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A measurement of interfacial tension between tetradecane and ethylene glycol water solution by means of the pendant drop method
iiiim ELSEVIER
Fluid Phase Equilibria 125 (1996) 159-168
A measurement of interfacial tension between tetradecane and ethylene glycol water solution by means of the pendant drop method H. Inaba ", K. Sato Department of Mechanical Engineering, Faculty of Engineering, Okayama Universi~, Tsushima-naka 3-1-1. Okayama 700, Japan
Abstract Interfacial tension between tetradecane (CH3(CH2)t2CH3) (melting point, 5.8 °C; density, 770 kg m -3 (6°C)) and ethylene glycol (CH2OH- CH2OH) (density, 1119.5 kg m -3 (10°C)) water solution was measured by means of the pendant drop method. The measurements were performed for various temperatures of 10 ~ 50°C and mass concentrations of the water solution of 0 (water) ~ I00 mass%. It was clarified that the interfacial tension decreased exponentially in about 60 min after creation of the pendant drop. This paper reports the value of the static interfacial tension obtained when the temporal change of the interfacial tension with time ceases due to the equilibrium of mass diffusion between both liquids. The value of interfacial tension decreases linearly with an increase in temperature and mass concentration of the water solution. As a result, the empirical equation of static interfacial tension was derived in terms of temperature and mass concentration of the water solution.
Keywords: Experiments; Data; lnterfacial properties; Hydrocarbons; Water solution
I. I n t r o d u c t i o n
The authors have reported the study on a new latent cold heat energy storage technique by using a solidification of low freezing point oil droplets [1,2]. This technique is to use direct-contact cooling and solidification of a tetradecane oil droplet (melting point, 5.8 °C) created in a low-temperature ethylene glycol water solution o f 30 mass%. In this study, the oil droplets are made by an injection o f the tetradecane oil from a cylindrical single hole nozzle, and they ascend in the ethylene glycol water solution by buoyancy. The characteristics o f dispersion and motion o f the oil droplets are dominated by interfacial tension between tetradecane and ethylene glycol water solution. Therefore, it is indispensable to determine the interfacial tension between them; however, no report has been seen about it.
" Corresponding author. 0378-3812/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PH S0378-3812(96)03085-3
160
H. Inaba, K. Sato / Fluid Phase Equihbria 125 (1996) 159-168
Up to the present, a large amount of data on interfacial tension for hydrocarbon (including tetradecane)-water systems have been reported. For example, Aveyard and Haydon [3] dealt with normal alkanes (including tetradecane)-water system for various temperatures, and they determined the relationship between the carbon numbers of hydrocarbons and interfacial tension. Matsubara et al. [4] have reported interfacial and surface tension for n-pentane-water and R113-water systems for various temperatures, and they represented some practical data. Unfortunately, the data of interfacial tension between hydrocarbon and specified water solution have not been reported. A practical method to predict the interfacial tension was developed by Good and Elbing [5]. From their paper, the interfacial tension of a binary liquid system tr12 is estimated by the following equation:
Orl2 = Orl + 0"2 -- 2(~12 ~1~1~
(1)
where o"1 and tr 2 are surface tensions of pure liquid of the components 1 and 2, respectively. On utilizing Eq. (1), the surface tensions of tetradecane for various temperatures [6] and those of ethylene glycol water solution for various temperatures and concentrations [7] have been reported. However, the value of parameter ~b~2 or the method to predict it have not been mentioned. This paper reports the measurement of interfacial tension between tetradecane and ethylene glycol water solution for various temperatures and mass concentrations of the water solution. The measurements were performed by means of the pendant drop method. It was attempted to derive the empirical equation in order to calculate the value of interfacial tension between tetradecane and ethylene glycol water solution. In many cases, the interfacial tension varies with time until reaching at the equilibrium of mass diffusion between two liquids. This report mentions the temporal changing behavior of the interfacial tension.
2. Measuring device and procedure
2.1. Measuring device Fig. 1 shows a schematic diagram of the measuring device. It is mainly composed of the test liquid vessel, a fine stainless steel tube for producing a pendant drop, and a constant temperature water bath. A camera and a light source are arranged beside the constant temperature water bath to take a picture of the pendant drop. The test liquid vessel has the 10 cm cubed inner dimension. The two sides of the vessel walls, facing the camera and the light source, are made of a transparent acrylic resin plate of 5 mm thickness for photographing. The other sides of the vessel walls are made of a stainless steel plate of 2 mm thickness. A stirrer and high precision thermometer (T-type thermocouple, diameter of 0.1 mm; minimum temperature scale, 0.1 °C) are equipped in the test liquid vessel. The stainless steel tube for producing the pendant drop has an outer diameter of 1.5 mm and thickness of 0.5 mm. The tube is fixed vertically in the test liquid vessel, and the other side of the tube is connected to a Pyrex glass syringe. The size of the pendant drop can be varied by sliding the piston of the syringe. The camera has a 50 mm lens with bellows to enable close-up photography for the pendant drop. It is relatively difficult to distinguish the outline of a tetradecane oil drop created in the ethylene glycol water solution since the refractive index of the former is the almost same as the latter. Therefore, a
161
H. Inaba, K. Sato / Fluid Phase Equilibria 125 (1996) 159-168
Stainless steel tube ~
Pyrex glass syringe
Thermometer
Pendant drop " ~ ~ 7 .~ ~ ~ (fetradecane oil drop) ~ J d ' ~ I ~ " N"~ [ \ Y I~'~t'td ,/ql/ ,.-"(I
, .'~,. c.tgntsource
,Vat...4. l\uIC2J -" I
Be.o,,s
\
Camera
J !
L .'N_- >'3 "~-F ~
~ /
~ "M"/ ~
I
IN.. Light-shieldingplate
"" Heater Refrigerator
/
[~- -I ,~ Stirrer I
Test liquid vessel (Ethylene glycol v,'atersolution) Fig. 1. Schematic diagram of the measuring device.
light-shielding plate with a small circular hole is set between the test liquid vessel and the light source to make the outline clearer. Tetradecane and ethylene glycol water solution were poured into the well-cleaned and dried syringe and the test liquid vessel, respectively. Subsequently, the tetradecane was sent into the stainless steel tube. The constant-temperature water bath and stirrers were preliminarily operated until the test liquids and whole of the system reach the same temperature. When the entire system took a given temperature, the stirrer in the test liquid vessel was stopped in order to stabilize the water solution in the vessel. Then a pendant drop of tetradecane was made at the tip of the stainless steel tube by pressing out the tetradecane from the tube into the water solution. Fig. 2 shows a photograph of a pendant drop grown at the tip of the stainless steel tube. The value of interfacial tension o- is given by the following equation. A p . g • d~ H
(2)
where Ap is the density difference between these liquids, g is the gravitational acceleration, and d e is the dimension in a pendant drop as shown in Fig. 2. The parameter 1 / H is experimentally derived by Misak [8] as a function of d s / d e, where d s is the dimension in a drop, indicated in Fig. 2. About 10 photographs were taken on a certain measuring condition. The dimensions d e and d s were measured from the photographs of the pendant drop by using vernier callipers. The value of interfaciai tension was determined by averaging the obtained data on a given condition. Before photographing a pendant drop of test liquid, the enlargement of picture is determined by taking a photograph of a scale set in the test liquid vessel with the test liquid under each condition of temperature and concentration. When a photograph of a pendant drop is taken, a straight stainless steel wire (0.08 mm in diameter)
162
H. Inaba, K. Sato / Fluid Phase Equilibria 125 (1996) 159-168 dc
dr
I
~mm]
Fig. 2. Example of a photographof a pendantdrop and measuringpoint on it.
with a weight (about 20 g) is vertically suspended near the test liquid vessel. The image of the wire was used as a reference of the vertical direction to measure the d e and d s on the picture. The measurements were carried out ranging the temperature from 10 to 50 °C and the mass concentration of ethylene glycol water solution from 0 (water) to 100 mass%.
2.2. Test liquids used in this measurement Physical properties of tetradecane are indicated in Table 1. As noted in the table, tetradecane has an almost constant density of 770 kg m-3 for the temperature range of 6 ~ 60 °C [9]. Furthermore, the tetradecane has a slight solubility for water. The densities of ethylene glycol water solution are indicated in Table 2 for various concentrations and temperatures. The density data represented in Tables 1 and 2 are obtained by using a float-type gravimeter (measuring precision, + 0.5%). It has been confirmed that the measured data show good agreement with literature values [10] within + 1.0%. Therefore, the measured data are used for data reduction of interfacial tension in the present study. The tetradecane and ethylene glycol used are the highest grade in commercial use. Both liquids have a purity of 99.0 mass%. The ethylene glycol water solution was made by mixing the ethylene glycol and pure water which is made by an ion-exchange process and has a specific resistance of 5 × 108 ,(2 m. Before the measurement, tetradecane and ethylene glycol water solution were stored in the same vessel for a few days to reach at the equilibrium of mass diffusion between both materials, since tetradecane is a little soluble in ethylene glycol water solution.
Table I Physical properties of tetradecane Tetradecane (CH 3(CH 2) 12CH3) Density (6 ~ 60 °C) Solubilityfor water (40 °C)
770 kg m - 3 0.0114 g (water)/100 g (saturated soln.)
163
H. Inaba, K. Sato / Fluid Phase Equilibria 125 (1996) 159-168
Table 2 Density of ethylene glycol water solution
o (°c) C
(mass%)
10 20 30 40 50 60 70 80 90 100
10
20
30
40
50
1014.0 1028.0 1042.0 1056.0 1069.0 1083.0 ! 095.5 1106.0 1112.0 1119.5
1011.5 1025.5 1038.0 1051.5 1064.0 1078.0 1089.0 1100.0 1105.5 1113.5
1008.0 1021.5 1033.5 1046.5 1059.0 1072.0 1083.0 1093.0 1099.0 1106.0
1004.5 1017.5 1028.5 1041.0 1053.5 1065.0 1075.5 1085.0 1092.0 1099.0
1000.0 1012.0 1023.0 1035.0 1047.5 1058.0 1068.0 1078.0 1085.0 1091.0
2.3. Uncertainty analysis A high precision thermometer used in this measurement has the measuring precision of -4-0.1 °C. The uncertainty in the density of ethylene glycol water solution associated with the temperature measurement error is estimated to be within +0.0034% in consideration of the temperature dependence of the density as indicated in Table 2. The uncertainty in d e and d s measured from the photograph of the pendant drop by using vernier callipers is estimated to be within + 1.4%. The uncertainty in 1 / H , which is a function of d , / d e, is estimated to be within + 4.7%. As a result, the uncertainty in o" due to the measuring errors summed up on each parameter is estimated to be within
+5.2% [11]. 3. Results and discussion
3.1. Measuring precision of this experiment The precision and reliability of this measuring system was examined. Fig. 3 indicates the surface tension of tetradecane and water measured with the present apparatus. The measurement was 80
. . . .
u
. . . .
u
. . . .
u
. . . .
|
. . . .
u
. . . .
70 60 Z E U
Present meas.
50
Ref.
Water o Tetradecane •
40
a ..... b
30 •
•
.
.
•
. . . .
.Q
_ . . . .
. . _ _
. . . . .
o . _ .
20 . . . .
0
!
. . . .
10
I
. . . .
20
n
. . . .
n
.
30 40 0 ['C]
.
,
,
i
,
,
50
,
60
Fig. 3. Surface tension of tetradecane and water. (a) reprinted from Ref. [12]; (b) reprinted from Ref. [6].
164
H. Inaba, K. Sato /Fluid Phase Equilibria 125 (1996) 159-168
performed by forming an air bubble at the tip of the tube which is immersed in tetradecane or water in the test liquid vessel. In Fig. 3, the reference data are drawn together. The reference data of the tetradecane were measured by means of capillary rise method by Jasper [6], and are expressed by the following equation. tr--- 2 8 . 3 0 - 0.086880
(3)
where tr has the units mN m - t , and the variable 0 is the Celsius temperature (°C). The reference data of water is provided by Nishikawa and Fujita [12] as follows. tr = 75.43 - 0.12920 - 4.746 × 10-40 2 + 7.319 × 10-703
(4)
The measured and reference data coincide within the deviation of + 4.9%. From Fig. 3, it is noticed that this measuring system has a good accuracy. No temporal change was observed on the surface tension of tetradecane and water. Therefore, these measurements were performed immediately after the bubble creation.
3.2. Temporal change of interfacial tension In many cases, the interfacial tension or surface tension varies after the creation of an interface between two materials. Fig. 4 represents the temporal variations of the interfacial tension o" between tetradecane and ethylene glycol water solution, and tetradecane and water. In Fig. 4, the moment of drop formation is expressed as time t = 0 min. The reference data of interfacial tension between tetradecane and water at t = 0 min is indicated, which is derived by Aveyard and Haydon [3] by means of a drop weight method. About the tetradecane-water system, it is seen that the measured data and the reference one show a good agreement. In Fig. 4, the value of tr reduces sharply during about 60 min after the drop creation (t = 0 min) since the tetradecane has a slight solubility to water. Furthermore, the interfacial condition, for example, molecular orientation etc., has a great influence on the interracial tension, and it varies after the creation of interface between both liquids. Therefore, it is considered that the temporal change of tr is caused by the change of the interfaciai condition and
o •
Tetradecane - W a t e r Tetradecane - Ethylene glycol 4 0 m a s s % water solution
[]
Tettadecane - W a t e r at t ~ 0 a
60
501
[0 = 3 0 "C' )
Z E
30
~--
;
-" t > 6 0 rain static
20
, 0
,
inteffacial tension • - , • - - , t , , , , 50 100 150 t [min]
F i g . 4. T e m p o r a l
change of inteffacial tension. (a) Reprinted
f r o m R e f . [3].
H. Inaba, K. Sato / Fluid Phase Equilibria 125 (1996) 159-168
165
mass diffusion of tetradecane into the ethylene glycol water solution. In this study, the value of tr becomes almost constant after t = 60 min for all measuring conditions. Hence, the experimental data were measured after t = 60 min as a static interfacial tension.
3.3. Dependency of interfacial tension upon temperature and mass concentration of the water solution Fig. 5 shows the value of static interfacial tension tr between tetradecane and ethylene glycol water solution for various temperatures 0 and mass concentrations of the water solution C. At any value of C, the o" decreases lineally with an increase in 0, and the dependency of tr upon 0 decreases with increasing C. It is well-known that the value of interfacial tension between two liquids decreases with a decrease in difference of surface tensions of each liquid [5]. The difference in surface tensions of tetradecane and water decreases with an increase in temperature, as indicated in Fig. 3. Therefore, as shown in Fig. 5, it is seen that the interfacial tension between tetradecane and water becomes smaller with increasing temperature. The reference data for tetradecane-water system when the interface is created [3] are also plotted in Fig. 5. The reference data show that the value of tr at t = 0 min reduces linearly with an increase in 0. However, the data take higher values than those of the static interfacial tension at any temperature. From the present work, an empirical equation for the static interfacial tension tr for tetradecaneethylene glycol water solution system has been derived as follows.
(5)
tr = 45.72 - 0.11870 - 0.2821C + 1.093 × 10- 30- C
Eq. (5) and measured data correspond within the deviation of + 4.9%. Fig. 6 indicates the interfacial tension o" between tetradecane and ethylene glycol water solution for various mass concentrations C of the water solution. Eq. (5) is also drawn in Fig. 6. From Fig. 6, it is seen that there is a proportional relationship between o- and C.
o (2 : 0 mass% (Water) zx 30 mass% ~1 60 mass% • 100 mass%
Eq (5)
6O
. . . . . Tetradecane - Water at t-4) u
50
Z E
40 30 20 l0
~ . . i
0
. . . .
10
t
. . . .
20
|
. . . .
30
I
. . . .
40
i . . .
50
60
o ['cl Fig. 5. Interfacial tension b e t w e e n t e t r a d e c a n e and e t h y l e n e g l y c o l w a t e r s ol ut i on for v a r i o u s t e m p e r a t u r e s and m a s s c o n c e n t r a t i o n s of the w a t e r solution. (a) R e p r i n t e d from Ref. [3].
166
H. Inaba,
K. Sato / Fluid
50
Phase
. ..,
Equilibria
125 (1996)
. . . , . . . , . ..,
. ..
0 ('Cl
40 -~
z E
159-168
~
~
-
~
30
Eq. (5)
" ~
20
10
•
.
,
i
20
,
,
,
J
40
.
.
,
i
6O
,
.
,
i
,
80
.
,
100
C [mass%] Fig. 6. Dependency of interfacial tension upon mass concentration of the water solution.
Table 3 indicates the values of interfaciai tension obtained by measurements and calculated by the Eq. (5). The deviations of the measured values against the calculated ones are also indicated in Table 3.
Table 3 Interfacial tension between tetradecane and ethylene glycol water solution derived by measurement and that calculated by Eq. (5). The deviation of measured values against the calculated ones are also indicated C
0
cr (mN m - l )
(mass%)
(°C)
Meas.
Eq.
(%)
0.0
50.0 40.0 30.0 20.0 10.0 50.0 40.0 30.0 20.0 10.0 50.0 40.0 30.0 20.0 I 0.0 50.0 40.0 30.0 20.0 10.0
40.7 42.9 40.6 44.9 45.2 34.5 32.9 34.5 36. I 37.0 25.0 25.4 27.9 27.0 28.0 17.9 17.7 17.5 17.4 17.8
39.8 41.0 42.2 43.4 44.5 33.0 33.8 34.7 35.5 36.4 26. I 26.7 27.2 27.7 28.3 17.0 17. I 17.2 17.3 17.4
2.3 4.6 - 3.8 3.6 1.6 4.7 - 2.8 - 0.4 1.5 1.7 - 4.2 - 4.8 2.5 - 2.7 - 0.9 4.9 3.5 1.7 0.7 2.3
30.0
60.0
100.0
Deviation
H. Inaba, K. Sato / Fluid Phase Equilibria 125 (1996) 159-168
167
4. Conclusion The measurement of interfacial tension tr between tetradecane and ethylene glycol water solution was performed for various temperatures 0 and mass concentrations C of the water solution. From the measurement, the dependency of o" upon 0, C or time was clarified. Eventually, the empirical equation to estimate the value of static interfacial tension o" was derived in terms of 0 and C.
5. List of symbols C mass concentration of water solution d e, d, dimensions in pendant drop g gravitational acceleration 1/H parameter used in Eq. (2) t time
5.1. Greek symbols Ap o" 0
density difference interfacial tension or surface tension temperature
Acknowledgements The authors would like to express their thanks to Mr. Sou Tadatomo, graduate student of Okayama university, for carrying out the experiments.
References [I] H. lnaba and K. Sato, 1994. Fundamental study on latent cold heat storage by means of oil droplets with low freezing point, 1st report, flow and solidification characteristics of tetradecane droplets ascending in low-temperature water solution, Trans. JSME, 60-580: 4236-4243. [2] H. lnaba and K. Sato, 1996. Fundamental study on latent cold heat storage by means of oil droplets with low freezing point, 2nd report, nondimensional analysis of solidification and heat transfer characteristics of tetradecane oil droplets ascending in low-temperature water solution, Trans. JSME, 62-593: 325-332. [3] R. Aveyard and D.A. Haydon, 1965. Thermodynamic properties of aliphatic hydrocarbon/water interface, Trans. Faraday Soc., 61: 2255-2261. [4] H. Matsubara, M. Murase, Y.H. Mori and A. Nagashima, 1988. Measurement of the surface tensions and the interfacial tensions of n-pentane-water and RI 13-water systems, Int. J. of Thermophys., 9 (3): 409-424. [5] R.J. Good and B. Elbing, 1970. Generalization of theory for bstiination of inteffacial energies, Ind. Eng. Chem., 62 (3): 54-78. [6] J.J. Jasper, 1972. The surface tension of pure liquid compounds, J. Phys. Chem. Ref. Data, 1 (4): 914. [7] A. Horibe, S. Fukusako, M. Yamada and M. Tago, 1992. Surface tension of low temperature aqueous solution, Proc. 13th Japan Symposium on Thermophysical Properties, pp. 185-188.
168
H. Inaba, K. Sato / Fluid Phase Equilibria 125 (1996) 159-168
[8] M.D. Misak, 1968. Equations for determining I / H versus S value in computer calculations of interfacial tension by the pendant drop method. J. Colloid Interface Sci., 27 (1): 141-142. [9] H. Inaba and S. Morita, 1993. Fundamental study of cold heat storage System of O/W-type emulsion having cold latent heat dispersion material, Ist report, estimation of thermophysical properties, Trans. JSME, 59-565: 282-289. [10] JSME, 1975. JSME Data Book: Heat Transfer, 3rd edn., JSME, Tokyo, p. 299. [1 I] ASME, 1985. Measurement Uncertainty, JSME, Tokyo, p. 47. [12] K. Nishikawa and Y. Fujita, 1982. Heat Transfer, Rikogakusya, Tokyo, p. 457.
Fluid Phase Equilibria 125 (1996) 159-168
A measurement of interfacial tension between tetradecane and ethylene glycol water solution by means of the pendant drop method H. Inaba ", K. Sato Department of Mechanical Engineering, Faculty of Engineering, Okayama Universi~, Tsushima-naka 3-1-1. Okayama 700, Japan
Abstract Interfacial tension between tetradecane (CH3(CH2)t2CH3) (melting point, 5.8 °C; density, 770 kg m -3 (6°C)) and ethylene glycol (CH2OH- CH2OH) (density, 1119.5 kg m -3 (10°C)) water solution was measured by means of the pendant drop method. The measurements were performed for various temperatures of 10 ~ 50°C and mass concentrations of the water solution of 0 (water) ~ I00 mass%. It was clarified that the interfacial tension decreased exponentially in about 60 min after creation of the pendant drop. This paper reports the value of the static interfacial tension obtained when the temporal change of the interfacial tension with time ceases due to the equilibrium of mass diffusion between both liquids. The value of interfacial tension decreases linearly with an increase in temperature and mass concentration of the water solution. As a result, the empirical equation of static interfacial tension was derived in terms of temperature and mass concentration of the water solution.
Keywords: Experiments; Data; lnterfacial properties; Hydrocarbons; Water solution
I. I n t r o d u c t i o n
The authors have reported the study on a new latent cold heat energy storage technique by using a solidification of low freezing point oil droplets [1,2]. This technique is to use direct-contact cooling and solidification of a tetradecane oil droplet (melting point, 5.8 °C) created in a low-temperature ethylene glycol water solution o f 30 mass%. In this study, the oil droplets are made by an injection o f the tetradecane oil from a cylindrical single hole nozzle, and they ascend in the ethylene glycol water solution by buoyancy. The characteristics o f dispersion and motion o f the oil droplets are dominated by interfacial tension between tetradecane and ethylene glycol water solution. Therefore, it is indispensable to determine the interfacial tension between them; however, no report has been seen about it.
" Corresponding author. 0378-3812/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PH S0378-3812(96)03085-3
160
H. Inaba, K. Sato / Fluid Phase Equihbria 125 (1996) 159-168
Up to the present, a large amount of data on interfacial tension for hydrocarbon (including tetradecane)-water systems have been reported. For example, Aveyard and Haydon [3] dealt with normal alkanes (including tetradecane)-water system for various temperatures, and they determined the relationship between the carbon numbers of hydrocarbons and interfacial tension. Matsubara et al. [4] have reported interfacial and surface tension for n-pentane-water and R113-water systems for various temperatures, and they represented some practical data. Unfortunately, the data of interfacial tension between hydrocarbon and specified water solution have not been reported. A practical method to predict the interfacial tension was developed by Good and Elbing [5]. From their paper, the interfacial tension of a binary liquid system tr12 is estimated by the following equation:
Orl2 = Orl + 0"2 -- 2(~12 ~1~1~
(1)
where o"1 and tr 2 are surface tensions of pure liquid of the components 1 and 2, respectively. On utilizing Eq. (1), the surface tensions of tetradecane for various temperatures [6] and those of ethylene glycol water solution for various temperatures and concentrations [7] have been reported. However, the value of parameter ~b~2 or the method to predict it have not been mentioned. This paper reports the measurement of interfacial tension between tetradecane and ethylene glycol water solution for various temperatures and mass concentrations of the water solution. The measurements were performed by means of the pendant drop method. It was attempted to derive the empirical equation in order to calculate the value of interfacial tension between tetradecane and ethylene glycol water solution. In many cases, the interfacial tension varies with time until reaching at the equilibrium of mass diffusion between two liquids. This report mentions the temporal changing behavior of the interfacial tension.
2. Measuring device and procedure
2.1. Measuring device Fig. 1 shows a schematic diagram of the measuring device. It is mainly composed of the test liquid vessel, a fine stainless steel tube for producing a pendant drop, and a constant temperature water bath. A camera and a light source are arranged beside the constant temperature water bath to take a picture of the pendant drop. The test liquid vessel has the 10 cm cubed inner dimension. The two sides of the vessel walls, facing the camera and the light source, are made of a transparent acrylic resin plate of 5 mm thickness for photographing. The other sides of the vessel walls are made of a stainless steel plate of 2 mm thickness. A stirrer and high precision thermometer (T-type thermocouple, diameter of 0.1 mm; minimum temperature scale, 0.1 °C) are equipped in the test liquid vessel. The stainless steel tube for producing the pendant drop has an outer diameter of 1.5 mm and thickness of 0.5 mm. The tube is fixed vertically in the test liquid vessel, and the other side of the tube is connected to a Pyrex glass syringe. The size of the pendant drop can be varied by sliding the piston of the syringe. The camera has a 50 mm lens with bellows to enable close-up photography for the pendant drop. It is relatively difficult to distinguish the outline of a tetradecane oil drop created in the ethylene glycol water solution since the refractive index of the former is the almost same as the latter. Therefore, a
161
H. Inaba, K. Sato / Fluid Phase Equilibria 125 (1996) 159-168
Stainless steel tube ~
Pyrex glass syringe
Thermometer
Pendant drop " ~ ~ 7 .~ ~ ~ (fetradecane oil drop) ~ J d ' ~ I ~ " N"~ [ \ Y I~'~t'td ,/ql/ ,.-"(I
, .'~,. c.tgntsource
,Vat...4. l\uIC2J -" I
Be.o,,s
\
Camera
J !
L .'N_- >'3 "~-F ~
~ /
~ "M"/ ~
I
IN.. Light-shieldingplate
"" Heater Refrigerator
/
[~- -I ,~ Stirrer I
Test liquid vessel (Ethylene glycol v,'atersolution) Fig. 1. Schematic diagram of the measuring device.
light-shielding plate with a small circular hole is set between the test liquid vessel and the light source to make the outline clearer. Tetradecane and ethylene glycol water solution were poured into the well-cleaned and dried syringe and the test liquid vessel, respectively. Subsequently, the tetradecane was sent into the stainless steel tube. The constant-temperature water bath and stirrers were preliminarily operated until the test liquids and whole of the system reach the same temperature. When the entire system took a given temperature, the stirrer in the test liquid vessel was stopped in order to stabilize the water solution in the vessel. Then a pendant drop of tetradecane was made at the tip of the stainless steel tube by pressing out the tetradecane from the tube into the water solution. Fig. 2 shows a photograph of a pendant drop grown at the tip of the stainless steel tube. The value of interfacial tension o- is given by the following equation. A p . g • d~ H
(2)
where Ap is the density difference between these liquids, g is the gravitational acceleration, and d e is the dimension in a pendant drop as shown in Fig. 2. The parameter 1 / H is experimentally derived by Misak [8] as a function of d s / d e, where d s is the dimension in a drop, indicated in Fig. 2. About 10 photographs were taken on a certain measuring condition. The dimensions d e and d s were measured from the photographs of the pendant drop by using vernier callipers. The value of interfaciai tension was determined by averaging the obtained data on a given condition. Before photographing a pendant drop of test liquid, the enlargement of picture is determined by taking a photograph of a scale set in the test liquid vessel with the test liquid under each condition of temperature and concentration. When a photograph of a pendant drop is taken, a straight stainless steel wire (0.08 mm in diameter)
162
H. Inaba, K. Sato / Fluid Phase Equilibria 125 (1996) 159-168 dc
dr
I
~mm]
Fig. 2. Example of a photographof a pendantdrop and measuringpoint on it.
with a weight (about 20 g) is vertically suspended near the test liquid vessel. The image of the wire was used as a reference of the vertical direction to measure the d e and d s on the picture. The measurements were carried out ranging the temperature from 10 to 50 °C and the mass concentration of ethylene glycol water solution from 0 (water) to 100 mass%.
2.2. Test liquids used in this measurement Physical properties of tetradecane are indicated in Table 1. As noted in the table, tetradecane has an almost constant density of 770 kg m-3 for the temperature range of 6 ~ 60 °C [9]. Furthermore, the tetradecane has a slight solubility for water. The densities of ethylene glycol water solution are indicated in Table 2 for various concentrations and temperatures. The density data represented in Tables 1 and 2 are obtained by using a float-type gravimeter (measuring precision, + 0.5%). It has been confirmed that the measured data show good agreement with literature values [10] within + 1.0%. Therefore, the measured data are used for data reduction of interfacial tension in the present study. The tetradecane and ethylene glycol used are the highest grade in commercial use. Both liquids have a purity of 99.0 mass%. The ethylene glycol water solution was made by mixing the ethylene glycol and pure water which is made by an ion-exchange process and has a specific resistance of 5 × 108 ,(2 m. Before the measurement, tetradecane and ethylene glycol water solution were stored in the same vessel for a few days to reach at the equilibrium of mass diffusion between both materials, since tetradecane is a little soluble in ethylene glycol water solution.
Table I Physical properties of tetradecane Tetradecane (CH 3(CH 2) 12CH3) Density (6 ~ 60 °C) Solubilityfor water (40 °C)
770 kg m - 3 0.0114 g (water)/100 g (saturated soln.)
163
H. Inaba, K. Sato / Fluid Phase Equilibria 125 (1996) 159-168
Table 2 Density of ethylene glycol water solution
o (°c) C
(mass%)
10 20 30 40 50 60 70 80 90 100
10
20
30
40
50
1014.0 1028.0 1042.0 1056.0 1069.0 1083.0 ! 095.5 1106.0 1112.0 1119.5
1011.5 1025.5 1038.0 1051.5 1064.0 1078.0 1089.0 1100.0 1105.5 1113.5
1008.0 1021.5 1033.5 1046.5 1059.0 1072.0 1083.0 1093.0 1099.0 1106.0
1004.5 1017.5 1028.5 1041.0 1053.5 1065.0 1075.5 1085.0 1092.0 1099.0
1000.0 1012.0 1023.0 1035.0 1047.5 1058.0 1068.0 1078.0 1085.0 1091.0
2.3. Uncertainty analysis A high precision thermometer used in this measurement has the measuring precision of -4-0.1 °C. The uncertainty in the density of ethylene glycol water solution associated with the temperature measurement error is estimated to be within +0.0034% in consideration of the temperature dependence of the density as indicated in Table 2. The uncertainty in d e and d s measured from the photograph of the pendant drop by using vernier callipers is estimated to be within + 1.4%. The uncertainty in 1 / H , which is a function of d , / d e, is estimated to be within + 4.7%. As a result, the uncertainty in o" due to the measuring errors summed up on each parameter is estimated to be within
+5.2% [11]. 3. Results and discussion
3.1. Measuring precision of this experiment The precision and reliability of this measuring system was examined. Fig. 3 indicates the surface tension of tetradecane and water measured with the present apparatus. The measurement was 80
. . . .
u
. . . .
u
. . . .
u
. . . .
|
. . . .
u
. . . .
70 60 Z E U
Present meas.
50
Ref.
Water o Tetradecane •
40
a ..... b
30 •
•
.
.
•
. . . .
.Q
_ . . . .
. . _ _
. . . . .
o . _ .
20 . . . .
0
!
. . . .
10
I
. . . .
20
n
. . . .
n
.
30 40 0 ['C]
.
,
,
i
,
,
50
,
60
Fig. 3. Surface tension of tetradecane and water. (a) reprinted from Ref. [12]; (b) reprinted from Ref. [6].
164
H. Inaba, K. Sato /Fluid Phase Equilibria 125 (1996) 159-168
performed by forming an air bubble at the tip of the tube which is immersed in tetradecane or water in the test liquid vessel. In Fig. 3, the reference data are drawn together. The reference data of the tetradecane were measured by means of capillary rise method by Jasper [6], and are expressed by the following equation. tr--- 2 8 . 3 0 - 0.086880
(3)
where tr has the units mN m - t , and the variable 0 is the Celsius temperature (°C). The reference data of water is provided by Nishikawa and Fujita [12] as follows. tr = 75.43 - 0.12920 - 4.746 × 10-40 2 + 7.319 × 10-703
(4)
The measured and reference data coincide within the deviation of + 4.9%. From Fig. 3, it is noticed that this measuring system has a good accuracy. No temporal change was observed on the surface tension of tetradecane and water. Therefore, these measurements were performed immediately after the bubble creation.
3.2. Temporal change of interfacial tension In many cases, the interfacial tension or surface tension varies after the creation of an interface between two materials. Fig. 4 represents the temporal variations of the interfacial tension o" between tetradecane and ethylene glycol water solution, and tetradecane and water. In Fig. 4, the moment of drop formation is expressed as time t = 0 min. The reference data of interfacial tension between tetradecane and water at t = 0 min is indicated, which is derived by Aveyard and Haydon [3] by means of a drop weight method. About the tetradecane-water system, it is seen that the measured data and the reference one show a good agreement. In Fig. 4, the value of tr reduces sharply during about 60 min after the drop creation (t = 0 min) since the tetradecane has a slight solubility to water. Furthermore, the interfacial condition, for example, molecular orientation etc., has a great influence on the interracial tension, and it varies after the creation of interface between both liquids. Therefore, it is considered that the temporal change of tr is caused by the change of the interfaciai condition and
o •
Tetradecane - W a t e r Tetradecane - Ethylene glycol 4 0 m a s s % water solution
[]
Tettadecane - W a t e r at t ~ 0 a
60
501
[0 = 3 0 "C' )
Z E
30
~--
;
-" t > 6 0 rain static
20
, 0
,
inteffacial tension • - , • - - , t , , , , 50 100 150 t [min]
F i g . 4. T e m p o r a l
change of inteffacial tension. (a) Reprinted
f r o m R e f . [3].
H. Inaba, K. Sato / Fluid Phase Equilibria 125 (1996) 159-168
165
mass diffusion of tetradecane into the ethylene glycol water solution. In this study, the value of tr becomes almost constant after t = 60 min for all measuring conditions. Hence, the experimental data were measured after t = 60 min as a static interfacial tension.
3.3. Dependency of interfacial tension upon temperature and mass concentration of the water solution Fig. 5 shows the value of static interfacial tension tr between tetradecane and ethylene glycol water solution for various temperatures 0 and mass concentrations of the water solution C. At any value of C, the o" decreases lineally with an increase in 0, and the dependency of tr upon 0 decreases with increasing C. It is well-known that the value of interfacial tension between two liquids decreases with a decrease in difference of surface tensions of each liquid [5]. The difference in surface tensions of tetradecane and water decreases with an increase in temperature, as indicated in Fig. 3. Therefore, as shown in Fig. 5, it is seen that the interfacial tension between tetradecane and water becomes smaller with increasing temperature. The reference data for tetradecane-water system when the interface is created [3] are also plotted in Fig. 5. The reference data show that the value of tr at t = 0 min reduces linearly with an increase in 0. However, the data take higher values than those of the static interfacial tension at any temperature. From the present work, an empirical equation for the static interfacial tension tr for tetradecaneethylene glycol water solution system has been derived as follows.
(5)
tr = 45.72 - 0.11870 - 0.2821C + 1.093 × 10- 30- C
Eq. (5) and measured data correspond within the deviation of + 4.9%. Fig. 6 indicates the interfacial tension o" between tetradecane and ethylene glycol water solution for various mass concentrations C of the water solution. Eq. (5) is also drawn in Fig. 6. From Fig. 6, it is seen that there is a proportional relationship between o- and C.
o (2 : 0 mass% (Water) zx 30 mass% ~1 60 mass% • 100 mass%
Eq (5)
6O
. . . . . Tetradecane - Water at t-4) u
50
Z E
40 30 20 l0
~ . . i
0
. . . .
10
t
. . . .
20
|
. . . .
30
I
. . . .
40
i . . .
50
60
o ['cl Fig. 5. Interfacial tension b e t w e e n t e t r a d e c a n e and e t h y l e n e g l y c o l w a t e r s ol ut i on for v a r i o u s t e m p e r a t u r e s and m a s s c o n c e n t r a t i o n s of the w a t e r solution. (a) R e p r i n t e d from Ref. [3].
166
H. Inaba,
K. Sato / Fluid
50
Phase
. ..,
Equilibria
125 (1996)
. . . , . . . , . ..,
. ..
0 ('Cl
40 -~
z E
159-168
~
~
-
~
30
Eq. (5)
" ~
20
10
•
.
,
i
20
,
,
,
J
40
.
.
,
i
6O
,
.
,
i
,
80
.
,
100
C [mass%] Fig. 6. Dependency of interfacial tension upon mass concentration of the water solution.
Table 3 indicates the values of interfaciai tension obtained by measurements and calculated by the Eq. (5). The deviations of the measured values against the calculated ones are also indicated in Table 3.
Table 3 Interfacial tension between tetradecane and ethylene glycol water solution derived by measurement and that calculated by Eq. (5). The deviation of measured values against the calculated ones are also indicated C
0
cr (mN m - l )
(mass%)
(°C)
Meas.
Eq.
(%)
0.0
50.0 40.0 30.0 20.0 10.0 50.0 40.0 30.0 20.0 10.0 50.0 40.0 30.0 20.0 I 0.0 50.0 40.0 30.0 20.0 10.0
40.7 42.9 40.6 44.9 45.2 34.5 32.9 34.5 36. I 37.0 25.0 25.4 27.9 27.0 28.0 17.9 17.7 17.5 17.4 17.8
39.8 41.0 42.2 43.4 44.5 33.0 33.8 34.7 35.5 36.4 26. I 26.7 27.2 27.7 28.3 17.0 17. I 17.2 17.3 17.4
2.3 4.6 - 3.8 3.6 1.6 4.7 - 2.8 - 0.4 1.5 1.7 - 4.2 - 4.8 2.5 - 2.7 - 0.9 4.9 3.5 1.7 0.7 2.3
30.0
60.0
100.0
Deviation
H. Inaba, K. Sato / Fluid Phase Equilibria 125 (1996) 159-168
167
4. Conclusion The measurement of interfacial tension tr between tetradecane and ethylene glycol water solution was performed for various temperatures 0 and mass concentrations C of the water solution. From the measurement, the dependency of o" upon 0, C or time was clarified. Eventually, the empirical equation to estimate the value of static interfacial tension o" was derived in terms of 0 and C.
5. List of symbols C mass concentration of water solution d e, d, dimensions in pendant drop g gravitational acceleration 1/H parameter used in Eq. (2) t time
5.1. Greek symbols Ap o" 0
density difference interfacial tension or surface tension temperature
Acknowledgements The authors would like to express their thanks to Mr. Sou Tadatomo, graduate student of Okayama university, for carrying out the experiments.
References [I] H. lnaba and K. Sato, 1994. Fundamental study on latent cold heat storage by means of oil droplets with low freezing point, 1st report, flow and solidification characteristics of tetradecane droplets ascending in low-temperature water solution, Trans. JSME, 60-580: 4236-4243. [2] H. lnaba and K. Sato, 1996. Fundamental study on latent cold heat storage by means of oil droplets with low freezing point, 2nd report, nondimensional analysis of solidification and heat transfer characteristics of tetradecane oil droplets ascending in low-temperature water solution, Trans. JSME, 62-593: 325-332. [3] R. Aveyard and D.A. Haydon, 1965. Thermodynamic properties of aliphatic hydrocarbon/water interface, Trans. Faraday Soc., 61: 2255-2261. [4] H. Matsubara, M. Murase, Y.H. Mori and A. Nagashima, 1988. Measurement of the surface tensions and the interfacial tensions of n-pentane-water and RI 13-water systems, Int. J. of Thermophys., 9 (3): 409-424. [5] R.J. Good and B. Elbing, 1970. Generalization of theory for bstiination of inteffacial energies, Ind. Eng. Chem., 62 (3): 54-78. [6] J.J. Jasper, 1972. The surface tension of pure liquid compounds, J. Phys. Chem. Ref. Data, 1 (4): 914. [7] A. Horibe, S. Fukusako, M. Yamada and M. Tago, 1992. Surface tension of low temperature aqueous solution, Proc. 13th Japan Symposium on Thermophysical Properties, pp. 185-188.
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H. Inaba, K. Sato / Fluid Phase Equilibria 125 (1996) 159-168
[8] M.D. Misak, 1968. Equations for determining I / H versus S value in computer calculations of interfacial tension by the pendant drop method. J. Colloid Interface Sci., 27 (1): 141-142. [9] H. Inaba and S. Morita, 1993. Fundamental study of cold heat storage System of O/W-type emulsion having cold latent heat dispersion material, Ist report, estimation of thermophysical properties, Trans. JSME, 59-565: 282-289. [10] JSME, 1975. JSME Data Book: Heat Transfer, 3rd edn., JSME, Tokyo, p. 299. [1 I] ASME, 1985. Measurement Uncertainty, JSME, Tokyo, p. 47. [12] K. Nishikawa and Y. Fujita, 1982. Heat Transfer, Rikogakusya, Tokyo, p. 457.