ARTICLE pubs.acs.org/IECR
A Novel Centrifugal Method for Wettability Characterization of Granulates Paul D. Swenson,† Geza Horvath-Szabo,*,† Wael Abdallah,‡ and Dmitry Eskin† † ‡
DBR Technology Centre, Schlumberger, 9450-17 Avenue, Edmonton, Alberta, T6N 1M9, Canada Schlumberger Dhahran Carbonate Research Center, Dhahran, Kingdom of Saudi Arabia ABSTRACT: The minimum force needed for transporting glass microspheres across oil/water (O/W) interfaces was determined experimentally. From this data, the O/W contact angle was calculated with a mathematical model. First, the measured minimum centrifugal force was combined with a simplified model leading to an approximate contact angle. Then the results were refined by a numerical solution of the accurate mathematical model of particle transport through an oil/water interface. The contact angles calculated by the suggested approach were compared with the contact angles measured by goniometry on flat glass surfaces in the presence and absence of sodium dodecyl sulfate (SDS), Triton X-100, and Igepal CO-520 surfactants. The discrepancies were interpreted with the different surface chemistries/morphologies of glass microspheres and slides. The results show potential for this being a rapid screening method for chemical additives aimed at altering the wettability. This approach could be utilized in the oil and gas industry and especially to support enhanced oil recovery (EOR).
’ INTRODUCTION Currently, approximately one-third of the original oil in place (OOIP) is recovered from oil reservoirs by primary and secondary recovery techniques; i.e., two-thirds of the OOIP is left behind.1 For this reason, previously abandoned reservoirs are being used to investigate the potential of enhanced oil recovery (EOR) methods, such as CO2 and water flooding. The efficiency of water flooding can be enhanced with chemical additives.25 When the contact angle of an oil/water (O/W) system on a rock surface approaches 180°, the surface is considered to be oilwet and only a small fraction of oil is recoverable with water flooding in the absence of additives. When the contact angle of an oil/water system on a surface approaches 0°, the rock is waterwet and the oil recovery is much higher with water flooding. In naturally fractured reservoirs, such as carbonates, the rock wettability tends to be mixed and the rock surface is oil-wet.6 In such reservoirs water flooding by itself has poor displacement efficiency, especially when the interfacial tension between water and oil phases is high, because this contributes to the capillary retention of the discontinuous oil and thereby prevents its displacement. Therefore, chemical additives such as surfactants, which are simultaneously interfacial tension (IFT) reducers and wetting agents, are used in practice.713 These compounds reduce O/W IFT and shift the wetting characteristic of the rock toward the water-wet state. When the wettability of the reservoir rock is changed from an oil-wet to a more water-wet state, the water imbibition into pores is supported by the capillary pressure and the oil recovery is improved. One of the most significant research areas in the oil industry, which involves surfactants, is finding adequate screening methodology for assessing additives for EOR.1418 This may include testing the effect of additives on both the O/W IFT and wettability alterations. While the first is straightforward, the second could be challenging. Therefore, in this work we are focusing on the wettability alteration tests. Even though the r 2011 American Chemical Society
definition of the wettability is based on contact angles and easily interpretable visual schematics, it is impractical to establish methodologies on visual contact angle measurements in the oil industry because there are some inherent problems with the optical goniometry when it is applied to crude oils and real rock surfaces.1921 First of all, optical contact angle measurement is not attractive because one of the liquid phases needs to be optically clear. Also, a geometrically smooth, nonporous, and energetically homogeneous macroscopic surface of the rock phase is needed—a condition which is virtually impossible to satisfy. Therefore, the optical contact angle measurements should be replaced with an alternative approach. One such approach was recommended by Wu et al.,1 who presented a simple flotation test using calcite crystals treated with model naphthenic acid compounds to find the relative effectiveness of various surfactants. Gomari et al.17 characterized the wettability of acid-modified calcite via water adsorption isotherms and thermogravimetric analysis. All three methods provided results consistent with the contact angle experiments. Unfortunately, these methods provide relative and qualitative results only. Hence, a rapid screening method is developed to provide quantitative results indicating surfactant effectiveness. In this paper, we propose a method of contact angle determination, based on balancing the external mass (the centrifugal or gravitational force in our case) and the capillary forces acting on a solid particle crossing the oil/water interface. A minimum centrifugal force, which is needed for particle transport through the interface, can be found experimentally. This information allows us to calculate the contact angle, if the interfacial tension and densities of the particle, oil, and water are known. It is Received: October 12, 2010 Accepted: February 24, 2011 Revised: February 15, 2011 Published: March 22, 2011 5565
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force F∑ equals 0 and the particle is at rest at the interface. If F∑ is greater than 0, the particle moves into the water phase. It is important to emphasize that the sought particle equilibrium at the interface under action of the constant external force can be realized only if the minimum summary force is zero (min F∑ = 0). It is clear that a change in sign of the function F∑, caused by the particle displacement, indicates that the particle cannot cross the interface. The weight, W, of the particle is calculated as follows: W ¼ G ðFS FW ÞVabc þ ðFS FO ÞVadc ðFW FO Þh2 ac ð2Þ Figure 1. Schematics for modeling the transport of a spherical particle across an oil/water interface.
important to mention the paper of Nutt,23 who performed quantitative centrifugal experiments and modeled the transport of a particle across an airwater interface. In subsequent experiments, ethanol was added to the water phase to broaden the range of contact angles studied. For this investigation, the contact angle was measured by sessile drop goniometry and used to predict analytically the minimum centrifugal acceleration needed to transport the particle across the interface. The minimum centrifugal acceleration was found experimentally, and it was compared with the calculated results. In some cases, the disagreements were significant. Nutt’s model contained two key assumptions: (1) the air density is zero; (2) one of the radii of the air/water interface curvature, r2, is much greater than the other, r1. The first assumption restricts the applicability of Nutt’s model. It will also be seen from our modeling results, presented below, that the r2 . r1 assumption becomes less valid as the contact angle becomes higher than 90°. By employing a model similar to that employed by Nutt23 but free of the restrictions, we should be able to calculate the contact angle if the minimum centrifugal acceleration is determined experimentally. Ultimately, this would result in a rapid, quantitative method for evaluation of the contact angle without the inherent drawbacks of sessile drop goniometry.
’ CALCULATION OF THE CONTACT ANGLE BASED ON A MODEL OF A SOLID SPHERE TRANSPORT THROUGH OILWATER INTERFACE Modeling the transport of a spherical particle across a liquid/ liquid interface has been conducted by different investigators.2226 Here we present a robust method for calculating the contact angle based on the experimentally achieved force balance between the centrifugal, the buoyancy, and the capillary forces acting on a particle crossing the oil/water interface. The calculation diagram is presented in Figure 1. The contact angle, θ, is represented through the denser phase. Within our analysis, we neglect both the particle inertia and the viscous drag force because we consider a small particle that very slowly (see the description of the experiment below) crosses the interface. The summary force acting on the particle is F∑ ¼ W I
ð1Þ
where G is the centrifugal acceleration; h2 is the meniscus height; V is the volume of a particle section defined by the subscripts; FO, FW, and FS are the oil, the water, and the solids densities, respectively; ac defines the cross-sectional area of the particle at the ac level (see Figure 1). The first two terms on the right-hand side of eq 2 correspond to the portions of the particle immersed in water and oil, respectively. The third term accounts for the reduction in the apparent particle weight due to the additional buoyancy force caused by the additional hydrostatic pressure of the meniscus of thickness h2 (see, e.g., ref 25). The interfacial force at the oil/ water/solids interface, I, that balances the particle weight is calculated as I ¼ 2πRγOW sinðΦÞ sinðΦ RÞ
ð3Þ
where R = π θ is the supplement of the contact angle, γOW is the oil/water interfacial tension, and j is the angle determining the location of the oil/water/solids interface circumference. After substituting eqs 2 and 3 into eq 1 and performing routine math, we obtain F∑ ¼
" ! 4 2 cos3 Φ πGR 3 ðFS FO Þ GðFW FO Þ πR 3 cos Φ þ 3 3 3
þ πR 2 h2 sin2 Φ 2πRγOW sinðΦÞ sinðΦ RÞ
ð4Þ
The meniscus thickness h2 is calculated based on the Laplace equation that establishes a link between the shape of the oil/ water interface in the vicinity of the microsphere and the pressure increment through the curved interface: 1 1 þ pC ¼ γOW ð5Þ r1 r2 where pC is the capillary pressure; r1 and r2 are and the finite radii of curvatures. The radius r1 is in the plane of the figure, while r2 is orthogonal to this plane. In a Cartesian coordinate system (the zero is at point c; see Figure 1), eq 5 takes the form ! y00 y0 ðFW FO Þðh2 yÞG ¼ γOW þ ðy0 2 þ 1Þ3=2 xðy0 2 þ 1Þ1=2 ð6Þ The boundary conditions for this equation are y ¼ 0,
where I is the balancing surface force acting around the particle perimeter and W is the weight of the sphere in the centrifugal force field. Under the force equilibrium condition the summary
y ¼ h2 , 5566
y0 ¼ tgðΦ RÞ
ð7Þ
y0 ¼ 0
ð8Þ
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It is possible to solve the Laplace equation analytically if r2 . r1 (Nutt’s assumption23). Then the term associated with the radius r2 in eq 6 can be neglected and the equation takes the simplified form y00 ðy0 2 þ 1Þ3=2
¼ ξðh2 yÞ
ð9Þ
where ξ¼
ðFW FO ÞG γOW
The analytical solution of eq 9, describing the shape of the oil/ water interface near the microsphere, is trivial and is therefore not
Figure 2. Summary force acting on the particle versus the angle determining the location of the three phase circumference of oilwatersolid. Illustrative example with a specific set of densities, interfacial tension, gravitational acceleration, and particle radius data.
presented here. From that solution, we straightforwardly obtain the formula for calculating the meniscus thickness as rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ð1 cosðΦ RÞÞ ð10Þ h2 ¼ ξ Equation 4, while accounting for eq 10, allows for calculating the contact angle θ if the interfacial tension, γOW, the phase densities FO, FW, and FS, and the experimentally determined minimum relative centrifugal acceleration, G, needed to transport the particle across the interface are known. The contact angle calculated with eq 10 is denoted as θApprox. The analytical model provides a good first guess for a numerical solution of the accurate set of eqs 4 and 6, which are solved by iterations, although in some cases r2 . r1 is not a good assumption. Figure 2 illustrates the modeling approach developed. The two curves show the dependence of the summary force F∑ on the particle displacement expressed in terms of the angle Φ determining the location of the oil/water/solids interface circumference. The first curve (dashed line) was obtained as follows. The approximate formula for calculation of the meniscus thickness h2 (eq 10) was substituted into the equation for F∑ (eq 4). Then the equation of particle equilibrium at the interface, F∑ = 0, was solved to obtain the first approximation of the contact angle. The calculations were conducted numerically by iterations over the contact angle, θ. Then the obtained approximation of the contact angle, θApprox, was substituted into the accurate Laplace equation (eq 6), and the meniscus thickness h2(Φ) corresponding to θApprox was computed. After that, the function F∑ (Φ) was calculated by eq 4. This function is shown in Figure 2 by the dashed line. As one can see, the minimum force equilibrium condition, F∑ = 0, was not fulfilled at the approximate value of the contact angle θ = θApprox. Thus, the approximate solution θApprox was not accurate and had to be corrected. The accurate value of θ was obtained numerically by solving the following set of equations: F∑ = 0 (see eq 4) and eq 6. These equations were also solved by iterations over the wetting angle θ. Obviously, eq 6 was
Table 1. Summary of the Properties of Surfactants Investigated3234
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Table 2. Comparing Chemical Compositions of Whitehouse Scientific Microspheres with Corning Glass Slides
SiO2 Na2O
Whitehouse Scientific
Corning glass
microspheres (wt %)
slides (wt %)
74 11.9
73 14
CaO
8.15
MgO
4.13
7 4
Al2O3
0.98
2
other
0.84
numerically integrated at each iteration. The accurate solution is represented in Figure 2 by the solid line. Note that a few iterations are usually sufficient to get the (corrected) accurate solution, θCorr, because the first guess value θApprox is rather good. Nevertheless, we would like to emphasize that, in the considered illustrative example, the accurate contact angle, θCorr, was noticeably larger than its first guess. (Compare θCorr = 149.5° with θApprox = 134°.) Thus, as one can see, the contact angle correction is really important.
’ METHODS AND MATERIALS Glass microspheres with particle diameters of 4553, 150180, 250300, 450500, 8501000, 18002000, and 28003200 μm were provided by Whitehouse Scientific. Glass slides of similar composition to the composition of the microspheres were supplied by Corning Glassware. Light mineral oil and Triton X-100 were provided by Sigma-Aldrich. Igepal CO520 and chlorodimethyloctylsilane (97%) were provided by Aldrich. Ultrapure sodium dodecyl sulfate (SDS) was provided by MP Biomedical. Surfactant information can be reviewed in Table 1. A thermally controlled Sigma Laboratory Centrifuge 3K03H installed with a four-bucket swing-out rotor was used for the centrifuge separation experiments, which were performed at 25 ( 1 °C. Each of the buckets houses three centrifuge tubes. The deionized water was obtained from an EASYpure RoDi model D13321 (Barnstead International) which uses reverse osmosis, ion exchange, and UV treatment to produce high-purity water with resistivity ASTM Type I and TOC 15 ppb. It is important that the glass microspheres and glass slides have a very similar chemical composition so that they exhibit comparable properties. Microspheres and slides of identical compositions would be optimal, but such products were not obtainable. Since soda lime is a relatively common blend of glass, finding microspheres and slides of similar compositions was not difficult. A comparison of the microsphere and slide compositions can be found in Table 2. Both the microspheres and slides are hydrophilic as received. Before the microspheres will rest on the oilwater interface, they first must be rendered hydrophobic.2730 Since the slides must exhibit identical surface chemistry, they were also hydrophobized in the same manner as the microspheres. Before hydrophobic treatment, all the glass was sonicated first in deionized water, then in a 50/50 mixture of deionized water and 2-propanol, and again in deionized water each for 20 min. Before each sonication step, the samples were rinsed three times with the liquid it was to be sonicated in next. Then, to clear the glass of all surface contaminants, it was immersed in a 50/50 solution of H2O2 (35%) and NH3OH (5 N) at ∼70 °C for 1 h. Then samples were
Figure 3. Schematics for the centrifugation experiment.
again sonicated in deionized water, a 50/50 mixture of deionized water and 2-propanol, and again in deionized water for 10 min; they were then dried completely in a vacuum desiccator. Once dried, samples were left for 24 h in a 4 wt % solution of chloro(dimethyl)octylsilane solution in heptane, in a sealed glass container. After silanization, samples were sonicated in heptanes, deionized water, and 2-propanol for 10 min before finally being rinsed in HPLC-grade acetone (Sigma-Aldrich) and dried completely in a vacuum desiccator. Postexperiment slides and microspheres were qualitatively tested for hydrophobicity. If the microspheres floated rather than sank in deionized water, the surface was considered hydrophobic. Similarly, when a drop of deionized water formed a characteristic round droplet on the treated slide surface, the slide was considered hydrophobic. Gravity separation experiments were done before centrifugal separation experiments to find out approximately which microsphere diameter would penetrate the oilwater interface with only gravity acting on it. Gravity separation experiments were done with added surfactants as well. First, the water phase, containing the surfactant, was added to the test tube. Then, while the test tube was angled, the oil phase was slowly added, creating a clean oilwater interface. Only a single microsphere was studied in each experiment, so the shape of the meniscus was distorted by the presence of a single particle in agreement with the mathematical model. The microsphere was handled with tweezers that had been presoaked in the oil phase. With the tweezers initially wet with the oil phase the microspheres could be transferred individually from a watch glass to the test tube without having to close the tweezers on the microsphere, so the possible source of scratching was eliminated. The microspheres were released from the tweezers just above the interface so that the effect from the acceleration due to gravity was minimized. All experiments were allowed a minimum 60 min to equilibrate, and then the results were recorded. Centrifugal experiments also used a single microsphere and the same arrangement as in the case of the gravity separation experiments, but this time, as long as the microsphere had not crossed the interface, the test tube was centrifuged. A schematic of the arrangement is presented in Figure 3. The tubes were placed into the buckets of a swing-out rotor of the centrifuge. The buckets were closed with a screw cap to prevent evaporation. The mineral oil was situated on the top of the vapor water phase, so evaporation of water was hindered. The vapor pressure of the 5568
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mineral oil was very low to comply with the safety regulations of the centrifuge. Consequently, a temperature gradient could not be developed at interfaces due to evaporation. The test tubes would be centrifuged for 5 min at a set G-value, and then each tube would be visually checked to see if the microsphere had penetrated the interface. Then the G-value would be slightly increased and centrifuged again for 5 min. This was repeated until all the microspheres penetrated the water phase. The slowest acceleration and deceleration of the centrifuge were used to eliminate overshoot and increase accuracy. The purpose of these experiments is ultimately to find the minimum external force needed to transfer the microsphere from the oil phase to the water phase. All the IFT and contact angle measurements were performed at ambient temperature of 25 ( 2 °C. Interfacial tension measurements between the oil and water or aqueous surfactant solutions were carried out using the inverted pendant drop technique. Before formation of the drop, the cell was fully filled with the aqueous phase, leaving about 1 cm3 of vapor/gas phase on top of the liquid. The syringe was inserted through a specially designed neck, which prevented the escape of vapor from the chamber. Hence, the possibility of evaporation was minimized. With a screw-type syringe, a drop of oil was made at the tip of the capillary in the aqueous phase. The drop was formed about 2 cm below the meniscus of the water. The drop was illuminated with a light source, and its image was captured with a CCD camera. The contact angle measurements were performed with the same setup as was used for the IFT studies. An aqueous drop was first formed in the oil phase at the end of the syringe, and then it was deposited on the flat surface with the syringe. After this, the observation of the drop started. Contact angle equilibrium was usually established within 10 min. Longer equilibration time did not change the results. The schematic of the arrangement is presented in Figure 4. Image-capturing software developed by TECLIS (http://www.teclis.eu/) analyzed the shape of the drops and provided either the IFT of the pendant drop or the contact angle of a sessile drop on a glass slide.
Figure 4. Schematics for contact angle measurement.
’ RESULTS AND DISCUSSION A sensitivity analysis of the mathematical solution is provided in Figure 5. Sensitivity analysis are usually based on the investigation of the analytical formula. We performed a simplified
Figure 5. Simplified sensitivity analysis of the numerical solution. One variable was varied by (10% while all the other variables were held constant. The central parameter values around which the sensitivity was tested are reported in the table on the right. 5569
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sensitivity analysis because, in our case, a numerical solution provides the final value of θCorr. On the right-hand side of Figure 5, a table contains the set of parameters around which one of the parameters was varied. Each variable was changed by (10% and the change in the calculated contact angle was monitored, while all other variables were held constant. For particle radius and the densities of the solid, water, and oil the values provided by the manufacturer or the literature were used. If a range was provided, then an average was used (i.e., 450500 μm was provided by Whitehouse Scientific but 475 μm was used for the sensitivity analysis). It can be seen that a 10% increase in a certain variable does not lead to an equal change of the contact angle as a 10% decrease in the same variable. For variables such as water density, oil density, and interfacial tension, this nonlinearity is more prominent. Since some variables have large effects on the results, their accuracies needed to be increased in the cases where manufacturers have not provided sufficiently accurate values. Therefore, we experimentally tested the actual values of parameters used for our experiments. Table 3. Interfacial Tensions and Their Standard Deviations between Mineral Oil and Water with Added Surfactantsa interfacial tension heavy phase water
light phase
(mN/m)
number of runs
air
73.07 ( 0.26
12
Surfactants were all tested at their critical micelle concentrations (cmc's), so their IFTs were also measured at their cmc values in water. The obtained IFT values are reported in Table 3. The cmc values were collected from the open literature, and they are reported in Table 1. It is stated in the literature that the interfacial tension between water and air at 25 °C is 71.98 mN/ m.31 The measured value for the IFT between water and air was 73.07 ( 0.26 mN/m. Since the measured IFT is close to the literature value, the goniometry setup used is accurate. The interfacial tensions reported in Table 3 are time independent because all runs were given enough equilibration time, so a constant IFT was achieved. The interfacial tension versus time functions can be seen in Figure 6. All IFT values flattened to a constant IFT over time, and this was the value we used for all subsequent calculations. For the centrifugal separation experiments, the particle radii were measured with a micrometer and the densities of all three phases were also measured. In addition, the accuracy of the centrifuge was verified by using a stroboscope. There was a slight amount of overshoot in the acceleration of the centrifuge but not enough to change the results noticeably. It should be noted as well that the values for particle radii and densities provided by the manufacturer were very close to the measured values. Table 4. Comparison between Published and Measured Property Values of Model Materials
water
mineral oil
51.04 ( 0.32
22
SDS
mineral oil
9.89 ( 0.09
14
Igepal CO-520
mineral oil
8.90 ( 0.17
13
oil density
0.838 g/mL at 25 °C
mineral oil
9.32 ( 0.15
13
water density
0.997 g/mL at 25 °C
0.997 g/mL at 24 °C
solid density
2.4302.490 g/cm3
2.474 g/cm3
particle diameter
450500 μm
472.30 ( 0.13 μm
Triton X-100
manufacturer or literature
a
The concentrations of the surfactants were at their critical micelle concentrations (cmc's).
measured 0.847 at 23 °C
Figure 6. Time dependent interfacial tension between mineral oil and water containing various surfactants at their cmc's (top left, no surfactant; top right, SDS; bottom left, Igepal CO-520; bottom right, Triton X-100). The cmc's are reported in Table 1. 5570
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Table 5. Contact Angles of Aqueous Phase in Oil and Their Standard Deviations Obtained with Centrifugation Method on Glass Microspheres relative acceleration
interfacial tension (mN/m)
θApprox (deg)
θCorr (deg)
no surfactant
66.23 ( 1.11
51.04 ( 0.32
104.46 ( 1.25
110.50 ( 0.98
number of repeated experiments SDS
3 16.24 ( 2.43
22 9.89 ( 0.09
3 122.77 ( 15.45
3 133.33 ( 21.55
surfactant (concn = cmc)
number of repeated experiments Igepal CO-520 number of repeated experiments Triton X-100 number of repeated experiments
3
14
3
3
8.84 ( 0.56
8.9 ( 0.17
89.02 ( 3.67
92.33 ( 4.25
3
13
3
3
10.93 ( 1.21
9.32 ( 0.15
98.15 ( 7.46
102.50 ( 8.54
3
13
3
3
A comparison can be seen in Table 4. For all variables, the measured value is very close to the value provided by the manufacturer or found in the literature. The results from the centrifugal separation experiments are shown in Table 5. Each experiment monitors the transport of a single, spherical, hydrophobic glass particle across the wateroil interface. All surfactants were tested at their cmc's. The relative acceleration (normalized by dividing with the normal gravitational acceleration) reported in Table 5 is the minimum relative centrifugal acceleration required to transport the particle across the interface. The analytically calculated contact angles, θApprox, were corrected by the numerical solution, resulting in θCorr to increase the accuracy as described earlier. Interestingly, the repeatabilities of the contact angles in the presence of surfactants are worse than the repeatability in the absence of surfactants. To understand this finding, we should consider that although some adsorption of oil or water might be expected on the interfaces in the absence of surfactants, assuming some limited mutual solubility of the oil and water phases, this process is quick compared to the adsorption of surfactant molecules from a micellar solution. This is because the exchange of surfactant molecules between micellar and unimer states takes time. The rearrangement and film formation of the unimers on the O/W and solid/liquid surfaces takes time as well. In other words, the contact angle, which can be obtained from the centrifugation experiment, will be time dependent in the presence of surfactants. This possibility was not realized prior to the centrifugal experiments; therefore, the time used for inspecting the tubes after each centrifugation step was not standardized. However, on the basis of the obtained results it has become clear that the precise methodology of the centrifugation should be standardized if one wants to use this approach for wettability characterization of surfactant-containing systems. Because keeping track of time could be demanding in some cases, an alternative approach, which would not suffer from this time dependency issue, is recommended below for testing the wetting alteration efficiency of surfactants with this centrifugation methodology. The step-by-step increase of the rotation speed of the centrifuge combined with the repeated visual inspection of the tubes is time-consuming because we might not see particles crossing the interface in a high number of experiments. This step-by-step approach was only introduced to assess the theory. To use the developed methodology more economically and for screening the effect of water-soluble additives on the contact angle and wettability, two altered procedures are recommended as follows. (i) Aqueous solutions of an additive with concentrations increasing in a wide range are injected into a set of centrifuge tubes. The oil phase containing the particle is layered on the top
of the aqueous phases. Because the wettability usually changes monotonically with a change in the additive concentration, a continuous additive concentration range, in which particles are able to cross the O/W interface, is established. Similarly, the additive concentrations at which the particles could not cross the interface define a different continuous concentration range. The border concentration between these two ranges can be plotted together with the contact angle calculated from the centrifugal speed. Then the whole centrifugation experiment with a new set of solutions can be repeated at a higher speed and the inspection, calculation, and plotting are repeated. As a result of this procedure, the contact angle can be obtained as a function of the additive concentration. (ii) The effectives of different additives on the contact angle can simply be compared by comparing the minimum concentrations of the additives at which particle crossing was observed at a well-selected single rotation speed. Alternatively, the additive effectiveness can be compared in sedimentation experiments performed in a gravitational field. In this case the minimum surfactant concentration needed for particle crossing is determined for a set of selected particle sizes. The validation of the contact angle measured on a small size object is far from easy, but it is in the center of interest as the focus of research is shifting toward small size systems. What follows below is the discussion of one major theoretical and two experimental issues, which hinder the validation. As for the theoretical issue, there is a debate about the existence and correct numerical value of the line tension, which has been causing controversy about contact angle measurements with small liquid droplets, or contact angles measured on small particles. If line tension31 exists, then the contact angles measured on flat surfaces are dependent on the size of the liquid drop. In addition, the contact angles measured on small spherical objects will be different from the contact angles measured on flat surfaces. This difference will be dependent on both the numerical value of the line tension and the curvature of the three-phase contact line. Unfortunately, it is difficult to estimate an impact of the line tension on the contact angle in real cases because of missing and controversial data. Additionally, there is an emerging theory based on the Gibbsian thermodynamics of interfaces and a novel adsorption isotherm. This theory can also be used for explanation of the observations, which have so far been interpreted by the existence of line tension.3234 Hence, out of purely theoretical considerations, we cannot expect to obtain the same contact angle on flat surfaces and spherical objects, although this difference is only significant when the curvature of the three-phase contact line is high. The first experimental issue, which causes problems most frequently, is the difference in microroughnesses 5571
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of surfaces manufactured by different processes. The difference between the manufacturing of flat surfaces and the manufacturing of small spherical spheres made of glass results in different surface roughnesses leading to different contact angles. The second experimental issue we need to mention is the differences of the chemical compositions of the glasses available on the market. We were not able to find a manufacturer who would provide spherical glass particles and flat surfaces manufactured from the same glass. In addition, identical bulk compositions would not necessarily result in identical surface compositions. Furthermore, the authors of this work are not aware of any Table 6. Variation of Contact Angle with Exposure Time to Hydrophobization Solution for Glass Spheres (θSphere) and Glass Slides (θPlain) under Identical Treatment Conditionsa exposure time
θSphere (deg)
θPlain (deg)
30 s
64.67 ( 4.81
142.45 ( 3.57
60 s
81.00 ( 3.44
2 min 5 min
79.50 ( 17.23 69.58 ( 13.06
10 min
83.67 ( 10.19
30 min
104.00 ( 13.61
113.19 ( 15.55 137.00 ( 3.35
Standard deviations are also presented. θSphere was measured with centrifugation, while θPlain was measured with goniometry. a
publication which would provide systematic analysis between the composition of the glass surface and the efficiency of silanization. Therefore, it is generally not possible to compensate the surface composition differences of glasses with different silanization methodologies. Consequently, summarizing all the above discussed in this paragraph, we should not expect similar contact angles measured on small spherical glass beads and flat glass sheets. Nearly the same contact angles can only be expected on specially manufactured glass model surfaces provided that the effect of the line tension is negligible. Although one cannot expect the same contact angles on flat and spherical glass surfaces, it is worth to have a comparison by using microspheres and slides of the same degrees of silanization. Therefore an additional set of centrifugal experiments was initiated, in which we did not use surfactants. Instead we varied the hydrophobization by changing the time that the slides and microspheres spent in the chloro(dimethyl)octylsilane solution (actually, they were treated in the same beaker at the same time to ensure identical treatment) to obtain a range of contact angles to be investigated. The exposure time was varied from 30 s to 48 h. Other than the exposure time to the hydrophobization solution, the preparation and cleaning steps were kept identical. The contact angles measured by the centrifugal method, θSphere, are compared to those measured by goniometry on the flat surfaces, θPlain, in Table 6. The contact angles reported are time independent because all runs were given enough equilibration
Figure 7. Time dependency of aqueous contact angles in mineral oil measured on Corning glass slides. The aqueous phase contained various surfactants at their cmc's (top left, no surfactant; top right, SDS; bottom left, Igepal CO-520; bottom right, Triton X-100). 5572
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Table 7. Comparison of Contact Angles Measured by Centrifugation (θCorr) on Glass Spheres and by Goniometry (θPlain) on Glass Slides in the Absence and Presence of Various Surfactantsa θCorr (deg)
θPlain (deg)
110.50 ( 0.98
131.31 ( 3.71
surfactant (concn = cmc) no surfactant number of repeated experiments SDS number of repeated experiments Igepal CO-520 number of repeated experiments Triton X-100 number of repeated experiments
3
11
133.33 ( 21.55
139.02 ( 4.09
3
8
92.33 ( 4.25
141.5 ( 1.68
3
6
102.50 ( 8.54 3
113.31 ( 3.86 7
a
The compared spherical and plain surfaces went through identical hydrophobizing treatments. Standard deviations are also presented.
to grant particle crossing through the O/W interface is determined based on simultaneous centrifugation of a number of test tubes with increasing additive concentration. Then the border concentration, separating the ranges of successful and unsuccessful particle interface crossings, is determined. These methodologies are based on an improved mathematical method, which solves precisely the bulk and interfacial forces acting on a particle crossing either the gas/liquid or the liquid/liquid interface. It was concluded that the difference in contact angles measured on spherical glass particles and glass sheets of similar bulk chemical composition is statistically significant in the absence of surfactants. This difference can still be observable in the presence of surfactants in spite of the fact that in the latter systems the repeatability of the contact angles is worse.
’ AUTHOR INFORMATION Corresponding Author
time that a constant IFT was achieved. The contact angles over time can be seen in Figure 7. All contact angles flattened to a constant value over time, and this is the value that was used for comparison with the calculated contact angle. Only a few θPlain were measured, i.e., those corresponding to the 30, 60, and 300 s treatment times, because the disagreement between θSphere and θPlain was disappointingly large. No attempt was made to investigate the effect of the line tension, i.e., the curvature of the three-phase contact line, on the observed contact angle. It is clear from the data that the differences between the flat and special surfaces are statistically significant. It was known from the beginning of the study that the glass microspheres and the glass slides were not of identical composition (cf. Table 2), but were simply of similar composition because of the commonness of the soda-lime blend of glass. The amounts of impurities, such as K2O, SO3, and B2O3, are not provided by Corning even though they are most likely present. However, we must recognize that even in the case of perfectly matching bulk chemistries the interfacial compositions of the slides and microspheres could be different. Moreover, the surface morphologies can also be quite different. These differences originate from the different manufacturing processes of slides and spheres. Hence, we could not use the contact angles measured on slides to verify the contact angles measured on microspheres in the absence of surfactants. We also interrogated this large contact angle difference in the presence of surfactants. Surfactants could form an adsorption layer on glass surfaces and cloak slight surface chemical differences. As is visible from Table 7, the difference between the contact angles measured on flat and spherical surfaces is still observable.
’ CONCLUSIONS A centrifugal approach was developed as a rapid, parallel screening method for chemical additives. Simplified screenings can also be performed in a gravitational field. The minimum centrifugal force necessary to transport the oil-wet particle through the O/W interface can be captured by the successive rotation speed increase and visual observation steps. The contact angle can be calculated from this minimum centrifugal force. Quick screening procedures to compare the efficiencies of additives on wetting were also recommended. In these latter tests, the minimum/maximum additive concentration necessary
*E-mail:
[email protected].
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