Determination of the spreading coefficient of one liquid on another by means of interferometric measurements of liquid-lens thickness

Colloids and Surfaces, 46 (1990) 99-113 Elsevier Science Publishers B.V., Amsterdam

99 -

Printed

in The Netherlands

Determination of the Spreading Coefficient of One Liquid on Another by Means of Interferometric Measurements of Liquid-Lens Thickness KEN-ICHI

ENDOH*,

ATSUSHI

MIKAMI

Department of Mechanical Engineering, Yokohama 223 (Japan)

and YASUHIKO

Keio University,

H. MORI**

3-14-1 Hiyoshi, Kohoku-ku,

(Received 6 April 1989; accepted 24 August 1989)

ABSTRACT This paper describes a new scheme for determining the spreading coefficient of one liquid on another and its application to n-decane-on-water and n-pentane-on-water systems. The scheme is based on classical Langmuir’s capillarity theory for the configuration of an oil lens floating on a water surface [J. Chem. Phys., 1 (1933) 7561 and an optical interference method recently devised by ourselves [Rev. Sci. Instrum., 59 (1988) 20181 which enables the measurement of the thickness of the lens. The spreading coefficient of n-decane on water has been determined to be - (0.35f0.10) mN m-l at 25°C andtendstodecreasewith increasingtemperatureupto50”C. The spreading coefficient of n-pentane on water at 34.3”C has been determined to be - (0.040 + 0.015) mN m-i. It is concluded that the new scheme enables the determination of spreading coefficients whose magnitude may be as small as 0.1 mN m-l or even smaller.

INTRODUCTION

The purpose of this work is to investigate the feasibility of a new scheme for determining the equilibrium (or final) spreading coefficient of one liquid (liquid A) on another liquid (liquid B ) , which is defined as S A/B=CTB-CJA-CT,~B

(I)

where aA9on and aABdesignate liquid A/gas, liquid B/gas and liquid A/liquid B interfacial tensions, respectively, when the three phases (liquid A, liquid B and gas) are mutually saturated [ 11. The spreading coefficient is one of the fundamental properties widely referred to in the literature on interfacial phenomena. It has an importance not only in the field of surface chemistry [l-3] but also in heat-transfer engineering. For example, it can be a critical param*Present address: Dai Nippon Printing Co., Ichigaya, Tokyo 162, Japan. **To whom correspondence should be addressed.

0166-6622/90/$03.50

0 1990 Elsevier Science Publishers

B.V.

100

eter that determines the performance of direct contact evaporators or condensers [ 4-61. In spite of its potential importance in various applications in science and engineering, no reliable method for determining its value has been established. The technical difficulty lies in the fact that the spreading coefficient has, in many liquid/liquid combinations, a negative value whose magnitude is so small as to be comparable with that of the measurement uncertainty of each interfacial tension. Thus, the conventional procedure for determining the spreading coefficient, which is simply to substitute interfacial tension data obtained by individual measurements into Eqn ( 1) , can lead to an unexpectedly large error [l-4,7,8]. To circumvent this difficulty, it is necessary to establish an alternative for determining the spreading coefficient that does not essentially rely on interfacial tension data. However, surprisingly little effort has been directed to this task. In our view, the most promising method for determining a spreading coefficient having a negative value of small magnitude is to measure the thickness of a lens of liquid A floating at a liquid B/gas interface (Fig. 1) and then calculate directly the spreading coefficient from the thickness. The method is based on Langmuir’s classical capillarity theory for the geometry of oil lenses on water [91. A particular version of the theory which is relevant to the present problem is outlined here: As the volume of a lens of liquid A, which is less dense than liquid B, increases to some extent, both the upper and lower surfaces at the central part of the lens become practically flat and parallel to each other, and the distance between the upper and lower surfaces (i.e. the thickness of the lens at its central part, t) approaches a constant value t, which is independent of the lens volume. The thickness t, is related to the equilibrium spreading coefficient SA,n of liquid A on liquid B, which must have a negative value, as follows: t&,=--

2sA,B k?

PI3

(2)

PA~~-PA)

where PA and pi are the densities of liquid A and liquid B, respectively, and g is the acceleration due to gravity. Thus, the theory permits us to determine, with no reference to the interfacial tensions, the spreading coefficient provided we know the lens thickness t, as well as the densities of the liquids.

Gas

_ Liquid

B

Fig. 1. A lens of liquid A floating on a substrate of liquid B.

.

101

Langmuir himself made an attempt to determine t, for petrolatum and tetradecane lenses on water. He plotted the experimentally determined average lens thickness, f= V/(xR2), against the reciprocal lens radius, l/R, and extrapolated the plot to l/R = 0 where tshould agree with t,, V and R being the volume and the radius of each lens. To our knowledge, this technique for determining t, was used later only by Platford [lo], who intended to determine the spreading coefficients of octanol-hexadecanol mixtures on water. Langmuir’s technique for determining t, apparently has some defects. First, one must prepare lenses of greatly different sizes to make a reasonably accurate extrapolation to l/R=O. A large test chamber is needed in which even the largest lenses can be held without being influenced by the chamber wall. This may bring about a significant technical difficulty when, for example, lenses are to be equilibrated at a high temperature and/or a high pressure. Secondly, any change in the volume of a lens possibly resulting from evaporation, condensation or dissolution before measuring its radius leads to an error in estimating tand then t,. Recently Ohyama and Mori [ 111 devised an interferometric technique for measuring a film thickness of the order of 10 pm-1 mm. The technique was so modified further by Ohyama et al. [ 121 as to enable the measurement of an instantaneous, local thickness at the central part of each liquid lens. This paper reports on our first effort to apply the technique to measuring the liquidlens thickness under a well-defined condition (in the sense of surface chemistry), with the intention of determining the spreading coefficient. An experimental apparatus constructed for this purpose and measurements with n-decane and n-pentane on water, leading to the determination of their spreading coefficients, are described. EXPERIMENTAL

An experimental apparatus was constructed which basically consisted of an optical interferometer and a cell containing a hydrocarbon lens as well as substrate water. Since the principle and the basic design of the interferometer have already been reported [ 121, the description of the interferometer given below is focussed on particular details of its construction applied to the present work. The cell was newly designed, considering both optical and surface-chemical aspects of the experimentation, and its construction is described in some detail. Then follow descriptions of the fluid samples used and the experimental procedure. Interferometer

Figure 2 schematically shows the arrangement of the optical components, which constitute the interferometer, and the test cell. Except for the camera

102

Surface

mirror Pin hole

Fig. 2. Schematic diagram illustrating the layout of the interferometer and the test cell.

located above the screen on which interferograms were to be formed, they were all securely aligned and rigidly fixed on a massive cast-iron surface plate which had been mounted on a desk equipped with pressurized-air supports to minimize the possible effect of ambient vibrations. A beam from a 30 mW He-Ne laser tube was expanded to about 80 mm in diameter and then directed vertically downward to pass through a half-area of an optical planar-convex lens, which was 100 mm in diameter and set, at a height of just its focal length ( N 120 or 180 mm), above a hydrocarbon lens in the test cell. The rays that emerged from the optical lens were focused on the hydrocarbon lens, and reflected at its front and rear surfaces to pass through another half-area of the optical lens. Finally the rays were irradiated on the screen, where they formed an interferogram composed of concentric, semicircular interference fringes [ 121. The interferogram was photographed with a camera which was supported separately from the desk bearing the other optical components and the test cell. Pictures of individual interferograms were analyzed and processed on a Nat model 350E analysis projector connected to an NEC PC-9801F computer to deduce data on the hydrocarbon lens thickness. The thickness thus deduced may have an error of ‘_ 0.01 mm because of a minute inaccuracy in positioning the interferometer relative to the test cell [ 121 and limits in the precision of the interferogram analysis.

Test cell We prepared two test cells illustrated in Figs 3 (a) and (b). These cells were quite similar to each other except for some additional appurtenances attached to the one for measurements at elevated temperatures. Figure 3 (a) illustrates the structure of the other cell, which was used in the measurements with ndecane lenses at room temperature (25 5 1 “C). It consisted of a cylindrical PMMA [poly (methyl methacrylate) ] container, which had an optically flat glass window at its top, and a cylindrical borosilicate glass dish of 180 mm in diameter, which was to be set inside the PMMA container and to hold sub-

103 Hydrocarbon reservoir

Water re5ervoi

r

Hydrocorbon/Mitor

Fig. 3. Cross-sectional views of the test cell for room-temperature experiments, (a), and for elevated-temperature experiments, (b). External attachments such as liquid reservoirs are not drawn to scale. The supplies of hydrocarbon/water vapor mixture and of hot air indicated in (b) were used only in the experiments using n-pentane as the lens-forming liquid.

strate water inside. The rim of the glass dish was oblique to its bottom. In experiments the PMMA container was so inclined that the rim of the glass dish became horizontal. We contrived a particular configuration of the cell as mentioned above in order to prevent the rays reflected at the bottom of the glass dish and that of the PMMA container from interfering with the rays reflected at the liquid-lens surfaces and, at the same time, to ensure a flooding of the water over the whole circumference of the rim of the glass dish when an additional amount of water was supplied from an external reservoir to the dish. Such a flooding, which was not attained satisfactorily with the cell used in the previous study [ 121, was considered to be essential to purge, at the stage of preparation of each experimental run, contaminants possibly adsorbed at the water surface. Connected to the cell were the assemblies for supplying water and a hydrocarbon into the cell as well as a drain tube. They were all made of glass and Teflon and were so tightly fitted to the PMMA container wall with the aid of Viton O-rings as to insulate the atmosphere in the cell from the outside. Consequently the atmosphere could consist of air saturated with the vapors of water and the hydrocarbon in use. The total pressure of the ternary air/water/hydrocarbon mixture was nearly equal to the laboratory pressure ( 1: 101.3 kPa).

104

The other cell illustrated in Fig. 3 (b) was constructed for measurements at temperatures moderately elevated above room temperature. It was equipped with a water jacket whose temperature could be controlled to t 0.1 K in a range of 2 30” C with the aid of a PID controller to which an electric heater in the jacket was connected. The cell was a little larger than the one for room-temperature use: the glass dish to contain water was, for example, enlarged to 200 mm in diameter. At its top the cell had a double window; the space between two optically-flat glass plates was held in a vacuum in the experiments with ndecane lenses. When n-pentane was used as the lens-forming liquid, heated air was passed through the space to prevent the lower glass plate from becoming opaque because of condensation of the vapors inside the cell. In the experiments with n-pentane, a mixture of n-pentane and water vapor was continuously supplied from an external borosilicate glass boiler to the cell, which purged the air from the cell. The vapors of n-pentane and water were simultaneously generated in the boiler under the coexistence of the liquid and vapor phases of either substance. The temperature in the water jacket, and thereby that in the test cell, were controlled to 34.3 ’ C, at which the sum of the saturated vapor pressures of n-pentane and water becomes equal to the 101.3 kPa, to which the total pressure in the cell was very close. Thus, we could expect that a thermodynamic equilibrium would be established, with a reasonable accuracy, in the cell. Every Viton O-ring used in the cell was replaced by a Teflon-coated one before the experiments with n-pentane, because of the insufficient chemical stability of an FPM rubber against n-pentane vapor. Fluid samples The hydrocarbons selected for the experiments were n-decane and n-pentane supplied by Tokyo Kasei Kogyo Co., Tokyo. The certified purity of either liquid was 99%. They were distilled once with an all-glass distillation apparatus in our laboratory before use except for the n-decane sample used as received from the supplier, which was also tested for comparison in a preliminary experiment. Water was prepared in three grades: city tap water; water taken from an Auto-Still WAR-30 apparatus (Yamato Scientific Co., Tokyo), which comprises a reverse osmosis device and an ion-exchange device as well as an allglass distillation unit; and water taken from the Auto-Still and then distilled again in another all-glass distiller. We refer to these water samples as ‘tap water’, ‘singly distilled water’ and ‘doubly distilled water’, respectively. The former two were used only in the preliminary experiment, coupled with the distilled or undistilled sample of n-decane. In the other experiments the doubly distilled water was exclusively used. Since the surface properties of water can be affected appreciably by even a trace amount of surface-active contaminant, possibly resulting in a significant

105

change in the spreading behavior of a hydrocarbon on water, it may be worthwhile to describe the properties of the distilled waters we used. As to the static surface tension, it has been confirmed that even the singly distilled water shows values in agreement with those recommended by Ref. [ 131 within the stated uncertainty of the latter over the temperature range 1%200°C [ 7,8]. However, a more sensitive test, the ‘bubble persistence test’ [ 141, shows a difference between the two distilled waters. Air bubbles trapped in the doubly distilled water burst immediately (within 0.5 s) every time they rise to the free surface, indicating the surface is practically free of surface-active material. In contrast, bubbles in the singly distilled water do not always burst immediately at its surface, some persisting for several seconds [ 151. Thus the surface cannot always be called ‘clean’ in the strict sense. PFOCedUFe

Before each series of experiments the test cell was taken apart, cleaned, reassembled, and again cleaned. The cleaning processes before and after assembly, which are considered crucial for experiments of this kind, generally followed those described in Ref. [ 151 and are detailed in Ref. [ 161. Here we only mention that every component of the cell which was to come into contact with a test fluid was finally rinsed, after assembly, with a large amount of the same fluid sample as the one to be used in the succeeding experimental runs. Each experimental run was started by feeding a specified volume of a hydrocarbon liquid stored in the external reservoir to the water surface through a glass capillary whose tip was beneath the surface and open upward. After the hydrocarbon had formed an apparently stable lens, the interferogram observed on the screen was photographed repeatedly through the lens-aging process, which extended from some 10 min to 500 h. The hydrocarbon liquid was added from time to time to the lens during its aging process in some experimental runs, but not in others. Each interferogram thus recorded on a 35-mm photographic film was analyzed to deduce the lens thickness at each instant.

Evaluations offluid

properties

for

data processing

The physical properties needed in the course of data processing were the refractive index of the lens-forming liquid and the mass densities of both the lens-forming and substrate liquids. The former was measured by ourselves with an Abbe refractometer (model lT, Atago Co., Tokyo), which was coupled with a He-Ne laser as a light source and with a temperature-controlled-water feeding device (Uni-ace 110, Tokyo Rika Co., Tokyo) for adjusting the temperature of each hydrocarbon sample to the one set in the relevant lens-thickness measurements. The latter were evaluated in accordance with the data given in Ref.

106

[ 171, assuming that the densities of respective liquids are not affected by a minute mutual dissolution. RESULTS AND DISCUSSION

Behavior of hydrocarbons on water surface It is needless to say that the present method for determining the spreading coefficient SA,n is dependent on the formation of stable lenses of liquid A on the surface of liquid B. Whether n-alkanes, particularly lower homologs up to n-octane, spread to form multilayers or form discrete lenses on the water surface has been a subject of controversy for over 60 years, as briefly surveyed in Ref. [ 181. Thus, our first priority in this work was to observe how the hydrocarbon samples behave on the water surface in our experimental apparatus. The first observational experiment was done with all possible combinations of the two grades of n-decane with the three grades of water. We found that lenses stable for over a few hours could be obtained only with the distilled ndecane coupled with the doubly distilled water or the singly distilled water. The lens thickness was appreciably larger on the doubly distilled water than on the singly distilled water. In cases of lower-grade couples, n-decane finally spread over the whole water surface in the glass dish. Based on the above observation, we decided to use exclusively the combination of the distilled ndecane and the doubly distilled water in the later experiments. To be consistent, distilled n-pentane was selected for use with the doubly distilled water and was found to form apparently stable lenses. It may be necessary to pay special attention to the behavior of n-pentane on water mentioned above. In their (presumably very careful) experiments, de1 Cerro and Jameson [ 181 observed a quite complex behavior of n-pentane on water. They wrote that n-pentane did not form stable lenses, but neither did it spread to form a film of uniform thickness. There exists an apparent difference between their observations and ours. The difference must be an experimental artifact possibly caused by insufficiencies in purifying the fluid samples, cleaning the test cell, equilibrating the interfaces, etc. At present we have no definite evidence to show which of the two observations represents more accurately the inherent behavior of n-pentane on water. n-Decane lenses at room temperature First we performed some experimental runs in the following way: with the water surface in the glass dish renewed by flooding an amount of water, ndecane of l-2 cm3 volume was supplied to the surface to form a single lens. nDecane was added from time to time to the lens until its volume and diameter increased to 3-4 cm3 and about 120 mm, respectively, at the time lapse of 140-

107

1.2 E' .l.O -

0

0

1 0

u. 11 A 100

Time

I, 200

,

hours

I 300

Fig. 4. Variation of the thickness of an n-decane lens with the time lapse after its formation. The arrows on the abscissa indicate the instants at which n-decane was added to the lens.

‘61: 0

100

200 Time

300

,

400

500

600

hours

Fig. 5. Variation of the thickness of an n-decane lens with the time lapse after its formation. The initial volume of the lens was 4.0 cm3. No addition of n-decane to the lens was made after its formation.

310 h after the initial lens formation. The measurement of lens thickness was repeated in this manner to determine the variation of the thickness over such a long time lapse. Figure 4 exemplifies the variation of the thickness obtained in one of the experimental runs. The arrows on the abscissa indicate the instants at which n-decane was added to the lens. The results of runs of this kind indicate that the lens thickness changes little with an increase in the lens volume exceeding 2 cm3, nor does it vary significantly with a time lapse of over 50 h.

108

@ $j ;

-0.6

-0.6

0

100

200

300 Time

GO0

500

600

hours

Fig. 6. Spreading coefficient of n-decane on water deduced from the data given in Fig. 5.

Figure 5 shows the result of an experimental run in which n-decane was never added in the course of ‘aging’ of a lens which had initially been formed by 4.0 cm3 n-decane fed to the water surface. It is seen that after a remarkable contraction within the first 50 h the lens attained a nearly constant thickness of about 0.6 mm, which is in good agreement with the asymptotic thickness seen in Fig. 4. In Fig. 5 we note that a long-period fluctuation in thickness, which is larger than the simple measurement error, persisted after a time lapse of 100 h. The fluctuation may be ascribed at least in part to a variation in the temperature of the test cell. Substituting the instantaneous thickness data given in Fig. 5 for t, in Eqn (2 ) , we obtain the variation of the spreading coefficient SA,n = Sdecane,,.,ater with time lapse, which is shown in Fig. 6. Here we see that after 100 h Sdecane,water fell in the range of 20.1 mN m-l around -0.35 mN m-l. This is consistent with the results obtained in all of the other runs using n-decane lenses at room temperature. n-Decant lenses at elevated temperatures The experiments were performed, using the test cell illustrated in Fig. 3 (b) and following a short-cut procedure. An n-decane lens was aged for over 50-60 h at room temperature, and then the temperature in the cell was raised to 30” C. After 2 h or more at the new temperature level, a lens thickness measurement was made just once. Successively the temperature was raised to 40°C and then to 5O”C, and a thickness measurement was performed at each temperature level in the same way as stated above. Two sets of measurements were made with two individually prepared lenses, and the results obtained are plotted in Fig. 7 with the thickness data converted into the values of Sd_.,e,water.Also

109

- 2.0 20

I , LO 30 Temperature

T.

50 ‘C

60

Fig. 7. Spreading coefficient of n&cane on water plotted against temperature. The closed circle and vertical bar on the circle indicate the average and the fluctuation range, respectively, of the spreading coefficient obtained at room temperature (see Fig. 6), while the open circles and triangles indicate the values of the spreading coefficient obtained in two different runs using the test cell equipped with a temperature-control device [Fig. 3 (b) 1.

indicated in Fig. 7 for comparison is the value of Sdscane,water obtained with the other test cell at room temperature. Here we see that Sdecaneiwater tends to decrease with increasing temperature. However, this finding should be accepted with some reservation because of the short-cut procedure adopted in lensthickness measurements at elevated temperatures. Long-term observations of lenses are required at elevated temperatures as well in order to confirm the temperature dependence of Sdecane,water indicated above.

n-Pentane lenses We observed that n-pen&me lenses with initial volumes of 1.0-3.0 cm3 tended to become thin with a time lapse exceeding lo-50 min after their formation, showing little change in their radii, and they disappeared within another 2040 min. The smaller the initial volume, the shorter the life of the lens. This is presumably ascribed to a slight amount of residual air in the test cell, which must have resulted in the evaporation of n-pentane from the lenses. Figure 8 shows variations of the thicknesses of three different n-pentane lenses having the largest initial volume, 3.0 cm3, after their formation. It is recognized that each of these lenses had a nearly constant thickness for about 40 min, until its thinning became remarkable at later stages of its life. Substituting the thickness data given in Fig. 8 into Eqn (2), we get the Spentaneiwater versus time diagram given in Fig. 9. The values of Spentane,water based on ‘nearly-constant thickness data’ fall in the range - (0.040 2 0.015) mN m-l, which we assume to be the range of possible values of the equilibrium spreading coefficient of n-

I

OO

I

10

I

I

20

LO minutes

,

Tim:’

I

I

50

60

Fig. 8. Variation of the thickness of n-per&me lenses with the time lapse after their formation. Each symbol corresponds to each sample lens whose initial volume was 3.0 cm3.

E

0

t E

-0.15;

I 10

I 20

I Tim:’

,

I Lo minutes

I 50

I 60

:

Fig. 9. Spreading coefficient of n-pentane on water deduced from the data given in Fig. 8.

pentane on water in our experimental system. The uncertainty in Spentane,water determined above is relatively large ( +-40% ) . It must reflect a thickness-measurement error attributed to our optical system, minute vibrations of the sample lenses, the degree of contamination of the fluid interfaces, which must have differed from run to run, etc. It should be stressed here, however, that the we have determined above is so small that it would magnitude of SWntanejwater hardly be determined within + l,OOO%uncertainty by the conventional method, which relies on individual measurements of the three interfacial tensions. Thus, we can reasonably claim an advantage of the present scheme for determining

111

the spreading coefficient over the conventional method, particularly when their magnitudes are small. Evaluation of deviation of measured lens thickness t from t, Thus far we have assumed that each measured lens thickness t well approximates t,, the thickness of an infinitely large lens, and have substituted the former for the latter in Eqn (2). Errors possibly caused by this assumption are examined here, using the calculation scheme of Pujado and Striven for lens configurations [ 191. The results of calculations for n-decane and n-pentane lenses on water are illustrated in Figs 10 (a) and (b ), respectively, in each of which aA and a, are, respectively, fixed to certain values given in the literature [7,17,20] and on is so varied as to yield several different values of SA/B. For each value of SA/B the variation of the thickness at the center of a lens with its radius, R, is indicated. In the diagrams given in Figs 10(a) and (b) one can read an expected deviation of t from its asymptotic value for R+co, i.e. t,, once SA,B and R are known. Since we employed lenses of R 2: 50 mm and detected their near-center thicknesses in the present experiments, the thickness data we obtained presumably overestimate the relevant t, values by 34% for n-decane lenses and 3% or less for n-pentane lenses. This in turn 2 SMB= -3mN/m ‘\ _/--

*=

1.

0.07 ,A

_

E

,

x-\_

-2

/

‘. 0.0s I

/ /

_/----

-1.5

I

_.__

e1

-s

0.03

e

--

----_

*-

0.

: --__

I I

-025 I

Radius

I

a! !

R,

mm

,

_.___

/

Radius

R

.mm

Fig. 10. Dependence of lens central thickness t on the lens radius R (solid lines). The relative deviations oft from t,, the thickness of an infmitely large lens, are indicated by broken lines. The diagrams represent the solutions of calculations which are made, based on the theory of Pujado and Striven [ 191, assuming different values of SAla, while a,, and uAeare fixed as follows: (a) ndecane/water, aA=23.37 mN m-l [ 171, a-=50.5 mN m-l [20]; (b) n-pentane/water, aA= 14.59 mN m-l [7], u-=47.78 mN m-’ [7].

112

should result in an overestimation of 1SAjBj by 6-10% for n-decane and about 6% or less for n-pentane, which are far smaller than the uncertainties in ISA/u\relevant to the scatters in lens-thickness data and are thus neglected here. GENERAL DISCUSSION

The interferometric technique developed by Ohyama et al. [ 121 has proved to be fit for lens-thickness measurements. Although some optical problems still remain to be considered in refining the technique [16,21], it is already usable for the purpose of determining spreading coefficients, whose magnitudes may be as small as 0.1 mN m-l or less. On the other hand, it is essentially difficult to assure the adequacy of the technique for preparing liquid lenses. Each lens must be rigorously equilibrated on the substrate liquid at a desired thermodynamic state, while every fluid interface should be kept clean in the sense of surface chemistry. The lens preparation technique we tested in the present work is a product of our previous experience [11,12,15,16,21], but it still needs to be refined further toward the fulfilment of the above condition. Some of the findings obtained in the present work are unexpected, and they should be observed carefully. For example, the time required for the spreading coefficient of n-decane on water to approach its final value (to be more exact, the value that we assumed as such) was found to be very long (50-100 h). Such a long-term relaxation of the spreading coefficient must be dependent on the particular geometry and dimensions of the test cell used as well as on the low vapor pressure of n-decane in the gaseous phase at a given temperature ( N 25°C). The relaxation time will presumably shorten as the dimensions of fluidmterfaces are reduced and the vapor pressure of the lens-forming liquid increases. The dependences of the relaxation time on these parameters could also be the subject of research, along with the determination of the equilibrium spreading coefficient on which our effort has been focussed so far, because we rarely encounter real systems in which complete equilibration of fluid interfaces is ensured. Based on their measurements of interfacial tensions using the pendant drop method, Mori et al. [ 71 derived the spreading coefficients of n-pentane and nhexane on water, which increase with an increase in temperature. (Even though individual values of the spreading coefficients derived by Mori et al. [ 71 have much larger uncertainties than those given in the present work, these values possess apparently clear, positive temperature dependences.) The temperature dependence of the spreading coefficient of n-decane that we found in the present work (Fig. 7) is contrary to the above. It will be a task of future study to reveal whether the temperature dependence (in the range 25-50’ C ) truly reverses as the number of carbon atoms in the chain increases from 6 to 10.

113 ACKNOWLEDGMENT

We are grateful to H. Yoshigiwa, a student at the Department of Mechanical Engineering, Keio University, for his assistance in part of the experimental work.

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W.D. Harkins, The Physical Chemistry of Surface Films, Reinhold, New York, 1952, pp. 94106. J.T. Davies and E.K. Rideal, Interfaciai Phenomena, Academic Press, New York, 1963, pp. 20-34. A.W. Adamson, Physical Chemistry of Surfaces, 4th ed., Wiley, New York, 1982, pp. 103111. M. Bentwich, U. Landau and S. Sideman, Int. J. Heat Mass Transfer, 13 (1970) 945. Y.H. Mori, K. Nagai, H. Funaba and K. Komotori, Trans. ASME, J. Heat Transfer, 103 (1981) 508. Y.H. Mori, Int. J. Multiphase Flow, 11 (1985) 571. Y.H. Mori, N. Tsui and M. Kiyomiya, J. Chem. Eng. Data, 29 (1984) 407. H. Matsubara, M. Murase, Y.H. Mori and A. Nagashima, Int. J. Thermophys., 9 (1988) 409. I. Langmuir, J. Chem. Phys., 1 (1933) 756. R.F. Platford, Can. J. Chem. Eng., 58 (1980) 393. T. Ohyama and Y.H. Mori, Rev. Sci. Instrum., 58 (1987) 1860. T. Ohyama, K. Endoh, A. Mikami and Y.H. Mori, Rev. Sci. Instrum., 59 (1988) 2018. International Association for the Properties of Steam, Release on Surface Tension of Water Substance, 1976. J.A. Kitchener and CF. Cooper, Q. Rev. Chem. Sot., 13 (1959) 71. T. Nosoko, T. Ohyama and Y.H. Mori, J. Fluid. Mech., 161 (1985) 329. K. Endoh, M. Eng. Thesis, Graduate School of Science and Technology, Keio University, Yokohama, 1988. TRC Thermodynamic Tables-Hydrocarbons, Thermodynamics Research Center, Texas A&M University, Texas, 1987. C. de1 Cerro and G.T. Jameson, J. Colloid Interface Sci., 78 (1980) 362. P.R. Pujado and L.E. Striven, J. Colloid Interface Sci., 40 (1972) 82. H.Y. Jennings, Jr., J. Colloid Interface Sci., 24 (1967) 323. T. Ohyama, M. Eng. Thesis, Graduate School of Engineering, Keio University, Yokohama, 1986.