A: Physicochemical and Engineering Aspects 170 (2000) 45 – 50
Interfacial tension measurement by the rotating meniscus
Pablo Contreras
a,* , Mihaela Olteanu
baPDVSA-INTEVEP, Apartado76343-Caracas1070A, Venezuela bDepartment of Physical Chemistry, Uni6ersity of Bucharest, Bucharest, Romania
Received 16 July 1999; accepted 8 November 1999
Abstract
The interfacial tension of some pure liquid – liquid systems was calculated from the shape of a rotating meniscus. This technique is presented as an alternative method to determine the interfacial tension when the liquid – liquid ratio during the test is expected to affect the relative rates of desorption of the surfactant from the interface. The profile of each meniscus has been studied by analysis of each image with the use of a video camera and a computer. The pressure difference across the interface, combined with Laplace’s equation was used to obtain the general differential equation. The approach developed by Bashforth and Adams and extended by Sugden was used to obtain, for the first time, a real value of the ratio of curvature at the apex. This parameter was necessary to obtain an approximation of the solution and thus the interfacial tension for each system. A computer program and a mathematical convergence method were used to reach the solution. The values obtained were comparable with the calculated data according to the theoretical equation of Fowkes and the values reached by other experimental techniques. Ultra low interfacial tensions have been obtained from crude oil/alkaline solutions systems too. The possibility of studying the interfacial rheological behavior using this technique has been analyzed © 2000 Elsevier Science B.V. All rights reserved.
Keywords:Interfacial tension; Ultra low tensions; Interfacial rheology
www.elsevier.nl/locate/colsurfa
1. Introduction
Most of the problems of surface chemistry are related more or less with the study of surface tension (ST) or interfacial tension (IT), in static or dynamic conditions. Thus, an important number of techniques have been developed in order to obtain this thermodynamic property. Practically all existing methods rely on a detailed analysis of interfacial shape [1,2]. A recent review made by
Franses et al. presents a description of the dy-namic techniques involving drops, bubbles, liquid jets and menisci [3]. Rusanov and Prokhorov have presented an extended study about methods for measuring ST and IT [1]. These authors classified the techniques based on: profiles of menisci with fixed shape, measuring extreme values of parame-ter of menisci, methods using menisci at stability, dynamic methods and methods using rotating field. This last group includes the spinning drop technique, which is one of the most common and is recommended for systems with ultralow interfa-cial tensions particularly (10− 6mN m− 1).
Limita-* Corresponding author.
E-mail address:[email protected] (P. Contreras)
0927-7757/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 ( 9 9 ) 0 0 4 9 9 - 9
tions of this method have been discussed by Tay-lor [4].
In this work the rotating meniscus (RM) is presented as an option to obtain IT values in static conditions without the limitation of the ratio between the phases, one of the main prob-lems of the methods mentioned above. It is based on a detailed analysis of interface shape in equi-librium condition. The curvature radius at the meniscus bottom has been calculated, as an inde-pendent value for each system, without the con-sideration of any simplification. The IT is obtained directly from a differential equation. The ability to calculate IT values and to obtain the interfacial area as a function of time with the use of a high precision video camera constitutes an alternative method to study the interfacial rheology.
Theoretical aspects of RM technique are dis-cussed as follows. If a cylindrical tube of radius R (Fig. 1), containing two liquids of densitiesr1and r2, is rotated with an angular velocityv, about its
vertical axis, the meniscus between the fluids reaches an elevation z, as a consequence of its deformation. After an equilibrium time, the elon-gation ceases when the ITg, balances the
elonga-tion force due to the centrifugal field. The equation describing the meniscus shape has been obtained from the pressure drop in the axis of rotation. Here, P1 is the pressure at any point in phase 1, and P2 at any point in phase 2,
P1− P2= (r2−r1)
gz −
v2x2
2
n
+ 2gb (1)
where x is the distance from the centre on the tube toward the wall, b is the radius of curvature on the bottom of the meniscus and g is the gravity constant [5,6].
This last expression is equivalent with the ex-pression formulated by Bird et al. to describe the shape of the surface in a liquid which rotated in a tube, but without the influence of the IT (the last term, 2g/b). Bird uses the equations of variation for isothermal systems, applying the expressions of movement in cylindrical coordinates [7].
For equilibrium of a non-spherical meniscus (Fig. 1), the analysis must take into account the deviation from the sphericity, in order to obtain the exact solution of Eq. (1), at zero contact angle, z¦ (1 + z%2)3/2+ z% x(1 + z%2)1/2 =(r2−r1) g
gz − v2x2 2
n
+ 2 b (2)where the two left terms are the inverse of R1and
R2, the two radii of curvature.
Unfortunately, it has not been possible to ob-tain an explicit solution to Eq. (2) in terms of z, the usual experimental parameter. Only approxi-mate solutions of entirely adequate accuracy have been performed.
The approach developed by Bashforth and Adams, to study the capillary rise problem, was employed to obtain a real curvature ratio value at the apex b. These authors simultaneously with Sugden said that in the case of a figure of revolu-tion, the two radii of curvature, R1and R2, must
be equal at the apex and equal to b. Taking into account this idea, it is possible to estimate b for any system [2,8].
The function f(x) = z is obtained by video im-ages of the interface in equilibrium condition, which can be processed directly in a computer (Fig. 2).
Fig. 1. Equilibrium of a non-spherical meniscus of height z, formatted between two liquids of densities r1 and r2 which
rotate with an angular velocityv, in a tube of radius R. R1
Fig. 2. Rotating meniscus technique: (A) glass tubing, (B) meniscus, (C) motor, (D) tachometer, (E) video camera and (F) computer. cr= (r2−r1)v2 4g , (5) cg=(r2−r1)g g (6)
where cris the rotating constant and cg the gravi-tational content.
2. Experimental
The rotating cell used is displayed in Fig. 2. A capillary tube of 0.4 cm internal radius and ap-proximately 25 cm length, previously washed and dried in a furnace, was arranged in a vertical motor, of 30 – 2500 RPM with 0.1 KW. The veloc-ity of rotation v was fixed and measured with a digital tachometer.
Four model systems were studied: n-hexane/wa-ter, glycerin/n-hexane, water/decane and water/ toluene. Distilled water was used, the rest of the fluids were of analytical grade of Merck. The capillaries were filled with 4 ml of each phase and left at rest vertically for 24 h at 24°C.
To measure systems of low or ultra low interfa-cial tensions, two systems were selected. A clean system, acid oil (heptane-oleic acid) in contact with alkaline solutions and Urdaneta crude oil of Venezuela (19 °API, 3.5 of total acid number), in contact with alkaline solution. In this last case, a nonionic tensoactive, Plantaren 1200, an alkyl polyglycoside of Henkel, was added at two of the alkaline solutions. A reference tube with crude oil/distilled water was analyzed too. All these experiments were run at 20°C. Tubes were left in repose for 30 days.
The procedure of IT determination can be re-sumed briefly. Each tube was inserted and fixed in the motor, rotation velocity was adjusted and finally verified with the tachometer. After the equilibrium, 20 min for the model systems, and 90 min for the crude oil, meniscus images were taken to be analyzed directly in a computer. A video camera, a capture and video editor programs were used. Three of these images for systems of rela-tively high, medium and low interfacial tensions are displayed in Fig. 3. The IT was calculated according to theoretical procedure.
Fig. 3. Pictures of the meniscus scanned of glycerin/n-hexane system at 24°C, Urdaneta crude oil/water and Urdaneta crude oil/alkaline solution system at 20°C and 1500 RPM.
A mathematical adjustment of each interfacial curve was made and the coefficients a, b, c,…g of
f(x) were estimated. The form of the meniscus is
presented as the function f(x) = z, therewith a polynomial equation of sixth degree could be written. With the b value and the rest of the Eq. (2) parameters, the IT was calculated. A method of convergence was used to reach a solution ap-proximation. The dimensionless parametersa and b (Eqs. (3)–(6)), defined by Princen in order to characterize the shape of the meniscus were calcu-lated too.
a=2crb3, (3)
Table 1
Results for the models systems
System Dr (gr cm−3) RPM z (cm) b (cm) a (10−2) b (10−3) g (mN m−1 ) Experimental/calculated (RM) 1200 n-Hexane/water 0.34 0.7 0.26 2.3 4.4 51.1*@20°C/48.5@28°C 0.60 1550 3.6 0.22 6.3 Glycerin/n-hex- 8.4 33.8*@24°C/34.9@24°C ane Decane/water 0.27 1535 1.3 0.21 1.6 2.3 51.2 [9]@20°C/45.2@24°C 1550 2.6 0.22 Toluene/water 0.13 1.3 1.7 35.7 [11]@20°C/31.4@24°C
* This work with Wilhelmy plate. 3. Results and discussion
A summary of results for the model systems is shown in Table 1. First of all, the radius of curvature at the apex, b, is in accordance with that observed in the images between 0.21 and 0.26 cm. Likewise, the theoretical approximation valid-ity is confirmed. The values of the dimensionless parameters a and b allows the relation between the parameters involved to be checked. In general a and b tend to be high if the inertial effect of Dr is bigger. The maximum value observed is for glycerin/n-hexane and the minimum for the toluene/water. At the same time, the results cor-roborate that z depends basically on theDr val-ues, for systems with similar IT and at the same rotating velocity.
As we can see in Table 1, the IT obtained by the RM is comparable with the values of the Wilhelmy plate. For glycerin/n-hexane, the differ-ence is around 1.1 mN m− 1 and for the other
liquids the difference is a direct consequence of temperature variance.
Additionally the IT values presented in Table 2, calculated with RM, are similar to the theoretical values obtained with the equation of Fowkes [10,11]. It should be pointed out that the IT calculated with the RM is close to the values of Fowkes, except for decane/water, maybe due to the experimental errors.
The results for the clean system, acidic oil (heptane-oleic acid) are in Fig. 4. The main aspect here is the fact that is possible to obtain IT values of until 10− 4 mN m− 1 as with other known
techniques. Additionally, these results put in evi-dence the effect of the liquid – liquid ratio, when it
effects the relative rate of desorption of the sur-factant from the interface. The IT (Fig. 4) remains as an ultra low IT after 0.1% of NaOH, against the observation of other authors [12,13]. They have found that the IT for high alkalinity (\ 0.1%) grows to reach 1 mN m− 1using a spinning
drop tensiometer.
Table 2
Experimental results obtained by RM and theoretical values calculated by the Fowkes equation
System g (mN m−1) g (mN m−1) Fowkes equation Calculated RM n-Hexane/water 48.5@28°C 50.5@28°C 34.4@24°C Glycerin/n-hex- 34.9@24°C ane 45.2@24°C 50.8@24°C Decane/water
Fig. 4. Interfacial tension with RM for the system: heptane-oleic acid (13 mol m− 3), in contact with alkaline solution at
20°C. The ionic strength was kept constant, 171 mol m− 3with
Table 3
Experimental results obtained by RM for Urdaneta crude oil/water, alkaline solutions and alkaline solutions+nonionic surfactant (Plantaren 1200), 1:1, at 1500 RPM and 20°C, after 30 days of rest
System Z (cm) b (cm) g (mN m−1)
Oil phase Aqueous phase
1.8
Urdaneta crude oil Water 0.21 26.1
3.3 2.71×10−2
Alkaly, 0.04% NaOH 3.4×10−3
Urdaneta crude oil
Alkaly, 0.07% NaOH
Urdaneta crude oil 3.9 1.41×10−2 1.9×10−3
4.0 7.45×10−2
Urdaneta crude oil Alkaly, 0.04% NaOH +plantaren 1200a 3.4×10−3
5.0 6.82×10−2
Alkaly, 0.07% NaOH +plantaren 1200a 6.6×10−4
Urdaneta crude oil
aAlkyl polyglycoside, 3.25×10−4M.
This behavior has been the subject of numerous discussions due to the importance in enhanced oil recovery. Wade et al. suggests that the minimum is a consequence of a middle phase formation, which is too small in extent to be detectable [14]. The use of a spinning drop tensiometer with a phase volume ratio of 1:200 (oil:water), produces questionable results. In our proposition, the RM technique is an alternative to this kind of study. Only at high alkalinity, (more than 1% of NaOH), the phase volume ratio does not change apprecia-bly [15].
The simultaneous adsorption of ionized and unionized acid upon the interface and its syn-ergetic effect is another of the explanations of this behavior [13]. After the minimum, the IT in-creases because the unionized acid becomes ion-ized, but again in this case, an inappropriate technique to measure the IT produces this ques-tionable conclusion.
The results for crude oil systems are in Table 3. The radius of curvature was calculated in each case. As observed, b changes considerably, being smaller when the interfacial tension decreases. Thus, the crude oil/water system has a b of 0.21 cm and IT of 26.1 mN m− 1, in the case of crude
oil/alkaline solutions, b is of the order of 10− 2cm
due to the fact that IT is smaller. The effect of the nonionic tensoactive was evaluated as well. Values of b of 10− 2cm and IT of 10− 3– 10− 4mN m− 1
were obtained for systems with a meniscus of 4 and 5 cm in height.
It is remarkable that the IT reported in all this work reflects exactly the values of the system
studied due to the fact that we do not take only a small portion of the oil, like practically all the known techniques.
One parallel aspect derived from this work is the possibility to estimate IT in dynamic condi-tions and some rheological properties of one in-terface. The Marangoni viscosity zM, of oil/water
soluble films, could be estimated from the varia-tion of the interfacial area S, with the time(S/(t. This property expressed in cm s− 1, analogous to
the viscosity of three-dimensional systems, that depends simultaneously upon the properties of this phase and upon the rate of attainment of equilibrium between the substrate and the ad-sorbed film, could be obtained from the relation of the surface tension gradient Dg [16].
In fact, this viscosity is the parameter that we are using to study the presence of mixed film in some particular cases of interest. The results will be published later.
4. Conclusion
We suggest that the rotating meniscus might be used to measure the IT, keeping in mind the possibility of volume changes of phases. The re-sults are comparable with theoretical and experi-mental values published. Ultra low IT can be measured too. The option of determining IT and the area generated as a function of time opens the possibility to employ the technique to study some rheological properties.
References
[1] A.I. Rusanov, V.A. Prokhorov, Interfacial Tensiometry, In: D. Mo¨bius, R. Miller (Eds.) Elsevier, Amsterdam, 1996 (Chapter 7).
[2] H. Princen, in: E. Matijevic´ (Ed.), Surface and Colloid Science, vol. 2, Wiley, New York, 1969.
[3] E. Franses, O. Basaran, C. Chang, Curr. Opin. Colloid Interface Sci. 1 (1996) 296.
[4] K. Taylor, B. Hawkins, in: L. Schramn (Ed.), Emulsions, Fundamentals and Applications in the Petroleum Industry, American Chemical Society, Washington, 1992 Chapter 7. [5] H. Princen, I. Zia, S. Mason, J. Colloid Interface Sci. 23
(1973) 99.
[6] R. Bird, W. Stewart, E. Lightfoot, Feno´menos de Trans-porte, Reverte, Espan˜a, 1982.
[7] R. Defay, I. Prigogine, A. Bellemans, D.H. Everett, Sur-face Tension and Adsorption, Longmans, London, 1968.
[8] A. Adamson, Physical Chemistry of Surfaces, Wiley, New York, 1967.
[9] K. Birdi, Lipid and Biopolymer Monolayers at Liquid Interfaces, Wiley, New York, 1989.
[10] F. Fowkes, Advance Chemistry 43 (1964) 99.
[11] M. Olteanu, Coloizi, Editura Universitate, Bucuresti, 1993.
[12] J. Rudin, D.T. Wasan, Colloids Surf. 68 (1992) 67. [13] J. Rudin, D.T. Wasan, Colloids Surf. 68 (1992) 81. [14] H. Wade, E. Vazquez, J.L. Salager, M. El-Mary, C.
Koukounis, R.S. Schechter, in: K.L. Mittal (Ed.), Solu-tion Chemistry of Surfactants, vol. 2, Plenum Press, New York, 1978.
[15] T. Ramakrishnan, Ph.D. Dissertation. A Model for In-terfacial Activity of Acidic Crude Oil/Caustic Systems, ITT, Chicago, 1983.
[16] M. Joly, in: E. Matijevic´ (Ed.), Surface and Colloid Science, vol. 5, Wiley, New York, 1969.
