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An improved experimental technique for determining dynamic surface tension of water and surfactant solutions
An Improved Experimental Technique for Determining Dynamic Surface Tension of Water and Surfactant Solutions J. A. CASKEY ~ a~D W. B. BARLAGE, JR. Department of Chemical Engineering, Clemson University, CIemson, South Carolina 29631
Received March 17, 1970; accepted July 20, 1970 Oscillating jets issuing from elliptical orifices have been widely used as a method for determining the dynamic surface tension of pure liquids and surfaetant solutions. However, such variables as iet diameter and wave length have been measured by complicated optical and photographic methods. A technique is presented for direct measurement of these data on the jet using a coordinate eathetometer. The jet stream was vertical and issued from an elliptical diaphragm orifice made of 2 mil Mylar film. The orifice was made nonwetting by carefully coating it with paraffin. This jet was found to give values of dynamic surface tension for water which were independent of exposure time and jet flow rate and which agreed closely with equilibrium values. For the surfaetant solutions studies, values of dynamie surface tension were also found to be independent of any jet flow rate used. Four surfactants were used in the investigation: dodeeyltrimethylammonium chloride, hexadeeyltrimethylammonium ehloride, dodecyl sodium sulfate, and hexadeeyl sodium sulfate.
assumed that surface concentration is only a function of surface tension at constant temperature, then Eq. [1] may be used to calculate surface concentration from dynamic surface tension data. Oscillating jets issuing from elliptical orifices have been widely used for measuring dynamic surface tension. Bohr (5) developed an equation relating dynamic surface tension to jet radii, volumetric flow rate, liquid density, and wavelength. Defay and Hommelen (6) simplified Bohr's equation to the following form:
INTRODUCTION
Gibbs' adsorption isotherm can be written as follows for ionized surfactants in the presence of excess electrolyte: -(o~/a
In c)~ = kT~V.
[1]
Equation [1] written for a two-component system requires two extra-thermodynamic assumptions: (1) the surface excess or deficit of the solvent is zero, and (2) the activity coefficient of the solute in solution is unity. The validity of Eq. [1] has been checked by several investigators (Brady (1), Davies and Rideal (2), Hayden an.d Phillips (3), Matuara et al. (4)) and found to be reliable for bulk surfactant concentrations less than the critical micelle concentration. In this investigation, Eq. [1] was used to obtain data for equilibrium surface concentration as a function of equilibrium surface tension for all surfactants studied. If it may be
4PD'~[1 +
37(b/a)2/24]~2~
where b/a = ( ~ - r~)/(~, q- r~); 1• =
(r~ + r d / 2 .
[3] [4]
Defay and Hommelen obtained dynamic surface tensions whieh were within 4-0.2 % of those values calculated by the Bohr equation. One constraint on Eq. [2] is that the liquid viscosity should not be greater than 0.01 poise.
Present address, Department of Chemical Engineering, Virginia Polytechnic Institute, Blacksburg, Virginia 24061.
Journal of Colloidand Interface Science~Vol. 35, No. 1, January t971
46
DYNAMIC SURFACE TENSION OF WATER AND SURFACTANT SOLUTIONS The one assumption of Bohr (5) which is difficult to obtain experimentally is that of no velocity profile within the jet. This problem has been attacked differently by several investigators. Hansen et al. (7) construeted an orifice from glass capillary tubing which purposely gave a velocity profile. Correction factors were applied to Eq. [2] to compensate for this velocity profile. Sutherland (8) made an orifice by sealing 1 or 2 mm lengths of glass capillary tubing of elliptical cross section to glass tubing 5 mm in internal diameter. The only condition he gave for choice of the orifice was that it gave the "right" surface tensions. Delay and I-Iommelen (6) constructed similar orifices. They standardized each orifice by using pure liquids and then multiplied the values of surface tension obtained with Eq. [2] by a correction factor to obtain agreement with literature values. Owens (9) using a diaphragm type orifice found that the surface tension of water calculated from Eq. [2] did not equal the accepted equilibrium value. I-Ie applied a correction factor to each wave. These correction factors were found to fit an equation of the form shown below. C.F. = 1-- (1/e(°'95~+L05)).
[5]
The form of Eq. [5] illustrates the phenomena that the first few waves give apparent surface tension values which are higher than accepted equilibrium values, particularly for water. As exposure time increases, the apparent dynamic surface tension values of water have been found to decrease approaching equilibrium values listed in the literature. Investigators who have observed this phenomena are Netzel et al. (10), Vandegrift (11), and Owens (9). Data of these investigators for water are shown in Fig. 1. These data seem to indicate that water has a time-dependent dynamic surface tension, or else Bohr's model does not adequately describe the first few waves of the jet stream. APPARATUS Method of Measurement. One technique previously used to measure jet radii and wavelength is that of Stoeker (12) or some
47
modification of his method. This technique consists of using each wave as a cylindrical convergent lens and illuminating the jet with a parallel beam of light. The emergent light beam is focused on a photographic plate. A photograph is then taken from which the necessary measurements can be made with a microscope. Owens (9) used a one-dimensional cathetometer to measure the wavelength of a horizontal oscillating jet. However, the maximum and minimum radii of each wave were assumed constant along the jet and equal to the major and minor radii of the elliptical orifice. This assumption may be true for pure liquids, but it is not true for surfactant solutions. When an elliptical jet is placed in the vertical position, ri, ~ , and X of Eqs. [2], [3], and [4] will change from wave to wave owing to the effect of gravity as well as to the effect of changing surface concentration of any surfactants present. Although a horizontal jet may eliminate the problem of gravity, it is still necessary to measure changes in r~, r ~ , and X along the jet due to the presence of any surfactants. In this investigation a Gaertner twocoordinate cathetometer, Model 2173A, was used as a faster and easier method of directly measuring r~, )~, and X of Eqs. [2], [3], and [4]. This instrument was ac-
-
Y
r
--~--
o----o llO
NETZEL
• .....
•
ET
I
AL
OWENS VANDEGRIFT
,oc o
E ~.
I
•\
90-
z
\
O\
o
O
z hJ }--
8C
ta (O
7C
~,
O\o
% ~'-e
o
"-. o.e
"O OZ'.0
0 ~ 0 ~ 0
0 0 0
6o
I I
"
I 2
EXPOSURE
I 5 TIME,t
I 4
I 5 (MSEC)
FIG. 1. Dynamic surface tension of water.
Journal of Colloid and Interface Science, ¥ o l . 35, No. 1, J a n u a r y 1971
48
CASKEY AND BAt~LAGE
curate to ~-0.0001 inch, and had a 4-inch range in each coordinate direction. A telemicroscopic lens was used giving a 30X magnification. Figure 2 is a photograph of the vertical oscillating jet used in this study. The picture was taken perpendicular to the axis of the jet and the major axis of the elliptical orifice. Figure 2 also shows examples of ~, the wavelength for a given node as well as r~ and r~ for that node. The value of ri used in Eqs. [3] and [4] was the arithmetic average of the values at the top and bottom of the node. The dynamic surface tension at an exposure time corresponding to a jet length L could then be cMculated from Eq. [2] using the values of ri, r~, k, and L measured from the oscillating jet. No experimental difficulties were encountered in measuring ri, rm, and k by this direct method. Elliptical Orifice. In this investigation an attempt was made to improve the diaphragm type elliptical orifice used by previous investigators by constructing an orifice of 2.0 mil Mylar film which had been very carefully coated with paraffin on both sides to make the surfaces nonwetting to water. This was done in an effort to reduce initial velocity profiles within the jet. The orifice was checked to determine if it was truly elliptical using the Gaertner cathetometer. It was found to be elliptical with a mQor diameter of 1.732 mm and an eccentricity of 0.617. The Mylar film was secured to a Parker ~-inch stainless steel tubing nut by epoxy cement thus forming the diaphragm orifice. Additional equipment was required to supply the ellipticM orifice with liquid at a temperature of 25.0 ° -4- 0.1°C and constant flow rate. Experimental. The orifice was checked for consistency with Bohr's model by determining the dynamic surface tension Of water at several flow rates ranging from 1.70 to 2.45 cma/sec. The water used was distilled and then deionized to a conductivity of less than 2 X 10-6 mhos. Four surfactants were chosen for the study: dodecyltrimethylammonium chloride, hexadecyltrimethylammonium chloride, dodecyl sodium sulfate, and hexadecyl sodium sulfate. Deionized water with a conductivity of less than 2 X Journal of Colloid and Interface Science, Vol. 35, No. 1, J a n u a r y 1971
..
)k
FIG. 2. Photograph of oscillating jet.
DYNAMIC SURFACE TENSION OF WATER AND SURFACTANT SOLUTIONS 10-6 mhos was used. Surfactant solutions were mixed in a base solution of 0.1 N sodium chloride. Sodium chloride was added to the surfactant solutions as Bureik (13) has shown the presence of an inorganic electrolyte increases the rate of surfaetant adsorption at a gas-liquid h~terfaee. The surfaetants were considered to be of sufficient purity for this investigation if a plot of V vs. In c did not give a minimum at the critical mieelle eoneentration. As purchased, only dodeeyl sodium sulfate showed a minimum in the surface tension eurve. It was purified b y recrystallization from an aqueous solution until the minimum disappeared. All equilibrium surface tension data for the surfactant solutions were taken with a du R~oiiy tensiometer applying the correction factors of Zuidema and Waters (14). It was found for all surfactants used that equilibrium surface tension values were obtained within 60 min. In order to eliminate eoneentration and temperature changes in the surfaetant solutions due to evaporation, all solutions were aged in covered Petri dishes. The room eontaining the experimentM apparatus was temperature controlled at 25.0 ° 4- 0.2°C. Dynamie surface tension data were calculated from readings of r i , r~, and X measured directly with the coordinate eathetometer as outlined above. I
{.) ""
I
I
49
RESULTS AND DISCUSSION The dynamic surface tension data obtained for water are shown on Fig. 3 and compared with the data of Vandegrift (11). From Fig. 3 it can be seen that the data for all water flow rates fall on the same line within the limits of experimental accuracy. The slope of this line was found to be - 0.099 dyne/(em)(milliseeond) b y application of a linear regression to the data. Although this line shows the dynamic surface tension of water to decrease slightly with increasing exposure time, the slope is not significantly different from zero, at least for exposure times greater than 4 milliseconds. Figure 4 shows the results obtained from the equilibrium surface tension measurements. The data for dodecyl sodium sulfate agreed with the data obtained by other investigators (l~atijevic (15), and NIatuara e t a l . ~ (4)). No published results were found for the other three surfactants. The results presented in Fig. 5 were calculated from the data shown in Fig. 4 by means of Eq. [1] and show equilibrium surface tension as a function of surfaetant surface concentration. Figure 5 does not show these data for hexadecyl sodium sulfate as this surfactant showed no measureable dynamic surface tension. The results presented in Figs. 6 through 8 and Table I show dynamic surface I
I
FLOW
l
I
RATE
IO0--
w z
- -
VANDEGRIFT
6. 1.70 e 1.88
THIS
o 2.02
CC/SEC
o
~.
90-
o--o
WORK
o 2.08
z 0 z ,,,
o
2.23
• 2.45 80
~J
@ ID .
. . .
~,,
6* ° 4 -
"°
•
@
70 O3 I
I
8
12
EXPOSURE F I G . 3. D y n a m i c
I
J6 TIME , t
I
20
I
I
24
28
(MSEC)
surface tension of water.
Journal of Colloid and Interface Science, Vo]. 35, No. 1, J a n u a r y 1971
50
CASKEY AND BARLAGE
70
60
~, 50 >-
--,,,--...,,
• 4O
•
CI6 H'5'sN(C H3)'5Cl
~ ~ 4 ~ - - ' I
30 I
u53
I(~ 4
I
i
I
no-2
no-,
=
C
I0
MMOLES/LITER
FIG. 4. Equilibrium surface tension data. 400 PPM 2.07 CM~/SEC
70 ~
70
~
0
~o
co 5 0
~J z >o
50
800 PPM [] 1,925 CMS/SEC • 1.8i8 CMS/$EC ~) I 0 I 0.0Z
>" 4 0
I
0.05 TE $EC
1
0,04
I
0.05
50 I
I
I
I
I
I
2
5
4
5
FIG. 6. Dynamic surface tension: C12H2~N-
(CHs)~C1.
NXIO I0 GMOLES/CM 2
FIG. 5. Equilibrium surface tension factant surface concentration.
vs.
sur-
tension data which were calculated by means of Eq. [2] using cathetometer measurement of r~, r~, and X. Table I shows that the dynamic surface tension of 60 ppm hexadecyl sodium sulfate remained essentially constant at 72.5 dynes/ cm for all exposure time. Since the solubility of hexadecyl sodium sulfate is only about 60 ppm in 0.1 N sodium chloride solutions at 25°C, it was impossible to increase the rate of adsorption by increasing the bulk concer~tration of this surfactant. As Burcik (13) has shown that counterions with valence
numbers greater than one are sometimes effective in increasing adsorption rates, two other inorganic electrolytes were used: MgCI~ and A1C13. However, Table I shows that neither had any measurable effect on increasing the rate of adsorption of hexadecyl sodium sulfate. Figures 9 and 10 show the surface concentrations of dodecyltrimethylammonium chloride, hexadecyltrimethylammonium chloride, and dodecyl sodium sulfate as a function of exposure time. These data were obtained by combining the results shown in Fig. 5 with those shown in Figs. 6 through 8 and making the assumption that surfactant
Journal of Colloid and Interface Science, ¥ol. 35, No. 1, J a n u a r y 1971
DYNAMIC SURFACE TENSION OF WATER AND SURFACTANT SOLUTIONS
z
50___£0PPM e 1.915 CM3/SEC 0 1.944 CM3/SEC
~I~ ~ ~ w~- ~ 0 " ~ 0
70
8_oo P__~PM .
60
~
5 f
C 12H25 (CH5)3CI
C~S /EC
~
51
0 •
4 0 0 PPM 8 0 0 PPM
u
[] 2.05 CM3/SEC I I 2.]4 CMS/SEC
'~"~-. ~
50
(.9 I
I
0.01
I
0.02
i
0 D5
0.04
I
0.05
(CH3)3CI
x
TE SEC
z
I
/
/
FIG. 7. Dynamic surface tension: C~6I-I~3N(CH3) 3C1. I, 0.01
I
0.02
~\
I~
5-Sx-~-CM 3/SE¢
. . . .
0
40
Dynamic
I 0.03 T E SEC
surface
I 0 .O4
tension:
012H25-
TABLE I DYNAMIC SURFACE TENSION RESULTS: I-IEXADECYL SODIUM SULFATE Cone of C16H~S04Na (p#rn)
FIG. 9. Surface time.
I 0.05
S04Na.
Wave
I
I
0.03
I
0.04
0 05
concentration
vs.
exposure
2_
1.580 CM3/SEC ~ I I 0.01 0.02
F I G . 8.
500 PPM 8 0 0 PPM
T E SEC
260 PPM
7O
[] •
Salt present 0.1 N
Flow rate
(cm~/sec)
Surface tension
(dynes#m)
~
4
d 0 o 0
3
0
2
CI2H25SO4N a
x
Z
I
I
I
I
I
0.01
0.02
0.03
0.04
0.05
T E SEC
1 2 3
10 10 10
NaC1 NaC1 NaC1
2.29 2.29 2.29
73.8 71.2 72.4
FIG. 10. Surface concentration time.
1 2 3
60 60 60
NaC1 NaC1 NaC1
2.04 2.01 1.992
78.0 73.2 75.2
surface c o n c e n t r a t i o n is a f u n c t i o n o n l y of surface tension.
1 2 3
60 60 60
MgC]2 MgC12 MgCl2
1.887 1,887 1.887
72.3
SUMMARY
72.5 70.6
Dynamic surface tension measurements employing a vertical oscillating jet were
4 5 1
60 60 60
MgC12 MgC12 MgC12
1.887 1.887 2.16
70.1 70.4
m a d e for b o t h w a t e r a n d s u r f a c t a n t so]utions. M e a s u r e m e n t s of t h e m a x i m u m a n d
73.9
minimum radii of the jet and wavelengths of
2 3
60 60
A1C18 A1CIa
2.16 2.16
73.8 72.7
t h e nodes were m a d e directly from t h e jet, u s i n g a t w o - c o o r d i n a t e c a t h e t o m e t e r . This: t e c h n i q u e p r e s e n t s a m u c h simpler a n d
vs.
exposure
Journal of Colloid and Interface Science, VoL 35, No. 1, January 1971~
52
CASKEY AND BARLAGE
faster method for measurement of these variables t h a n the complicated photographic techniques previously employed. B y using a diaphragm orifice constructed from 2 rail M y l a r film and made nonwetting b y coating both sides with paraffin, it was possible to produce an oscillating jet which gave values of dynamic surface tension for water which were independent of exposure t i m e and jet flow rate and which agreed closely with equilibrium values. ACKNOWLEDGMENT The authors thank the United States Public Health Service and Department of the Interior for support of this work through a Graduate Traineeship and Research Grant WP-00911. NO1VIENCLATUP~E c = bulk surfactant concentration, gm moles/l. C.F. = correction factor applied to Eq. [2] to convert dynamic surface tension to equilibrium surface tension. D = volumetric flow rate, cmS/sec. /c = Boltzmann constant, 8.314 X 107 ergs/(gm mole) (°K) L = jet length, era. N = surfactant surface concentration, gm moles/cm 2. r~ -- m a x i m u m jet radius for any given w a v e , ¢m.
r~ -- m i n i m u m jet radius for any given wave, cm (average of radii at top
t TE T 7 ), p
= = = = = =
and b o t t o m of wave for vertical jets). exposure time, msec. exposure time, sec. temperature, °K. surface tension, dynes/era. length of any wave on jet, cm. liquid density, g m / c m 3. REFERENCES
1. BRADY, A. P., J. Colloid Sci. 4,417 (1940). 2. DAVIES, J. T., AND RIDEAL, E. K., "Interfacial Phenomena," 2nd ed., p 197. Academic Press, New York, 1963. 3. HAYDEN, D. A., AND PHILLIPS, J. M., Trans. Faraday See. 54,698 (1958). 4:. MATUARA, 1~., KIMIZUKA, H., MIYAMOTO, S., AND SHI~OGAWA, R., Bul. Chem. Soc. Jap. 31,532 (1958). 5. BOER, N., Phil. Trans. A209, 281 (1909). 6. DEFAY, ~,.,AND HOMMELEN, J. 1~., J. Colloid Sci. 1S, 553 (1958). 7. ~-~ANSEN,1~. S., WALLACE,T. C., AND WOODY, 1~. W., Phys. Chem. 62,210 (1958). 8. SUTHERLAND, K. L., Aust. J. Chem. 1, 319 (1954). 9. OWENS, D. K., J. Colloid Interface Sci. 29, 496 (1969). 10. NETZEL, D. A., HOCH, G., AND MARX, T. I., J. Colloid Sci. 19,774 (1964). 11. VANDEGRIFT, A. E., #. Colloid Interface Sei.
23, 43 (1967). 12. STOCKEd,H., Z. Phys. Chem. 94,149 (1920). 13. BURCIK,E. J., J. Colloid Sci. 8, 520 (1953). 14. ZVlDE~A, H . H., AND WATtleS, G. W., Ind. Eng. Chem. Anal. Ed. 13,312 (1941). 15. MATIJEVI6, E., Trans. Faraday Soc. 54, 1382 (I958).
Journal of Colloid and Interface Science, Vol. 35, No. 1, January 1971
Received March 17, 1970; accepted July 20, 1970 Oscillating jets issuing from elliptical orifices have been widely used as a method for determining the dynamic surface tension of pure liquids and surfaetant solutions. However, such variables as iet diameter and wave length have been measured by complicated optical and photographic methods. A technique is presented for direct measurement of these data on the jet using a coordinate eathetometer. The jet stream was vertical and issued from an elliptical diaphragm orifice made of 2 mil Mylar film. The orifice was made nonwetting by carefully coating it with paraffin. This jet was found to give values of dynamic surface tension for water which were independent of exposure time and jet flow rate and which agreed closely with equilibrium values. For the surfaetant solutions studies, values of dynamie surface tension were also found to be independent of any jet flow rate used. Four surfactants were used in the investigation: dodeeyltrimethylammonium chloride, hexadeeyltrimethylammonium ehloride, dodecyl sodium sulfate, and hexadeeyl sodium sulfate.
assumed that surface concentration is only a function of surface tension at constant temperature, then Eq. [1] may be used to calculate surface concentration from dynamic surface tension data. Oscillating jets issuing from elliptical orifices have been widely used for measuring dynamic surface tension. Bohr (5) developed an equation relating dynamic surface tension to jet radii, volumetric flow rate, liquid density, and wavelength. Defay and Hommelen (6) simplified Bohr's equation to the following form:
INTRODUCTION
Gibbs' adsorption isotherm can be written as follows for ionized surfactants in the presence of excess electrolyte: -(o~/a
In c)~ = kT~V.
[1]
Equation [1] written for a two-component system requires two extra-thermodynamic assumptions: (1) the surface excess or deficit of the solvent is zero, and (2) the activity coefficient of the solute in solution is unity. The validity of Eq. [1] has been checked by several investigators (Brady (1), Davies and Rideal (2), Hayden an.d Phillips (3), Matuara et al. (4)) and found to be reliable for bulk surfactant concentrations less than the critical micelle concentration. In this investigation, Eq. [1] was used to obtain data for equilibrium surface concentration as a function of equilibrium surface tension for all surfactants studied. If it may be
4PD'~[1 +
37(b/a)2/24]~2~
where b/a = ( ~ - r~)/(~, q- r~); 1• =
(r~ + r d / 2 .
[3] [4]
Defay and Hommelen obtained dynamic surface tensions whieh were within 4-0.2 % of those values calculated by the Bohr equation. One constraint on Eq. [2] is that the liquid viscosity should not be greater than 0.01 poise.
Present address, Department of Chemical Engineering, Virginia Polytechnic Institute, Blacksburg, Virginia 24061.
Journal of Colloidand Interface Science~Vol. 35, No. 1, January t971
46
DYNAMIC SURFACE TENSION OF WATER AND SURFACTANT SOLUTIONS The one assumption of Bohr (5) which is difficult to obtain experimentally is that of no velocity profile within the jet. This problem has been attacked differently by several investigators. Hansen et al. (7) construeted an orifice from glass capillary tubing which purposely gave a velocity profile. Correction factors were applied to Eq. [2] to compensate for this velocity profile. Sutherland (8) made an orifice by sealing 1 or 2 mm lengths of glass capillary tubing of elliptical cross section to glass tubing 5 mm in internal diameter. The only condition he gave for choice of the orifice was that it gave the "right" surface tensions. Delay and I-Iommelen (6) constructed similar orifices. They standardized each orifice by using pure liquids and then multiplied the values of surface tension obtained with Eq. [2] by a correction factor to obtain agreement with literature values. Owens (9) using a diaphragm type orifice found that the surface tension of water calculated from Eq. [2] did not equal the accepted equilibrium value. I-Ie applied a correction factor to each wave. These correction factors were found to fit an equation of the form shown below. C.F. = 1-- (1/e(°'95~+L05)).
[5]
The form of Eq. [5] illustrates the phenomena that the first few waves give apparent surface tension values which are higher than accepted equilibrium values, particularly for water. As exposure time increases, the apparent dynamic surface tension values of water have been found to decrease approaching equilibrium values listed in the literature. Investigators who have observed this phenomena are Netzel et al. (10), Vandegrift (11), and Owens (9). Data of these investigators for water are shown in Fig. 1. These data seem to indicate that water has a time-dependent dynamic surface tension, or else Bohr's model does not adequately describe the first few waves of the jet stream. APPARATUS Method of Measurement. One technique previously used to measure jet radii and wavelength is that of Stoeker (12) or some
47
modification of his method. This technique consists of using each wave as a cylindrical convergent lens and illuminating the jet with a parallel beam of light. The emergent light beam is focused on a photographic plate. A photograph is then taken from which the necessary measurements can be made with a microscope. Owens (9) used a one-dimensional cathetometer to measure the wavelength of a horizontal oscillating jet. However, the maximum and minimum radii of each wave were assumed constant along the jet and equal to the major and minor radii of the elliptical orifice. This assumption may be true for pure liquids, but it is not true for surfactant solutions. When an elliptical jet is placed in the vertical position, ri, ~ , and X of Eqs. [2], [3], and [4] will change from wave to wave owing to the effect of gravity as well as to the effect of changing surface concentration of any surfactants present. Although a horizontal jet may eliminate the problem of gravity, it is still necessary to measure changes in r~, r ~ , and X along the jet due to the presence of any surfactants. In this investigation a Gaertner twocoordinate cathetometer, Model 2173A, was used as a faster and easier method of directly measuring r~, )~, and X of Eqs. [2], [3], and [4]. This instrument was ac-
-
Y
r
--~--
o----o llO
NETZEL
• .....
•
ET
I
AL
OWENS VANDEGRIFT
,oc o
E ~.
I
•\
90-
z
\
O\
o
O
z hJ }--
8C
ta (O
7C
~,
O\o
% ~'-e
o
"-. o.e
"O OZ'.0
0 ~ 0 ~ 0
0 0 0
6o
I I
"
I 2
EXPOSURE
I 5 TIME,t
I 4
I 5 (MSEC)
FIG. 1. Dynamic surface tension of water.
Journal of Colloid and Interface Science, ¥ o l . 35, No. 1, J a n u a r y 1971
48
CASKEY AND BAt~LAGE
curate to ~-0.0001 inch, and had a 4-inch range in each coordinate direction. A telemicroscopic lens was used giving a 30X magnification. Figure 2 is a photograph of the vertical oscillating jet used in this study. The picture was taken perpendicular to the axis of the jet and the major axis of the elliptical orifice. Figure 2 also shows examples of ~, the wavelength for a given node as well as r~ and r~ for that node. The value of ri used in Eqs. [3] and [4] was the arithmetic average of the values at the top and bottom of the node. The dynamic surface tension at an exposure time corresponding to a jet length L could then be cMculated from Eq. [2] using the values of ri, r~, k, and L measured from the oscillating jet. No experimental difficulties were encountered in measuring ri, rm, and k by this direct method. Elliptical Orifice. In this investigation an attempt was made to improve the diaphragm type elliptical orifice used by previous investigators by constructing an orifice of 2.0 mil Mylar film which had been very carefully coated with paraffin on both sides to make the surfaces nonwetting to water. This was done in an effort to reduce initial velocity profiles within the jet. The orifice was checked to determine if it was truly elliptical using the Gaertner cathetometer. It was found to be elliptical with a mQor diameter of 1.732 mm and an eccentricity of 0.617. The Mylar film was secured to a Parker ~-inch stainless steel tubing nut by epoxy cement thus forming the diaphragm orifice. Additional equipment was required to supply the ellipticM orifice with liquid at a temperature of 25.0 ° -4- 0.1°C and constant flow rate. Experimental. The orifice was checked for consistency with Bohr's model by determining the dynamic surface tension Of water at several flow rates ranging from 1.70 to 2.45 cma/sec. The water used was distilled and then deionized to a conductivity of less than 2 X 10-6 mhos. Four surfactants were chosen for the study: dodecyltrimethylammonium chloride, hexadecyltrimethylammonium chloride, dodecyl sodium sulfate, and hexadecyl sodium sulfate. Deionized water with a conductivity of less than 2 X Journal of Colloid and Interface Science, Vol. 35, No. 1, J a n u a r y 1971
..
)k
FIG. 2. Photograph of oscillating jet.
DYNAMIC SURFACE TENSION OF WATER AND SURFACTANT SOLUTIONS 10-6 mhos was used. Surfactant solutions were mixed in a base solution of 0.1 N sodium chloride. Sodium chloride was added to the surfactant solutions as Bureik (13) has shown the presence of an inorganic electrolyte increases the rate of surfaetant adsorption at a gas-liquid h~terfaee. The surfaetants were considered to be of sufficient purity for this investigation if a plot of V vs. In c did not give a minimum at the critical mieelle eoneentration. As purchased, only dodeeyl sodium sulfate showed a minimum in the surface tension eurve. It was purified b y recrystallization from an aqueous solution until the minimum disappeared. All equilibrium surface tension data for the surfactant solutions were taken with a du R~oiiy tensiometer applying the correction factors of Zuidema and Waters (14). It was found for all surfactants used that equilibrium surface tension values were obtained within 60 min. In order to eliminate eoneentration and temperature changes in the surfaetant solutions due to evaporation, all solutions were aged in covered Petri dishes. The room eontaining the experimentM apparatus was temperature controlled at 25.0 ° 4- 0.2°C. Dynamie surface tension data were calculated from readings of r i , r~, and X measured directly with the coordinate eathetometer as outlined above. I
{.) ""
I
I
49
RESULTS AND DISCUSSION The dynamic surface tension data obtained for water are shown on Fig. 3 and compared with the data of Vandegrift (11). From Fig. 3 it can be seen that the data for all water flow rates fall on the same line within the limits of experimental accuracy. The slope of this line was found to be - 0.099 dyne/(em)(milliseeond) b y application of a linear regression to the data. Although this line shows the dynamic surface tension of water to decrease slightly with increasing exposure time, the slope is not significantly different from zero, at least for exposure times greater than 4 milliseconds. Figure 4 shows the results obtained from the equilibrium surface tension measurements. The data for dodecyl sodium sulfate agreed with the data obtained by other investigators (l~atijevic (15), and NIatuara e t a l . ~ (4)). No published results were found for the other three surfactants. The results presented in Fig. 5 were calculated from the data shown in Fig. 4 by means of Eq. [1] and show equilibrium surface tension as a function of surfaetant surface concentration. Figure 5 does not show these data for hexadecyl sodium sulfate as this surfactant showed no measureable dynamic surface tension. The results presented in Figs. 6 through 8 and Table I show dynamic surface I
I
FLOW
l
I
RATE
IO0--
w z
- -
VANDEGRIFT
6. 1.70 e 1.88
THIS
o 2.02
CC/SEC
o
~.
90-
o--o
WORK
o 2.08
z 0 z ,,,
o
2.23
• 2.45 80
~J
@ ID .
. . .
~,,
6* ° 4 -
"°
•
@
70 O3 I
I
8
12
EXPOSURE F I G . 3. D y n a m i c
I
J6 TIME , t
I
20
I
I
24
28
(MSEC)
surface tension of water.
Journal of Colloid and Interface Science, Vo]. 35, No. 1, J a n u a r y 1971
50
CASKEY AND BARLAGE
70
60
~, 50 >-
--,,,--...,,
• 4O
•
CI6 H'5'sN(C H3)'5Cl
~ ~ 4 ~ - - ' I
30 I
u53
I(~ 4
I
i
I
no-2
no-,
=
C
I0
MMOLES/LITER
FIG. 4. Equilibrium surface tension data. 400 PPM 2.07 CM~/SEC
70 ~
70
~
0
~o
co 5 0
~J z >o
50
800 PPM [] 1,925 CMS/SEC • 1.8i8 CMS/$EC ~) I 0 I 0.0Z
>" 4 0
I
0.05 TE $EC
1
0,04
I
0.05
50 I
I
I
I
I
I
2
5
4
5
FIG. 6. Dynamic surface tension: C12H2~N-
(CHs)~C1.
NXIO I0 GMOLES/CM 2
FIG. 5. Equilibrium surface tension factant surface concentration.
vs.
sur-
tension data which were calculated by means of Eq. [2] using cathetometer measurement of r~, r~, and X. Table I shows that the dynamic surface tension of 60 ppm hexadecyl sodium sulfate remained essentially constant at 72.5 dynes/ cm for all exposure time. Since the solubility of hexadecyl sodium sulfate is only about 60 ppm in 0.1 N sodium chloride solutions at 25°C, it was impossible to increase the rate of adsorption by increasing the bulk concer~tration of this surfactant. As Burcik (13) has shown that counterions with valence
numbers greater than one are sometimes effective in increasing adsorption rates, two other inorganic electrolytes were used: MgCI~ and A1C13. However, Table I shows that neither had any measurable effect on increasing the rate of adsorption of hexadecyl sodium sulfate. Figures 9 and 10 show the surface concentrations of dodecyltrimethylammonium chloride, hexadecyltrimethylammonium chloride, and dodecyl sodium sulfate as a function of exposure time. These data were obtained by combining the results shown in Fig. 5 with those shown in Figs. 6 through 8 and making the assumption that surfactant
Journal of Colloid and Interface Science, ¥ol. 35, No. 1, J a n u a r y 1971
DYNAMIC SURFACE TENSION OF WATER AND SURFACTANT SOLUTIONS
z
50___£0PPM e 1.915 CM3/SEC 0 1.944 CM3/SEC
~I~ ~ ~ w~- ~ 0 " ~ 0
70
8_oo P__~PM .
60
~
5 f
C 12H25 (CH5)3CI
C~S /EC
~
51
0 •
4 0 0 PPM 8 0 0 PPM
u
[] 2.05 CM3/SEC I I 2.]4 CMS/SEC
'~"~-. ~
50
(.9 I
I
0.01
I
0.02
i
0 D5
0.04
I
0.05
(CH3)3CI
x
TE SEC
z
I
/
/
FIG. 7. Dynamic surface tension: C~6I-I~3N(CH3) 3C1. I, 0.01
I
0.02
~\
I~
5-Sx-~-CM 3/SE¢
. . . .
0
40
Dynamic
I 0.03 T E SEC
surface
I 0 .O4
tension:
012H25-
TABLE I DYNAMIC SURFACE TENSION RESULTS: I-IEXADECYL SODIUM SULFATE Cone of C16H~S04Na (p#rn)
FIG. 9. Surface time.
I 0.05
S04Na.
Wave
I
I
0.03
I
0.04
0 05
concentration
vs.
exposure
2_
1.580 CM3/SEC ~ I I 0.01 0.02
F I G . 8.
500 PPM 8 0 0 PPM
T E SEC
260 PPM
7O
[] •
Salt present 0.1 N
Flow rate
(cm~/sec)
Surface tension
(dynes#m)
~
4
d 0 o 0
3
0
2
CI2H25SO4N a
x
Z
I
I
I
I
I
0.01
0.02
0.03
0.04
0.05
T E SEC
1 2 3
10 10 10
NaC1 NaC1 NaC1
2.29 2.29 2.29
73.8 71.2 72.4
FIG. 10. Surface concentration time.
1 2 3
60 60 60
NaC1 NaC1 NaC1
2.04 2.01 1.992
78.0 73.2 75.2
surface c o n c e n t r a t i o n is a f u n c t i o n o n l y of surface tension.
1 2 3
60 60 60
MgC]2 MgC12 MgCl2
1.887 1,887 1.887
72.3
SUMMARY
72.5 70.6
Dynamic surface tension measurements employing a vertical oscillating jet were
4 5 1
60 60 60
MgC12 MgC12 MgC12
1.887 1.887 2.16
70.1 70.4
m a d e for b o t h w a t e r a n d s u r f a c t a n t so]utions. M e a s u r e m e n t s of t h e m a x i m u m a n d
73.9
minimum radii of the jet and wavelengths of
2 3
60 60
A1C18 A1CIa
2.16 2.16
73.8 72.7
t h e nodes were m a d e directly from t h e jet, u s i n g a t w o - c o o r d i n a t e c a t h e t o m e t e r . This: t e c h n i q u e p r e s e n t s a m u c h simpler a n d
vs.
exposure
Journal of Colloid and Interface Science, VoL 35, No. 1, January 1971~
52
CASKEY AND BARLAGE
faster method for measurement of these variables t h a n the complicated photographic techniques previously employed. B y using a diaphragm orifice constructed from 2 rail M y l a r film and made nonwetting b y coating both sides with paraffin, it was possible to produce an oscillating jet which gave values of dynamic surface tension for water which were independent of exposure t i m e and jet flow rate and which agreed closely with equilibrium values. ACKNOWLEDGMENT The authors thank the United States Public Health Service and Department of the Interior for support of this work through a Graduate Traineeship and Research Grant WP-00911. NO1VIENCLATUP~E c = bulk surfactant concentration, gm moles/l. C.F. = correction factor applied to Eq. [2] to convert dynamic surface tension to equilibrium surface tension. D = volumetric flow rate, cmS/sec. /c = Boltzmann constant, 8.314 X 107 ergs/(gm mole) (°K) L = jet length, era. N = surfactant surface concentration, gm moles/cm 2. r~ -- m a x i m u m jet radius for any given w a v e , ¢m.
r~ -- m i n i m u m jet radius for any given wave, cm (average of radii at top
t TE T 7 ), p
= = = = = =
and b o t t o m of wave for vertical jets). exposure time, msec. exposure time, sec. temperature, °K. surface tension, dynes/era. length of any wave on jet, cm. liquid density, g m / c m 3. REFERENCES
1. BRADY, A. P., J. Colloid Sci. 4,417 (1940). 2. DAVIES, J. T., AND RIDEAL, E. K., "Interfacial Phenomena," 2nd ed., p 197. Academic Press, New York, 1963. 3. HAYDEN, D. A., AND PHILLIPS, J. M., Trans. Faraday See. 54,698 (1958). 4:. MATUARA, 1~., KIMIZUKA, H., MIYAMOTO, S., AND SHI~OGAWA, R., Bul. Chem. Soc. Jap. 31,532 (1958). 5. BOER, N., Phil. Trans. A209, 281 (1909). 6. DEFAY, ~,.,AND HOMMELEN, J. 1~., J. Colloid Sci. 1S, 553 (1958). 7. ~-~ANSEN,1~. S., WALLACE,T. C., AND WOODY, 1~. W., Phys. Chem. 62,210 (1958). 8. SUTHERLAND, K. L., Aust. J. Chem. 1, 319 (1954). 9. OWENS, D. K., J. Colloid Interface Sci. 29, 496 (1969). 10. NETZEL, D. A., HOCH, G., AND MARX, T. I., J. Colloid Sci. 19,774 (1964). 11. VANDEGRIFT, A. E., #. Colloid Interface Sei.
23, 43 (1967). 12. STOCKEd,H., Z. Phys. Chem. 94,149 (1920). 13. BURCIK,E. J., J. Colloid Sci. 8, 520 (1953). 14. ZVlDE~A, H . H., AND WATtleS, G. W., Ind. Eng. Chem. Anal. Ed. 13,312 (1941). 15. MATIJEVI6, E., Trans. Faraday Soc. 54, 1382 (I958).
Journal of Colloid and Interface Science, Vol. 35, No. 1, January 1971