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Limitations of classical methods for measuring surface tension in visco-elastic liquids.

Abstract The surface tension of a water/detergent mixture and a visco-elastic waterborne paint sample were measured using the classical ring method in which a thin free liquid film (lamella) is formed between the ring and the parent liquid. Lamella tension was measured during the stretching of the lamella. Measurements of water/surfactant mixtures have shown essentially classical behavior of lamella tension (independence of tension on deformation). Measurements of a waterborne paint formulation, however, have shown that after stretching of the lamella, the lamella tension decreases. The lamella tension of the paint sample increases after contraction of the lamella. Comparison of experimental results with rheological properties of the paint have shown that bulk visco-elastic properties of liquid are found in both the bulk sample and the lamella. The conclusion is that for the study of surface properties of visco-elastic liquids such as waterborne paints, the applicability of classical methods is limited. Therefore, it was necessary to develop new methods and approaches to study the properties of these materials. These methods are described in this paper.

Keywords Surface tension, Lamella tension, Wire ring method, Viscosity, Elasticity

Introduction

The classical concept of surface tension of a liquid is that the surface tension depends only on temperature (1) and does not depend on the deformation of the free surface. In 1956, German researchers (2) established that there is a dependence of surface tension on the rate of deformation and proposed the concept of a dynamic surface tension. The modern explanation of this fact is that a separate surface phase (Gibbs layer), is generated which has a composition that is different than the bulk composition. Surface tension is determined from an equilibrium condition of the Gibbs layer. (3), (4) For Newtonian liquids with low viscosity, the characteristic time of establishment of an equilibrium condition in the Gibbs layer is a sorption process taking about [10.sup.-7] s. Therefore, in real time these phenomena are imperceptible, and the classical concept of the surface tension is accurate in most cases. The modern concept of a thin free liquid film (lamella), is that when two free liquid surfaces approach each other, the zone of interaction between the two layers forms a joint Gibbs layer giving rise to differences in local pressure. (5) These differences in pressure are the reason for the stability of the lamella. Liquids containing surfactants form powerful Gibbs layers and, therefore, stable lamellae. It is clearly known that various additives can have very profound effects on a paint film as it is formed, and these effects are related to the formation of Gibbs layers. Unfortunately, Gibbs layer effects are not well understood. The stability of the lamella causes a stability of bubbles and foams through Gibbs layer effects. The creation of foam in soap water with inflated bubbles is based on this behavior.

In many technologies, the stability or instability of lamellae can be a key factor. For example, a stable lamella of a sprayed paint can cause the formation of air bubbles on a painted surface, which can be a source of paint defects. Stability of foams and bubbles are important factors in some areas of the food and oil refining industries. In such cases, the study of lamella behavior is important as is the measurement of surface tension and the rheology of liquids. In this work, we have examined experimentally whether the deformation of a lamella influences its tension in visco-elastic liquids.

Experimental technique

Lamella tension

For the study of lamella tension, the classical method (5) for measuring surface tension was used involving a wire ring in a horizontal orientation which is immersed into a liquid and then slowly lifted out of the liquid (Fig. 1). The ring was suspended on a high-sensitivity balance based on thin film semi-conductors. The diameter of the ring was 41 mm; the diameter of the wire was 0.6 mm. The balance was placed in a closed box with humidity and temperature controlled at 60% and 24[degrees]C, respectively. A Petri dish with the test liquid was placed under the ring. The dish was covered with a lid containing an opening for the ring. This minimizes evaporation of volatiles from the liquid. Test experiments have shown that changes in the atmospheric composition in the box do not influence the measured data. The dish was lowered (stretching) or raised (contraction) with an electric up-down elevator motor. The measurements from the balance signals were fed into a computer. The sensitivity of the balance with the suspended ring was calibrated with an experimental liquid. Measurements were performed by moving the Petri dish upward to bring the ring into contact with the liquid surface and stopped when the ring was immersed to a depth of 3 mm in the liquid. After 30 s, the Petri dish was moved downward with a speed of 153 [micro]m/s. The balance signal was measured every 1.3 s. Typical dynamics of the balance signal are shown in Fig. 2a. As the ring was raised out of the liquid, a meniscus was formed on the ring. The balance signal grows and passes a maximum point (M). In the classical method for measuring surface tension with a wire ring, the force measured at point M is used for the calculation of the surface tension of the free surface of a liquid. The calculation is carried out with some theoretical amendments (5) which specify the influence of the meniscus weight. As the Petri dish was moved downward further, a cylindrical-shaped lamella was formed. The moment the lamella was formed, the balance shows a characteristic change in the balance signal (point L, Fig. 2a). Stretching of the lamella occurred as the Petri dish was moved downward even more. The point of contact of the lamella with the surface of the liquid showed a meniscus in the shape of a ring. After formation of the lamella, the balance signal slowly decreases because the cylindrical form of the lamella is unstable. As the lamella was stretched, the meniscus on the liquid surface slowly decreases in diameter, which reduces the perimeter of the lamella that is responsible for the total force of the lamella tension. At a lamella length of 3 mm, the movement of the Petri dish was stopped (at point B). The lamella tension at constant length was measured between points B and C. After a short pause (at point C), the Petri dish was moved upward. This reduces the lamella length. During this stage (between points C and D), the lamella tension was measured during contraction. After stopping the contraction (at point D), a pause for a second measurement of lamella tension without deformation was carried out. The movement of the Petri dish downward was then started again (point E). The lamella tension was measured again during stretching. The lamella was destroyed and the measurement of the balance signal was used as the zero point for the calculation of lamella tension changes. The results of measurements made during the cycle described were processed by a computer that used inputs of the balance signal, calibrated sensitivity, and the double perimeter length of the wire ring. The relative hardware error of measured lamella tension does not exceed [+ or -]0.05%. The measurements cycle was automatically repeated several times in order to study the behavior of the lamella as a function of time after stirring the liquid.

[FIGURE 1 OMITTED]

Viscosity/residual elasticity

For measurement of viscosity and residual elasticity, a wire ring with a diameter of 20.5 mm was used. The sample of liquid was stirred and poured into a 35-mm high container so that there was a liquid layer not <17 mm deep in the container. This container was placed on the vertical coordinate of the device and raised such that the ring suspended on the balance reached a depth of 7 mm in the liquid. The computer program carried out periodic reciprocating movements of the container in a vertical direction with pauses before changing the direction of movement. A typical cycle is shown in Fig. 2b. The movement of the container upward with a speed of 0.053 mm/s begins at point 2. From point 2 to point 4, the container was moved upward at a uniform speed. The stabilization of the movement of the ring inside the liquid occurs between point 2 and 3. Measurements of the viscous resistance force of the liquid to movement of the ring inside the liquid were carried out between points 3 and 4. At point 4, the movement of the container was stopped. Between points 4 and 5, relaxation of the ring in the liquid occurs due to deformation of the elastic element attached to the balance created between points 2 and 3. The motor for moving the container downward was started at point 5. The stabilization of moving the ring toward the surface of the liquid at constant speed of the container takes place between points 5 and 6. In the time interval between points 6 and 7, the measurements of viscous force taken at uniform speed of the ring inside liquid were made. At point 7, the motor was stopped. Between points 7 and 1, the relaxation of the ring in the liquid (after movement) occurs. The ring returns to the same level in the liquid where the measurements began at point 1. The cycle repeats a given number of times for measurement of the changes in viscosity and elasticity with time after stirring.

[FIGURE 2 OMITTED]

The results of the measurements were processed by the computer program. The first step of processing consists of calculation of the zero level of the measured force. The last 10 points at 4-5 and 7-1 were averaged. The average value of this force is accepted as a zero level. Thus, the Archimedes force working on the ring is automatically excluded. The viscosity was calculated at sites 3 and 4 and 6 and 7 as an average. Residual elasticity was calculated after slopping the ring movement at points 1 and 5. The relative error of measured viscosity and elasticity does not exceed [+ or -]2%.

The Oseen amendment for viscous movement of a wire ring (6) gives the formula for resistance force

F = v4[[pi].sup.2] [D.sub.r]U / In (7.406v / [rho] [Ud.sub.w]), (1)

in which v is dynamic viscosity, [D.sub.r] is diameter of a ring, U is speed of movement, [rho] is density of a liquid, and [d.sub.w] is the diameter of wire. The dynamic viscosity is calculated from the solution of equation (1). The residual elasticity is calculated from the formula

E = F / ([pi][D.sub.r][d.sub.w]). (2)

Here the physical sense of the residual elasticity (2) is residual pressure supporting the ring and obstructing its final relaxation in the liquid.

The sites 4-5 and 7-1 in Fig. 2b, where the ring moves inside liquid with various speed, can be used for calculation of viscosity at a wide range of shear rates.

Measurements of water surfactant mixture

In Fig. 3, the lamella behavior is shown in one of 40 cycles studied for a sample of distilled water with 12 vol% of a detergent containing ~10% sodium dodecylsulfate. The following is a description of the cycle. At stages of stretching (between points A and B, after point E) and at the stage of contraction (between points C and D), the change of tension is caused by the instability of the noncylindrical shape of the lamella. At stages of relaxation of the lamella without deformation (between B-C and D-E), a slow reduction of the lamella tension is observed. This directly relates to the instability of the lamella. The slow reduction of lamella tension over time is caused by the draining of liquid from the ring and from the lamella into the volume of the bulk liquid under the action of gravity. As a result, the lamella gets thinner and shows a decrease in lamella tension because it has less mass. There is no reason to believe that there is a decrease in surface tension of the bulk liquid in the Petri dish. This means that in this system (with the liquid--lamella at rest) the difference between tension on the meniscus and the lamella tension slowly grows. This difference stimulates capillary convection in the lamella. The growing capillary convection (together with gravitational force) accelerates the flow of liquid from the lamella and eventually the lamella breaks.

[FIGURE 3 OMITTED]

At the relaxation stage after stretching (between points B and C), the rate of slow reduction of lamella tension is -1.49 x [10.sup.-3] mN/m s. A comparison of the data points for D and E shows that lamella tension decreases with an average rate of -1.74 x [10.sup.-4] mN/m s which is less than the rate of decreasing lamella tension after stretching. It is possible to conclude that we have found the basic influence of lamella deformation. After stirring of the liquid is stopped, the rate of convection in the lamella is decreased. The deceleration of convection is apparently related to an increase in concentration of surfactants on the surface of the lamella during the contraction deformation.

At point D, the lamella length has returned to the value which it had initially at point A. It is important to note, that after the return of lamella length to the reference value, the tension of the lamella was not restored in full. Apparently, the convective phenomena in the lamella result in irreversible changes in the properties of the lamella at all stages.

In Fig. 4, the results of measurements at characteristic points for 40 consecutive cycles are shown. It is obvious that the measurements for M (maximum surface force) give a constant value. The averaging of these data gives a value of 37.0393 [+ or -] 0.0062. The standard deviation of the measured data is within hardware errors, which usually are about [+ or -]0.05. The consistency of these data measured for the plot of M means that the behavior of the water/detergent mixture is quite classical and the method of the wire ring is applicable to this system.

[FIGURE 4 OMITTED]

Results of measurements of lamella tension at characteristic points show a common tendency in reduction of lamella tension over time. For points B, the rate of decreasing lamella tension is -1.203 x [10.sup.-5] mN/m/s. It is impossible to explain this effect by hardware errors. We believe that this phenomenon is caused by the increased influence of surfactants over time because of the development of Gibbs layers. The development of the Gibbs layers result from an accumulation of surfactants on the liquid surface after the stirring of the liquid is stopped. During the course of experiments, the increasing concentration of surfactants on the liquid surface leads to formation of lamella with higher content of surfactant, which in turn decreases tension. This explains the observed behavior of decreasing lamella tension over time. Lamella are more sensitive to Gibbs layers than the surface tension of volumetric liquids. Therefore, it is possible to study Gibbs layers by studying the behavior of lamella.

In Table 1, correlation coefficients for measured lamella tension at different points in the cycles of measurements are shown. A high degree of correlation is obvious. This means that the disorder of the data seen in Fig. 4 is not due to errors in the measurements. By stopping the measurement cycle and drying the ring, it was found that this disorder originated from various weights of the liquid that stuck to the wire ring after the lamella broke.
Table 1: Correlation of lamella tension measured in different points of
cycles in water with detergent

Point               A    B      C      D      E

Correlation factor  1  0.856  0.858  0.838  0.994

The viscosity and elasticity of water were not measured because of
their low values


Measurements in waterborne visco-elastic paint

Similar measurements of lamella tension were carried out on samples of waterborne basecoat paint having visco-elastic properties using the same techniques as described for the water/detergent sample. The aqueous basecoat was supplied by PPG Industries with a proprietary composition typically used in the OEM auto industry as the colored paint layer. The measured results of alternating stretching and contraction deformation are shown in Fig. 5. Radical differences relative to the water/detergent measurements (Fig. 3) are visible. After stopping the deformation by stretching at point B, a decrease in lamella tension is observed for about 20 s. This is related to the slower stabilization of the meniscus during the stretching of the lamella because of the high viscosity of the liquid relative to the water/detergent mixtures. Also, at short times after stirring, irregular fluctuations of lamella tension were observed (caused by variations in the convection of liquid in the lamella). In fact, liquid flowing inside the lamella was observed visually. At short times after stirring, the contraction deformation of the lamella between points C and D does not cause changes in lamella tension. At increased time after stirring, the beginning of contraction deformation of the lamella causes a short-term decrease in tension. With even longer time after stirring, the total time of decreasing tension is increased and takes place during all stages of contraction deformation (see top curve in Fig. 5). However, the expected restoration of tension to that of point A does not occur. Reduction of lamella tension while contracting implies nonclassical behavior resembling the behavior of a more rigid body. This phenomenon increases with time after stirring. After stopping the contraction deformation, the relaxation of lamella tension increases, but never reaches the level of point A. The start of stretching deformation at point E causes first an increase of lamella tension and then a reduction. This phenomenon is related to a decreasing diameter of the circular meniscus as it connects the lamella to the liquid surface.

[FIGURE 5 OMITTED]

The lamella tensions measured in 24 consecutive experiments after stirring of the paint are shown in Fig. 6. The tendency of increasing lamella tension in the data is clearly visible. In the small graph within Fig. 6, the comparison of results for the points B and M is shown. It is obvious in the plot that the maximum force with which the paint resists the pulling of the ring from the liquid surface (M) grows much faster than the lamella tension. The fact that M shows increasing tension implies a nonclassical behavior of the visco-elastic paint sample and the nonapplicability of the wire ring method for the measurement of surface tension in its classical variant. The greater change of a maximum M in comparison with B shows that lamella tension is less sensitive to changes in real volumetric properties of the liquid than surface tension measured at point M. It follows that, for visco-elastic liquids, the application of the wire ring method in the measurement of lamella properties is more preferable than for the measurement of surface tension.

[FIGURE 6 OMITTED]

In Fig. 6, it can be seen that the lamella tension at all characteristic points grows with time and stabilizes within 2 h. In Table 2, the correlation coefficients of measured lamella tension at different points is shown. The high level of correlation means that the increasing lamella tension is the main process caused by relaxation of rheology and the development of Gibbs layers. The disorder of the results in separate experiments has a regular behavior caused by paint sticking to the ring during immersion, and then not completely draining from the ring.
Table 2: Correlation of lamella tension at different points of a cycle
of measurements in paint

      Point         B    C      D      E      F     C-D    F-E

Correlation factor  1  0.955  0.943  0.954  0.958  0.845  0.810


In Fig. 7, the dynamics of the increase and decrease of lamella tension are shown at deformation by contraction and stretching. It is visible that the effect of changing the direction of deformation on lamella tension qualitatively corresponds to a growth of lamella tension over time. In the last two columns of Table 2, the appropriate correlation factors are shown for changing direction of contraction and stretching deformation. The rather high level of correlation implies that the effects of deformation are caused by the same factors that cause an increase in lamella tension.

[FIGURE 7 OMITTED]

Comparisons of the observed effects of hysteresis of lamella tension by changing the direction of deformation with the change of viscosity and elasticity of the paint sample over time are also shown in Fig. 7. In Table 3, the values of the correlation factors for the curves in Fig. 7 are shown. The degree of correlation in Table 3 is very high. This is further evidence that a nonclassical behavior of lamella compared to the classical case where lamella tension depends on surface tension only. The lamella here display an elasticity caused by the bulk rheology of the visco-elastic paint.
Table 3: Mutual correlation data for curves shown in Fig. 7

Property     Viscosity  Elasticity  Contraction C-D  Stretching F-E

Correlation      1        0.991          0.989           0.991
factor


Comparison of the data for viscosity and elasticity with the effects of deformation of lamella allows for firm conclusions to be drawn. The bulk elasticity of the paint and the effects of deformation change immediately after stirring when the growth of viscosity over time (after stirring) docs not occur. This allows us to conclude that the growth of bulk viscosity is the reason for the growth of lamella tension, and that the growth of bulk elasticity is the reason for the occurrence of hysteresis in lamella tension.

Concluding remarks

In simple experiments with the use of the wire ring method, a number of phenomena inherent with lamella were shown:

(a) For water:surfactant mixtures, the common classical behavior of lamella is observed in which the wire ring method is applicable for measurement of both surface tension and lamella tension. The slow reduction of lamella tension caused by outflow of liquid from the lamella was observed. This results in one of the mechanisms for the destruction of a lamella (when the lamella tension becomes less than the surface tension of the free surface of the bulk liquid).

(b) The slow reduction of lamella tension from liquid at rest after stirring is connected to the accumulation of surfactants on the liquid surface and the development of Gibbs layers.

(c) Use of the wire ring method for measurements in thixotropic visco-elastic liquids, such as aqueous basecoat paints, has been shown to be nonapplicable in the classical sense. Rheological properties of the liquid and their dynamics after stirring considerably influence the force of resistance of the liquid on the ring's output on the free surface and do not allow for the correct measurement of the surface tension.

(d) Lamella generated by a thixotropic visco-elastic liquids show a relatively slow growth of tension with time after stirring, which is connected to the growth of bulk viscosity. These lamella shows a growth of elastic properties that is connected to the occurrence and growth of bulk elasticity after stirring. Thus, the wire ring method, for studying visco-elastic liquids is a more convenient tool for the study of lamella than for surface tension. Due to a relatively weak dependence of lamella tension on changing rheological properties, this parameter can be used as a surface characterization of visco-elastic liquids more effectively than surface tension.

The elasticity of lamella discovered in these experiments is fundamentally important in the study of the surface properties of visco-elastic liquids. The presence of lamella elasticity means that the air bubbles created from a strong lamella do not obey the Laplace law. The pressure inside such bubbles is determined not only by lamella tension, but also by its elasticity. The dynamics of bubbles in a visco-elastic liquid do not follow the normal dynamics of bubble creation/destruction. Normal behavior of diffusion/nucleation is not followed in these liquids. At increasing volume of bubbles, the pressure caused by resistance of the lamella to stretching is added to the Laplace pressure. At decreasing volume of bubbles, the pressure caused by resistance of the lamella to contraction is subtracted from the Laplace pressure. It is clear that these changes in pressure require a new approach to describe the various processes in two-phase systems in which one component is a visco-elastic liquid. In the solution of applied problems connected to the formation of lamella in visco-elastic liquids, it is recommended to combine the use of standard classical methods for measurement of surface properties and the use of the methods described in this paper to measure rheology. Through this new methodology, a new understanding for the release of air bubbles from aqueous paints has been gained.

Acknowledgments The purpose of the described research has been formulated with the participation of experts within PPG Industries Inc. The work was supported by a grant from PPG Industries.

References

(1.) Bakker, G, Handbuch der Experimentalphysik, Vol. 6, p. 315. Akadevmische Verlags-Gesellschaft, Leipzig (1928)

(2.) Euteneuer, GA, "Einflu[Beta] der Oberflachenspannung auf die Ausbildung von Flussigkeits-Hohlstrahlen." Forschung auf dam Gebiet des Ingenieurwesens, 22 109-122 (1956). doi:10.1007/BF02592597

(3.) Deryagin, BV, Churaev, NV, Muller, VM, Surface Forces, p. 398. Nauka, Moscow (1985)

(4.) Rusanov, AI, Gudrich, FCh (eds.), Sovremennaya teoriya ka- pillyarnosti (Modern Theory of Capillarity). Khimiya, Leningrad (1980)

(5.) Adamson, AW, Gast, AP, Physical Chemistry of Surfaces, p. 757. Wiley, New York (1997)

(6.) Oseen, CW, Hydrodynamik, 337 pp. Akad. Verlag. Leipzig (1927)

A. Bochkarev (*), V. Polyakova

Kutateladze Institute of Thermophysics, Prospect Akademika Lavrentieva, 1, Novosibirsk 630090, Russia

e-mail: aboch@online.nsk.su

M. Hartman, K. Olson

PPG Industries, Inc., Allison Park, PA 15101, USA

K. Oslon

e-mail: kgolson@ppg.com

J. Coat. Technol. Res., 7 (3) 347-353, 2010

DOI 10.1007/s11998-009-9193-1
COPYRIGHT 2010 American Coatings Association, Inc.
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Author:Bochkarev, A.; Hartman, M.; Olson, K.; Polyakova, V.
Publication:JCT Research
Date:May 1, 2010
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