa and a contact radius of 136 mm. 3.2 MTM Traction Measurements. A computercontrolled, mini-traction machine ~MTM! was used to determine the friction characteristics of the colloidal dispersions in the EHD and mixed lubrication regime. Details of the rig setup are found in reference @9#. In this test, a contact is formed between a polished steel ball ~19 mm diameter! and the flat surface of a disc; both being driven independently to produce mixed sliding/rolling motion. A force transducer measures the traction force applied to the ball specimen. In this study, all the parts in contact with the fluid to be tested were cleaned, first with toluene and then acetone and dried prior to a test. Friction measurements in all tests were carried out at a load of 30 N ~mean Hertz pressure of 0.93 GPa!. The combined roughness of the MTM contact was 15 nm, and friction measurements were taken over a range of entrainment speeds between 0.002 m/s and 2 m/s. The slide/roll ratio SRR is defined as the ratio of sliding speed to mean entrainment speed. 4 Experimental Results 4.1 Oleate-Capped Silver Colloid 4.1.1 Film Thickness Results. a. Pure Rolling. Film thickness results are shown in Fig. 1. The base fluid gives a straight line in a log ~film thickness! versus log ~entrainment speed! plot, with a slope of about 0.67, according to EHD theory. The base fluid/surfactant combination shows some scatter in the low speed range ~0– 0.05 m/s! and a boundary film of 3.5 nm, which is likely to be due to adsorption of the surfactant on the surface @13#. The colloid shows quite a different behavior. At slow rolling speeds, a boundary film was seen to develop over a period of up to 5 minutes, before stabilizing at a thickness of about 12 nm. Stabilization normally took about ten revolutions of the disc and so approximately 15 ball revolutions. Figure 1 shows the stabilized film thickness values and also indicates that this boundary film is independent of speed up to about 0.08 m/s but then diminishes, so that negligible boundary film remains in high-speed conditions. Upon reducing the speed again, the boundary film was found to reform again during about ten disc revolutions. The thickness of this boundary film in the slow speed region was approximately twice the size of the colloidal silver particles. b. MixedRolling/Sliding. Figure 1 also compares the behavior of silver colloid in hexadecane at 25°C in both rolling and 50 percent SRR. In mixed rolling/sliding contact, this colloid formed also a boundary film of similar magnitude to that obtained in pure rolling. However, at 50 percent SRR the film was only present up to an entrainment speed of 0.02 m/s, as compared to 0.08 m/s exhibited in pure rolling contact, after which the effect of the particles was negligible. 4.1.2 MTM Friction Results. MTM results are shown in Fig. 2. At speeds below 1 m/s, the base fluid/stabilizer combination produces a reduction in friction coefficient compared to the base Fig. 1 Film thickness results n -hexadecane, SRR effect, 25°C Journal of Tribology Downloaded From: http://asmedigitalcollection.asme.org/ on 12/11/2013 Terms of Use: http://asme.org/terms for silver colloid in JULY 2003, Vol. 125 Õ 553 Fig. 2 MTM friction results for silver colloid in n -hexadecane, 50 percent SRR, 30°C fluid alone that suggests that the stabilizer has a boundary lubricating effect also observed in the film thickness test. Figure 1 indicates that the colloidal sol provides no significant further contribution to friction in the EHD and mixed regimes ~above 0.1 m/s!. However, as the entrainment speed is reduced below 0.025 m/s, the silver nanoparticles give a friction coefficient below that obtained for the particle-free, base fluid/stabilizer blend. This entrainment speed of 0.025 m/s corresponds closely to the speed above which the colloid does not contribute to film thickness at 50 percent SRR. 4.2 Oleate-Capped Gold Colloid 4.2.1 Film Thickness Results. a. Pure Rolling. In pure rolling condition a quite scattered film thickness, ranging between 20 to 40 nm ~1 to 2 times the primary particle diameter!, was seen to form at very low speed ~0.002 m/s!. This behavior continues up to a speed of about 0.1 m/s where the fluctuations of film value cease and only the base fluid film thickness is registered. Further experimentation indicated that, as for silver colloid, this film thickness was dependent on time. When the speed was rapidly changed at low speeds, the film gradually built up to about twice the particle diameter, to reach a maximum of 30– 40 nm. This effect is not shown for the sake of clarity. This graph shows a small boundary film of 2.7 nm provided by the stabilizer adsorption. b. Mixed Rolling-Sliding. In mixed sliding/rolling the colloid response showed the same trend as the silver colloid. Figure 3 collects together the behavior of both pure rolling and mixed rolling/sliding conditions. Fig. 3 Film thickness results for gold colloid in n -hexadecane, SRR effect, 25°C Fig. 4 MTM friction results for gold colloid in n -hexadecane at 30°C, 50 percnet SRR and 30 percent SRR 4.2.2 MTM Friction Results. a. SRR Effect on Friction. As Fig. 4 indicates, at 50 percent SRR at 25°C, this gold colloid shows friction-reducing properties in the boundary regime at an entrainment speed of less than 0.01 m/s, where the film thickness of hexadecane is 2.5 nm. This reduction is higher than that provided by the stabilizer alone. In the mixed regime, the graph also shows a slight friction reduction. This may be explained by a smoothening effect of the surface due to the colloid, shifting the Stribeck curve slightly downwards. Finally in the EHD regime no contribution from the nanoparticles is observed. It can be seen that a reduction to 30 percent SRR causes the gold particles to influence friction at entrainment speeds of 0.05 m/s, i.e., at a higher speed than at 50 percent SRR. b. Temperature Effect on Friction. The temperature effect of the colloid, investigated by performing MTM tests at elevated temperatures and a constant 50 percent SRR, is observed as a significant friction reduction at slow speeds that becomes clearer at high temperature, compared to the base fluid-stabilizer blend. It is found that this gold-oleate colloid provides anti-friction and anti-wear characteristics to the base fluid not only under boundary but also mixed regime; this characteristic was not observed for the silver sol, which worked only in boundary regime. Increasing the temperature reduces the viscosity of the base fluid so that more asperitycolloid particles interactions occur. 4.3 Amine-Capped Gold Colloid 4.3.1 Film Thickness Results. a. Pure Rolling. Figure 6 shows the film thickness measurements for this gold colloid. The combination of base fluid/ stabilizer gives a small boundary film at slow speeds of 2.5 Fig. 5 Effect of temperature on gold colloid performance at 50 percent SRR 554 Õ Vol. 125, JULY 2003 Downloaded From: http://asmedigitalcollection.asme.org/ on 12/11/2013 Terms of Use: http://asme.org/terms Transactions of the ASME Fig. 6 Film thickness results for gold colloid in hexadecane at 25°C SRR effect nm. However, the colloid contribute 6 nm to film thickness in the boundary regime up to an entrainment speed of 0.01 m/s, where the film is lost and only the base fluid film thickness is registered. This colloid behaves as the oleate-capped gold of 20 nm particles did, except that the film contribution is smaller. The most likely explanation of this difference is the much smaller size of the colloidal particles. b. Mixed Rolling/Sliding. It is seen that the colloid shows a similar behavior in the low speed range from 0.002 to 0.006 m/s to pure rolling but above this speed the film falls to the value found for the colloid-free base fluid. 5 Discussion The results of the study carried out provide several aspects for discussion. Effect of Particle Size. The effect of particle size was evident because gold particles of 20 nm were more effective in reducing friction and wear than gold particles of 5 nm. This difference may be because the tiny 5 nm particles allow more asperities interaction than do the 20 nm particles. Rolling Contacts. It has been found experimentally by ultrathin film interferometry that tiny solid colloid particles of gold, and silver are entrained and do pass through lubricated contacts augmenting the EHD film thickness and forming an unevenlydistributed solid boundary film that develops over time and remains in the static contact, separating the mating surfaces. The film formed has usually a beneficial effect on both friction and wear in sliding and rolling/sliding contacts. The thickness of film formed by the colloids was about one or two times the particle size, suggesting an uneven layer of individual or tightly packed particles on the rolling surfaces. This study has revealed that in nominally pure rolling contacts, the particles are entrained when the base oil film thickness is less than the particle diameter (h,d), which practically means at slow rolling speeds or high temperatures. However, as the speed is increased and the base oil film thickness surpasses the particle size (h;d), this contribution is not observed any longer. It is thus likely that colloid particles adhere to the solid, rolling surfaces only if they are mechanically trapped in the inlet, i.e., if they are larger than the film thickness. This trapping mechanism has been discussed for larger solid particles @4#. Once the EHD fluid film thickness becomes greater than the diameter of the particles, most of the particles may then be rejected from the contact inlet by side and reverse fluid flow or just pass through the contact without adhering to the surfaces and thus without contributing significantly to film thickness. It is noteworthy that, for the colloids studied, a contribution to film thickness was seen at rolling speeds only up to a value when the mean oil film thickness reached approximately one or two Fig. 7 Flow pattern of an EHD contact times the particle diameter ~7–10 nm for silver, 20–30 nm for oleate-capped gold and 5– 6 nm for amine-capped gold!. Above this speed, the colloids behaved in a similar fashion to the corresponding surfactant-containing base fluids. Nevertheless, the authors have found that other colloids can form films able to survive high speeds and SRR conditions @14#. It was found that as the temperature is raised, the boundary film formed by colloidal particles survived up to higher entrainment speeds, although this contribution was lost as soon as the base fluid film thickness was about one or two times the particle diameter. This is simply because the viscosity of the fluid and thus the EHD film thickness decreases with temperature so then the effect of colloid film formation is more striking. This indicates that the particle size/fluid film thickness ratio controls the entrapment of particles. These colloidal sols generally showed good anti-friction and anti-wear properties, working best at the highest temperature tested ~100°C!. It is known that in the EHD contact inlet, the flow is divided in two regions. One is the region where the flow can pass through the contact and the other is the reverse-flow or back flow originated by the formation of two vortices that reject part of the flow from the contact. This is represented in Fig. 7 and it has been discussed in references @15–16#. In this figure the velocity profiles describe two main regions. Zone ~A! is the region of reverse flow where the particles are rejected from the contact inlet and zone ~B! is where the particles-containing fluid pass through the contact. This velocity profile has a neutral position ~S! called ‘‘stagnation point,’’ where the fluid forces acting on a particle will be balanced. If a solid particle is in zone ~B!, it has a high possibility of being entrained into the contact whereas particles in zone ~A! will be rejected. The flow streamlines for a point contact in slow rolling conditions were calculated for a 19 mm steel ball on glass disc and plotted in Fig. 8 using a streamline function defined in reference @15#. In this analysis, Grubin’s approximation @17# has been used as an approximation that although simplistic, can be used to speculate about the possible mechanism of entrapment. The forces acting on a particle at the point of contact with the mating surfaces is shown in Fig. 9. It can be seen that in pure rolling, the rubbing surfaces have friction forces that drag the particle into the contact as long as the particle is larger than the film thickness. Figure 8 shows that at slow speed, i.e., when the particle is much larger than the film thickness, the particle is ‘‘pinched’’ by the mating surfaces in the region where most or all the flow pass through the contact and then is entrained. However, at high speed, the stagnation point and back flow vortices move away of the contact inlet @15# and this makes difficult for the smaller particles to reach the point where they can be entrained by the surfaces. In these conditions, the probability that the particles are rejected from the contact is high because only the fluid forces would act on the particles and easily position them in the lines of reverse-flow. Journal of Tribology Downloaded From: http://asmedigitalcollection.asme.org/ on 12/11/2013 Terms of Use: http://asme.org/terms JULY 2003, Vol. 125 Õ 555 Fig. 8 Flow pattern in EHD point contact pure rolling Thus, the particles would not be able to make contact with the frictional surfaces to be entrained into the contact since the location of the stagnation or equilibrium point is farther away of the central contact than it would be for slow speeds. Fig. 10 Typical behavior of colloidal particles with varying slide-roll ratio Mixed SlidingÕRolling Contacts. This study reveals that the behavior of colloid particles in mixed rolling-sliding contacts differs from that in rolling contacts. Particles are still entrained at slow speeds in mixed rolling-sliding contacts, forming a boundary film. However, the ‘‘transition speed,’’ above which the film contribution is lost, decreases with increasing SRR and a pattern similar to Fig. 10 is seen. In practice, as seen for example in Fig. 5 for the oleate-capped gold colloid in hexadecane, this is manifested in a loss of boundary film at lower speeds as the slide/roll ratio increases. This response is probably related to the influence of sliding-rolling on streamline flow patterns in the inlet, as discussed by Hamrock @15#. In mixed sliding rolling contacts, the forces experienced by the colloid particles in the inlet region present two important changes as compared to the pure rolling case. Firstly, the fluid forces will vary as the slide roll ratio is increased; in these conditions, the stagnation point shift towards the slower moving surface and makes the flow streamline pattern asymmetrical, as shown in Fig. 11. It is also important to note that in Poiseuille flow, the forces of the fluid cause the colloid particles to migrate and move near the walls @18 –19#. However, in a Couette flow they remain in the flow central line. As the percentage of slide roll ratio increases, the Couette flow is also increased; this may push some of the particles to reverse-flow lines and could be a reason for rejection of particles from the contact inlet. Now, considering the frictional forces in a pure rolling contact. If the colloid particles move slowly or at the same speed of the mating surfaces then the frictional forces will drag them into the contact. In the case of a mixed sliding/rolling contact, the situation is more complex and will depend usually upon the relative speed of the particles with respect to the surfaces. If the particles make contact with the surfaces at a speed slightly slower than both surfaces, then, they will experience frictional forces that would drag and entrain them into the contact. It should be noted that the fluid itself might also provide a balance to any friction couple experienced. However, if the particles move at the mean entrainment speed, i.e., at an intermediate speed, they will experience a friction couple that could make the particle slip on the contact point and be rejected by back flow as shown in Fig. 12. The direction of the frictional force will depend on the direction of motion of the particle relative to the low surface. Thus, both, fluid and frictional Fig. 9 Forces acting on a particle in a pure rolling contact Fig. 11 Flow pattern in EHD point contact pure sliding 556 Õ Vol. 125, JULY 2003 Downloaded From: http://asmedigitalcollection.asme.org/ on 12/11/2013 Terms of Use: http://asme.org/terms Transactions of the ASME Acknowledgment The authors thank The National Council for Science and Technology ~CONACYT! and Instituto Tecnologico de Oaxaca, Mexico for their financial support in this work. References Fig. 12 Forces acting on a particle in a pure sliding contact forces have to combine to ensure that particles are entrained in conditions that appear to occur when: ~a! they are larger than the film thickness, and ~b! the SRR is low. 6 Conclusions Three metallic colloid systems have been prepared and tested under different conditions. The colloidal dispersions consisted of silver and gold nanoparticles sterically stabilized in n-hexadecane. • Colloidal nanoparticles penetrate into lubricated EHD contacts via a mechanical entrapment mechanism to form a boundary film influencing friction and wear. This film is solid-like and it is unable to renew on the surface at high speeds when the film thickness is thicker than the particle diameter. • These nanoparticles are entrained into rolling and sliding contacts only at slow speeds when the film thickness is smaller than the particle size contributing to film thickness. • For a given %SRR, a critical speed is observed. Below this speed, particles penetrate the contact and influence the film thickness and above this limit, they have no effect. • The study carried out presents direct experimental evidence that particle size/film thickness ratio determines particle entrapment of colloids and that, colloidal solid nanoparticles behave very similarly to their much larger brothers. @1# Palios, S., Cann, P. M., and Spikes, H. A., 1996, ‘‘Behavior of PTFE Suspensions in Rolling/Sliding Contacts,’’ Proc. 22th Leeds-Lyon Symp., D. Dowson et al., eds. Elsevier. @2# Cusano, C., and Sliney, H. E., 1981, ‘‘Dynamics of Solid Dispersions in Oil During The Lubrication of Point Contacts, Part 1-Graphite,’’ ASLE Trans., 25, pp. 183–189. @3# Wan, G. T. Y., and Spikes, H. A., 1986. ‘‘Two Phase Lubricants in Elastohydrodynamic Contacts-Graphite in Oil Dispersions,’’ Proc. 12th Leeds-Lyon Symp., D. Dowson et al., eds. Publ. Butterworths. @4# Wan, G. T. Y., and Spikes, H. A., 1988, ‘‘The Behavior of Suspended Solid Particles in Rolling and Sliding EHL Contacts,’’ STLE Trans., 31, pp. 12–21. @5# Reick, F. G., 1982, ‘‘Energy-Saving Lubricants Containing Colloidal PTFE,’’ Lubr. Eng., 38, pp. 635– 646. @6# Mishina, H., Kohno, A., Kanekama, U., Nakajama, K., Mori, M., and Iwase, M., 1993, ‘‘Lubricity of the Metallic Ultrafine Particles,’’ Jap. Journ. of Trib., 38, pp. 1109–1120. @7# Xue, Q., Liu, W., and Zhang, Z., 1997, ‘‘Friction and Wear Properties of a Surface Modified TiO2 Nanoparticle as an Additive in Liquid Paraffin,’’ Wear, 213, pp. 29–32. @8# Dong, J. X., Chen, G., and Qiu, S., 2000, ‘‘Wear and Friction Behavior of CaCO3 Nanoparticles Used as Additives in Lubricating Oils,’’ Lubr. Sci., 12, pp. 205–212. @9# Chiñas-Castillo, F., and Spikes, H. A., 2000, ‘‘The Behavior of Colloidal Solid Particles in Lubricated Contacts,’’ Tribol. Trans., 43, pp. 387–394. @10# Chiñas-Castillo, F., and Spikes, H. 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J., 1994, Fundamentals of Fluid Film Lubrication, McGraw-Hill, N.Y. @16# Tipei, N., 1968, ‘‘Boundary Conditions of a Viscous Flow Between Surfaces With Rolling and Sliding Motion,’’ ASME J. Lubr. Technol., Series F, 90, pp. 254 –261. @17# Cameron, A., 1981, Basic Lubrication Theory, Ellis Horwood Ltd., Chichester, U.K. @18# Segre, G., and Silberberg, A., 1961, ‘‘Radial Particle Displacements in Poiseuille Flow of Suspensions,’’ Nature ~London!, 189, pp. 209–210. @19# Ho, B. P., and Leal, L. G., 1974, ‘‘Inertial Migration of Rigid Spheres in Two-Dimensional Unidirectional Flows,’’ J. Fluid Mech., 65, pp. 365– 400. Journal of Tribology Downloaded From: http://asmedigitalcollection.asme.org/ on 12/11/2013 Terms of Use: http://asme.org/terms JULY 2003, Vol. 125 Õ 557