Elastohydrodynamic lubrication with water-in-oil emulsions

WEAR ELSEVIER

Wear

Elastohydrodynamic

179 (1994) 17-21

lubrication

with water-in-oil

emulsions

Wenyi Liu *, Darning Dong, Yoshitsugu Kimura, Kazumi Okada Institute of Industrial

Science, University of Tokyo 7-22-l Roppongi, Minato-ku,

106 Tokyo, Japan

Abstract Although water-in-oil (W/O) emulsions have higher viscosity than the base oils, they often form thinner elastohydrodynamic films than those formed with the base oils alone. This unreasonable behavior of W/O emulsions is studied experimentally and analytically. First, atmospheric and high-pressure viscosities of W/O emulsions are measured in a rolling-sphere viscometer. Secondly, the minimum thickness of their elastohydrodynamic films in line contact is determined with an X-ray transmission technique. Then a two-phase hydrodynamic film model is proposed, and Patir-Cheng’s average flow concept is employed to calculate the equivalent viscosity of the films. Finally, a full elastohydrodynamic solution is obtained by using a multigrid technique. Keywords: Elastohydrodynamic

lubrication; Emulsion

1. Introduction Water-on-oil (W/O) emulsions interest tribologists as lubricants owing to their fire-resistant property where there is possible risk from fire, and to their large heat capacity when their role as coolants is expected. On the other hand, when lubricating oil is contaminated with water, W/O emulsions are sometimes formed by the presence of dispersants. Several experimental works have been reported on EHL film thickness with W/O emulsions [l-4] which show unclear results. When determined in optical EHL experiments with point contact, the ratio of the minimum film thickness with W/O emulsions to that with their base oil ranges from 0.97 to 1.55 as summarized in ref. [4]. This seems still more unreasonable when marked increase in the viscosity of W/O emulsions with water concentration is taken into account [5]. This problem is examined experimentally and analytically here.

2. Experimental details 2.1.

WI0

emulsions

Four W/O emulsions were prepared with a nonadded paraffinic mineral oil having atmosphericviscosity of 49.3 x low3 Pa s at 40 “C, distilled water and polyoxyethylene-oleyl ether (hydrophile-lipophile balance * Corresponding

author.

0043-1648/94/$07.00 0 1994 Elsevier Science S.A. All rights reserved SSDI 0043-1648(94)06510-l

(HLB) 4.9) as the emulsifying agent. The concentration of the emulsifying agent was set so that it is 10 wt% of the water concentration for Al and A2, and 20 wt% for A3 and A4. The properties of these emulsions are shown in Table 1. 2.2. Viicosity of

WI0

emulsions

Viscosity of the W/O emulsions was determined at atmospheric pressure and at high pressures in a rollingsphere viscometer, which determines viscosity from the speed of a ball rolling down in an inclined cylinder filled with the emulsions. Viscosity at atmospheric pressure increases with water concentration as shown in Fig. 1. Viscosity also increases with pressure and, when plotted on a semi-logarithmic chart (Fig. 2) data fall on straight lines, being nearly parallel to that for the base oil, showing that it is represented by the Barus equation and that viscosityTable 1 W/O emulsions No.

Water cont. vol%

Emulsifying agent cont. vol%

Al A2 A3 A4

9.0 36.0 8.0 32.0

1.0 4.0 2.0 8.0

Average particle diameter (pm) 18.0
Atmospheric viscosity (10m3 Pa s)

53.2 133 48.5 115

A3

10-I Water concentration, Fig. 1. Atmospheric

viscosity

of W/O

do

loo

10’

10’

vol% Diameter of particles,

emulsions. Fig, 3. The distribution

function

for particle

km

diameter

of A2 em&ion.

l(P mm oil

Al A2 0 A?

IO

0.00

0.05 n

base oil

Fig. 2. High-pressure

0.10 Pressure, GPa 0

Al

viscosity

0

of W/O

A2

0.15

0

0

A3

+

A4 Fig. 4. Experimental sions.

emulsions.

pressure coefficients of the emulsions that of the base oil (17.7 GPa-‘).

are similar to

2.3, Distribution of water droplet diameter The diameter of water droplets in emulsion A2 was determined by a laser diffraction particle size analyzer. As Fig. 3 shows, it has a rather wide distribution ranging from the submicrometer range to about 10 ,um. Generally, water-droplet diameter in an emulsion follows a log-normal distribution. However, to simplify the mathematics in numerical calculation, it is approximated by a reciprocal Weibull distribution, F(d) = exp[ - C,(d -d,)-Cz]

(1)

where the constants are chosen to give the best fit: C, =0.368, C,= 1.732 and d, = 0.39 pm.

I

I

0.20

10

20 Water conccntratlon,

minimum

1

30 vol’7r

EHL film thickness

40

with W/O emul-

2.4. EHL film thickness

Minimum EHL film thickness was determined on a four-roller apparatus described elsewhere in detail f6], in which EHL films were formed between a center roller and three outer rollers. The rollers were made of hardened bearing steel, being 40 mm in diameter, Ra 0.04 pm in surface roughness, and 9 mm in contact width. They were run under a pure rolling condition at a surface speed of 3.14 m s-’ under a load of 1.8 kN causing 0.9 GPa mean Hertzian pressure; the temperature was kept at 40 “C. The minimum EHL film thickness was determined by measuring the intensity of X-ray transmitted through the clearance between a pair of the rollers. Results are given in Fig. 4. In contrast to the increase in viscosity, the thickness of the EHL films decreases with water concentration. Further, the

19

W. Liu et al. / Wear 179 (1994) 17-21

film thickness values are in the range of 0.446 under the present conditions.

Water patch

Emulsion

pm

3. Analytical 3.1. Two-phase hydrodynamic film model When the EHL film thickness determined above is compared with Fig. 3, it is found that the film thickness is smaller than the diameters of the majority of the water droplets, which seems to be the case in many applications. This suggests that EHL films are heterogeneous, to which hydrodynamics based on bulk viscosity is no longer applicable. An engineering model, i.e. a two-phase hydrodynamic film model, is then introduced. Fig. 5 illustrates an EHL film in line contact, in which the x-axis is taken in the direction of rolling and the y-axis parallel to the rolling axis. A certain part of the film is occupied by dispersed large water droplets, which form water patches, and the remaining part, the continuous phase, is emulsion suspending small water droplets in oil. Local viscosity qt takes either of the two values: viscosity of water in the water patches or that of emulsion for the continuous phase. The former can be assumed constant if an insignificant effect of interface tension is ignored, but the latter does vary in an EHL film. That is, the critical diameter defining the large and small droplets is, hypothetically, given by the local film thickness, which is a function of X, as are the water concentration in the continuous phase and its viscosity. 3.2. Equivalent viscosity

Although W/O emulsions show slightly non-Newtonian behavior [7], tentatively the Reynolds equation is used in the present analysis. Then an equivalent viscosity 77, which is a function of x is introduced, and PatirCheng’s average flow concept [8] is employed for its calculation. Fig. 6 illustrates a small element of an EHL film &Ay, which is large enough to assume a number of

water/

Fig. 6. An element of EHL film.

water patches in it, but still small compared with the size of the EHL conjunction. If h is assumed constant over this element, the right-hand side of the Reynolds equation is zero, so that

As the boundary conditions, a small pressure difference is assumed across the element in the x-direction, and ap/@ = 0 at the sides parallel to thex-axis. The population of the water patches and the concentration of water in the continuous phase are set to desired levels. Then numerical solution of the Reynolds equation is repeated in the element by using a finite difference method, where the water patches are randomly relocated each time and the local viscosity 7, at each point is employed accordingly, to give a reasonably averaged distribution of pressure p. When the pressure distribution is obtained, the average flow rate in the x-direction for a unit width is given by the left side of the equation, 1 A--h3 ap dy= r s 12% ax 0

--h3 * 1277. h

(3)

If )j on the right hand side is the average pressure in the element, r], represents an equivalent viscosity, which gives the same average flow rate in the x-direction through a single-phase film element having the same geometry under the same boundary conditions with respect to pressure. In Fig. 7, the equivalent viscosity of W/O emulsions relative to the viscosity of the base oil is plotted against 4 and 5, where 4 is the total water concentration of a W/O emulsion and [ is the fraction of water content which forms the water patches. With l= 1.0 the equivalent viscosity is reduced to the bulk viscosity of the W/O emulsion. Further, the relative viscosity qr for a constant value of 4 can be approximated with sufficient accuracy by a quadratic function,

droplet

Fig. 5. Concept of two-phase hydrodynamic film.

(4)

/

(prcsenl m&l)

J

1

Analytical (wth bulk vwos~ty)

) I

_’

1

0.5

0.0

1.0

15

Mlmmum EHL film thickness,

Fig. 8. Comparison Fig. 7. Relative viscosity versus water concentration fraction of small water particles 5 (viscosity of base

of experimental

and analytical

pm

EHL film thickness.

4 and volume oil=l.O).

‘I

3.3. Minimum EHL film thickness .A3

Fig. 7 suggests that EHL films with W/O emulsions can be thicker or thinner than those formed with their base oil, 4= 0, depending on the diameter of water droplets, which qualitatively explains the confusion in the results reported so far. A quantitative comparison of experimental and analytical results is then tried with W/O emulsion A2 in the following. For a given emulsion, 4 is assumed to be constant. This is different from the assumption made in the analysis of EHL with OiW emulsions [6,9], where increase in oil concentration by trapping of oil droplets between solid surfaces formed an essential point of the theory. In the case with W/O emulsions, exclusion of water is practically prevented by the high viscosity of oil phase to make the present assumption reasonable. By using the distribution function of the droplets diameter, Eq. (l), the equivalent viscosity of the W/O emulsion at the atmospheric pressure is represented by Eq. (4), and that at high pressures is obtained by the Bar-us equation with the same viscosity-pressure coefficient with the base oil as was noted above. Numerical calculation of EHL film thickness is conducted by using a multigrid technique after Venner [lo], where eight levels of grids are employed. The result is given in Fig. 8 together with the experimental and the analytical results based on the bulk viscosity of the emulsion. It is clear that the conventional calculation based on the bulk viscosity predicts a much thicker film than the experiment, while the present analysis leads to closer agreement. The same calculation is also carried out for the other samples, and the results are compared with the experimental results in Fig. 9 to give reasonable agreement.

,

,

Al

/o 0

A2, ”

lg ,

A4 0 ,

I

/

I , , ,

0.40

-I

0.40

0.45

0.50

Experimental Fig. 9. Comparison

of results

results,

for minimum

0.55

0.60

km EHL

film thickness.

4. Conclusions EHL film thickness with W/O emulsions is studied experimentally and analytically. The viscosity of W/O emulsions at atmospheric pressure increases with water concentrations, while their viscosity-pressure coefficient is similar to that of base oil. In contrast, the present experiments show EHL film thickness with W/O emulsions slightly decreases with water concentration. Analysis based on a newly proposed two-phase hydrodynamic film model has presented a quantitative explanation for this problem, where the diameter of water droplets plays a significant role.

Acknowledgement

The authors would like to express their thanks to Dr. Natsumeda for his cooperation in the numerical calculation of EHL film thickness, and to Dr. Yasutomi

W. Liu et al. I Wear I79 (1994) 17-21

for his cooperation in the determination of emulsion properties. This research has been supported by Japan Society for Promotion of Science and Ministry of Education, Science and Culture.

References PI H. Hamaguchi,

H.A. Spikes and A. Cameron, Elastohydrodynamic properties of water in oil emulsions, Wear, 43 (1977) 17. PI G. Dalmaz and M. Godet, Film thickness and effective viscosity of some fire resistant fluids in sliding point contacts, ASME J. Lube. Technol., IO0 (1978) 304. and film thickness measurements of a [31 G. Dalmaz, Traction water glycol and a water in oil emulsion in rolling-sliding point contacts, Proc. 7th Leeds-Lyon Symp. on Tribology, 1981, p. 231.

21

[41 G.T.Y. Wan, P. Kenny and H.A. Spikes, Elastohydrodynamic properties of water-based fire-resistant hydraulic fluids, Tribol. hat., 17 (1984) 309. (ed.), Emulsion Science, Academic Press, 1968 151 P. Sherman (quoted from Japanese translation, 1971) Chapter 4. lubrication with [61 Y. Kimura and K. Okada, Elastohydrodynamic oil in water emulsions, Proc. ISLE Int. Tribal. Con&, 1985, p. 937. [71 Liu Wenyi et al., EHL with W/O emulsions, 3rd Report, Proc. JAST Tribal. Co@, Tokyo, Japan, 1992, p. 347. [sl N. Patir and S.H. Cheng, An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication, ASME I. Lubr. TechnoZ., 100 (1978) 12. 191 Y. Kimura and K. Okada, Film thickness at elastohydrodynamic conjunctions lubricated with oil-in-water emulsions, Proc. ZMechE, Cl76/87 (1987) 85. [lOI

C.H. Venner, Multilevel solution of the EHL line and point contact problems, Ph.D. Thesis, University of Twente, 1991.