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Drop size dependence of contact angles of oil drops on a solid surface in water
Colloids and Surfaces A: Physicochemical and Engineering Aspects 181 (2001) 215– 224 www.elsevier.nl/locate/colsurfa
Drop size dependence of contact angles of oil drops on a solid surface in water Yongan Gu * Faculty of Engineering, Uni6ersity of Regina, Regina, Sask., Canada S4S 0A2 Received 31 May 2000; accepted 26 October 2000
Abstract Contact angle is a fundamental quantity in colloid and surface science. Of all the methods employed to measure the contact angles, direct measurement from sessile drops is probably the most popular approach. However, it has long been found that the measured contact angle is not unique for a given solid– liquid– fluid system. There are two types of contact angle multiple-value phenomena — the drop size dependence of contact angles and the contact angle hysteresis. In the literature, the contact angle dependence on the liquid drop size for the solid– liquid– vapour systems has been studied extensively. In this paper, the contact angle dependence on the oil drop size for a solid– oil– water system is measured by applying the axisymmetric drop shape analysis (ADSA) technique. More specifically, a natural sedimentation method is employed to deposit drops of a silicone oil with a density slightly higher than that of water onto the hydrophobic FC725 coated glass slide in the deionized ultra filtered (DIUF) water. It has been observed that the measured equilibrium contact angle decreases by approximately 7.3° as the equilibrium base radius of the silicone oil drop increases from 0.0205 to 0.4684 cm. According to the modified Young equation, the measured contact angle changes are then interpreted in terms of the so-called line tension effect. The line tension of the solid– oil– water system is found to be 0.82 mJ m − 1, which is very close to those for similar solid– oil– air systems. Unlike other conventional drop formation methods, the natural sedimentation method used in this study can eliminate all the appreciable mechanical disturbance and vibrations. Furthermore, this deposition can generate liquid drops in a much larger range of drop size such that the line tension effect becomes much more pronounced. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Contact angle; Sessile drop method, line tension; Solid– oil– water systems; Modified Young equations; ADSA technique
1. Introduction Accurate contact angle measurement of an oil drop on a solid surface in an aqueous phase is of * Tel.: +1-306-5854630; fax: + 1-306-5854855. E-mail address: [email protected] (Y. Gu).
interest in colloid science and interfacial phenomena. The wettability of the solid –oil –water system also plays an important role in a number of environmental, biological and industrial processes. There have been several techniques available for this purpose and some detailed descriptions of these methods can be found in the
0927-7757/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 ( 0 0 ) 0 0 8 0 4 - 9
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literature [1 – 5]. Of all the existing experimental methods, the sessile drop method is probably the most widely used contact angle measurement technique. In the sessile drop method, the contact angle is determined directly by aligning a tangent with the drop profile at the point of the solid –liquid –fluid three-phase contact circle on the solid surface. In addition to its simplicity, this method requires only small quantities of liquid sample and solid surface. However, usually an accuracy of 92° is claimed for the simple sessile drop method using a telescope equipped with a goniometer eyepiece. Alignment of the tangent is dependent on the operator’s skill and hence subjective. In recent years, Neumann and co-workers have developed a sophisticated sessile drop method, the axisymmetric drop shape analysis (ADSA) technique [6 – 8]. The ADSA technique can measure both the contact angles and the surface/interfacial tensions. The accuracy of the ADSA technique is approximately 0.1° for the contact angle measurements and 0.05 mJ m − 2 for the surface/interfacial tension measurements. It has long been found that, contrary to the prediction of the classical Young equation, the contact angle measured with the sessile drop method is not unique for a given solid –liquid – fluid system. This is often referred to as the contact angle multiple-value problem. Generally, there are two kinds of contact angle multiplevalue phenomena — the contact angle hysteresis and the drop size dependence of contact angles. Although the contact angle hysteresis phenomenon has been studied extensively, the phenomenon of the drop size dependence of contact angles is not fully investigated yet. Some recent progress on the contact angle dependence on the liquid drop size for the solid – liquid – air systems is reviewed in detail elsewhere [9]. In particular, it has been observed in experiment that for a given solid –liquid – air system, the contact angle can decrease up to 3 – 10° as the equilibrium base radius of the sessile liquid drop on the solid surface increases from 1 to 5 mm [10 – 12]. Physically, the contact angle dependence on the liquid drop size can be understood in terms of the so-called line tension effect, which is caused by the tension of the three-phase contact line. The
line tension concept was first described by Gibbs [13] and subsequently developed by many other researchers, particularly in the generalized theory of capillarity by Boruvka and Neumann [14]. In surface thermodynamics, in analogy to the surface/interfacial tension for a two-dimensional interface, the line tension of a three-phase equilibrium system can be defined as the free energy per unit length of the three-phase contact line [13,14]. Alternatively, it can be defined as the force operating in a one-dimensional three-phase contact line and tending to minimize its length in much the same way as the surface/interfacial tension always tends to minimize the interface area [14]. For a sessile liquid drop on an ideal solid surface in air, the mechanical equilibrium condition at any point along the three-phase contact circle can be expressed by the modified Young equation [14]: cos q= cos q −
| 1 , klv R
(1)
where cos q =
ksv − ksl , klv
(2)
q is the equilibrium contact angle corresponding to a finite base radius R of the three-phase contact circle; q the equilibrium contact angle corresponding to an infinitely large drop (i.e. R= ); klv, ksv and ksl are the surface tensions of the liquid –vapour interface, the solid –vapour interface, and the interfacial tension of the solid –liquid interface, respectively; and | is the line tension of the three-phase contact circle. Eq. (2) is the well-known classical Young equation, which indicates that for a given solid –liquid –vapour system, q is a constant solely dependent on its surface/interfacial tensions, klv, ksv and ksl. The modified Young equation, Eq. (1), relates the line tension | to the contact angle q and the base radius R of the three-phase contact circle. The line tension | and the equilibrium contact angle q of an infinitely large drop can be determined by measuring the drop size dependence of contact angles and plotting the experimental data in terms of cos q versus 1/R. The best curve-fitting technique can be employed to fit the data points
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to a straight line. According to Eq. (1), the slope and the intercept of the straight line are equal to − |/klv and cos q , respectively. Thus, the line tension | can be calculated from the slope if the liquid surface tension klv is given. Using the leastsquares curve-fitting technique and the ADSA technique, the line tension values for dodecane and ethylene glycol on three hydrophobic surfaces were found to be positive and of the order of 1 mJ m − 1 [11]. More recently, Duncan et al. [12] studied the drop size dependence of the contact angles of several n-alkane liquids on the FC721 coated surface again using the ADSA technique. A similar pattern of contact angle change with drop size was observed and the line tensions were all positive and of the order of 1 mJ m − 1. So far most experimental studies on the contact angle –drop size dependence have been conducted on the horizontal flat solid surfaces using the sessile drop method, such as the ADSA technique. Recently, Lin and Li [15] derived another form of the modified Young equation for the case where the three-phase line is in contact with an inclined solid surface. They incorporated the local inclination angle i of the inclined solid surface in the form of cos i into the line tension term in Eq. (1). For a solid – liquid – vapour system in which the shape of the solid surface is of revolution such as a cone or a cylinder, the modified Young equation can be written as [15]: cos q =cos q −
| cos i , klv Rc
(3)
where Rc is the radius of the three-phase contact circle on the conic or cylindrical solid surface. Obviously, for a horizontal flat surface, i= 0°, Eq. (3) will reduce to Eq. (1). For a vertical cylinder or flat plate as used in the Wilhelmy plate technique [3 – 5,16], i =90°, Eq. (3) then becomes the classical Young equation, Eq. (2), and the line tension term is absent from Eq. (3) in such a case. Later on, a new experimental technique was developed to measure the contact angle by analysis of the capillary profile around a cylinder (ACPAC) [17 –19]. The contact angles measured with the ACPAC technique were found to increase by approximately 4 – 6° as the term cos i/Rc increases from −2.0 to 10.0 cm − 1. According to
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Eq. (3), these contact angle data were then interpreted in terms of the line tension effect. The line tensions of four n-alkane liquids on the FC725 coated solid surface were determined to be positive and of the order of 1 mJ m − 1 [17], close to those published data for the FC721-decane and the FC721-dodecane systems [11,12]. A thorough literature search indicates that, however, no effort has been made yet to determine the drop size dependence of contact angels for any solid –liquid –liquid system, such as oil drops on a solid surface in an aqueous phase. Hence, the purpose of this paper is to study the contact angle dependence on the drop size in a solid –oil –water system using the ADSA technique and then to interpret the measured contact angle data in terms of the line tension effect. For such a solid –oil –water system, Eqs. (1) and (2) can be rewritten as: cos q= cos q −
| 1 , kow R
(4)
and cos q =
ksw − kso , kow
(5)
where, the subscripts o and w represent the oil phase and the water phase, respectively. With the measured contact angle dependence on the oil drop size, the same strategy as was described previously can be employed to determine the line tension of the solid –liquid –liquid system.
2. Experimental
2.1. Apparatus A block diagram of the apparatus used in the present experiment is shown in Fig. 1. In the set-up, a glass slide (2.5× 2.5 cm) pre-coated with the FC725 material is placed on the bottom of a square glass test cell (4.0× 4.0× 4.0 cm3), which is half filled with water. The glass slide can be set horizontally by properly leveling the test cell. The square glass test cell is placed between a light source and a microscope (a Leica Wild M3B microscope mounted with a Cohu 4910 CCD
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monochrome camera). The small oil drops in the oil-in-water mixtures are introduced into the water phase through a syringe. Due to their slightly higher density than that of the aqueous phase, the oil drops sink down slowly by natural sedimentation and eventually gently reside on the FC725 surface. After an oil drop is well focused, its instantaneous image is taken and the corresponding video signal is transmitted to a videopix digital processor, which performs the frame grab and digitization of the image. The entire experimental set-up is put on a vibration-free table. A SunSparc20 work station is used to acquire the digital image of the oil drop from the videopix and perform the subsequent image analysis, digitization and computation. In this study, the ADSA technique for the sessile drop case is used to measure the contact angles. The ADSA technique accomplishes the measurements by finding the best fit of the Laplace equation of capillarity to the real drop profile, which is obtained by digitizing the drop image. In comparison to other existing contact angle measurement methods, the ADSA technique is accurate, fully automatic and completely free of operator’s subjectivity. More technical details of the ADSA technique can be found in the literature [6 – 8]. The major principle of ADSA is summarized as follows. Theoretically, the equilibrium shape of a moderately curved liquid –fluid
interface should obey the governing Laplace equation of capillarity. On the other hand, ADSA acquires the actual drop profile from the digitized drop image. Then ADSA creates an objective function, which represents the discrepancy between the theoretically calculated Laplacian curve and the physically observed drop profile. ADSA optimizes the objective function numerically using the contact angle as an adjustable parameter. Once the objective function is optimized, i.e. the best fit of the Laplacian curve to the real drop shape is achieved, the contact angle is determined. Besides the digital image of liquid drop profile, the only additional input datum required by the ADSA program is the density difference between the liquid phase and the surrounding fluid phase, i.e. Dz = zo − zw between the oil phase and the aqueous phase in the present case.
2.2. Solid–oil–water system The oil phase used in the contact angle measurements is silicone oil No. 1 with density of zo = 1050 kg m − 3 and viscosity of vo = 172.7 mPa s (Aldrich Chemical Co.). Its surface tension against the air is kov = 26.8890.09 mJ m − 2 at 22°C. All the surface/interfacial tensions reported in this paper are measured using the ADSA technique for the pedant drop case [6–8]. This silicone oil is chosen as the oil phase because it is slightly
Fig. 1. Schematic diagram of the experimental set-up for using the ADSA technique to measure the drop size dependence of contact angles in a solid–oil–water system.
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heavier than water. Such oil drops will settle down slowly and eventually form small sessile drops on the FC725 solid surface in an aqueous phase. The aqueous phase is pure deionized ultra filtered (DIUF) water (Fish Scientific, Canada). The DIUF water has a density of zw = 998 kg m − 3, a conductivity of uw =1.21 ×10 − 4 S m − 1 and an equilibrium pH of 6.5. Its surface tension against the air is kwv =72.66 9 0.08 mJ m − 2 and its interfacial tension against the silicone oil No. 1 is kow = 32.08 90.10 mJ m − 2 at 22°C. Prior to the experimental use, the microscope glass slides were coated with a flurochemical surfactant coating material, FC725 (3M Product). This hydrophobic coating material enables oil drops to form acute contact angles on the glass slide in water. The FC725 solid surface is prepared using a dip-coating method [18]. The quality of the FC725 surfaces is examined carefully. First, it is known from the 3M Product Selection Guide that this fluorochemical surfactant coating material is very stable, even in many extremely aggressive chemical environments. The FC725 coating material is insoluble in organic liquids such as the silicone oil tested in this study. Secondly, the average roughness of the dip-coated FC725 surfaces as measured by using a Tencor Surface Profilometer (TSP) is less than 250 A, . In the previous paper [18], the contact angle hysteresis was measured to be within 5 – 7° for four n-alkane liquids on the FC725 surface in air. Similar contact angle hysteresis was found for two silicone oil – DIUF water interfaces on the same solid surface [19]. It should be pointed out that, although the solid surfaces used in this study are very smooth, they may still have a very small percentage of heterogeneity probably due to impurities of the coating material and dust in air. This might be the cause of the observed contact angle hysteresis. It has been shown elsewhere [20,21] that the advancing contact angle on a smooth but heterogeneous solid surface represents the equilibrium properties of the dominant material of the surface, whereas the receding contact angle more reflects the property of the impurity of the surface. Therefore, hereafter only the advancing contact angles of the silicone oil drops on the FC725 surface in the DIUF water are of concern.
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2.3. Formation of sessile oil drops on the FC725 surface in water Because of the small density difference between the oil and the aqueous phases, it is easy to make the oil-in-water mixtures. In experiment, the silicone oil-in-water (O/W) mixtures are prepared by adding 2 ml sample of the silicone oil into 200 ml of the DIUF water while a small stirrer (GiffordWood Homogenizer, Greerco Corp.) is kept stirring. Stirring is continued for 10 min after addition of the oil phase. The silicone oil drops are dispersed gradually in the aqueous phase, and eventually the O/W mixtures are formed. In this study, small sessile oil drops on the FC725 solid surface in the DIUF water are formed according to the following procedure. First, the square glass test cell is half filled with the DIUF water. Then the prepared silicone oilin-water mixtures are gently injected into the aqueous phase through a syringe. Since the oil phase is slightly heavier than the aqueous phase, the small oil drops will sink by natural sedimentation through the aqueous phase and ultimately form small sessile oil drops on the solid surface in water. Large sessile oil drops (R\ 0.1 cm) on the solid surface in water are generated in a similar way. Instead of injecting the oil-in-water mixtures into the DIUF water, the pure silicone oil is introduced directly into the test cell through a syringe. Because the size of the oil drop generated by this method depends on the size of syringe needle only, the oil drop size can be adjusted purposely by choosing different size of the syringe needle. Once the oil drop generated by the syringe becomes heavy enough, it leaves the tip part of the syringe needle, falls down through the aqueous phase by natural sedimentation and finally gently resides on the solid surface. It has long been realized that using a syringe either to form a liquid drop at its tip and then to deposit the drop directly onto a solid surface, or to add more liquid into an already formed liquid drop will inevitably cause severe mechanical disturbance and vibrations to the liquid –fluid interface and the three-phase contact line. This type of disturbance, in combination with the surface roughness and heterogeneity, can alter the pattern
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and the order of magnitude of the contact angle – drop size dependence and thus influence both the ‘sign’ and ‘value’ of the line tensions [22 –26]. However, in this study, due largely to the small density difference between the silicone oil and water as well as the small separation distance (falling height) between the syringe tip and the solid surface, the natural sedimentation deposition method virtually eliminates all the appreciable mechanical disturbance and vibrations during the formation of the sessile drops. This ensures the equilibrium state of the measured advancing contact angles and hence makes the experimental results more reliable. Furthermore, this deposition method can readily generate liquid drops whose size ranges from a few hundred micrometers to a few millimeters. In comparison to other conventional drop formation methods, the natural sedimentation method makes it possible to study the drop size dependence of contact angles in an even larger range.
2.4. Contact angle measurements In experiment, it is observed that, once a silicone oil drop makes contact with the FC725 solid surface in water, it begins to spread on the solid substrate. The spreading process of oil drop can be well characterized by its quickly decreased dynamic contact angle and its slowly increased base radius. As was indicated in the literature [19,27 –29], it takes time for possible adsorption of the dissociated ions in the aqueous phase onto the O/W interface to reach an equilibrium state. It has been observed in this study that variations of the dynamic contact angles measured 40 min after oil drops are deposited are roughly within 0.1°, equaling to an overall accuracy of the contact angles measured by the ADSA technique for the sessile drop case. Hence, the contact angle of an oil drop measured 40 min after it touches the solid surface in water can be considered as its equilibrium or static contact angle. During the measurements, for each oil drop, its digital image is acquired continuously until about 60 min after it is deposited. It should be emphasized that these equilibrium advancing contact angles are the Young contact angles [20,21], i.e. the contact an-
Fig. 2. Digital image of a sessile silicone oil (No. 1) drop on a FC725 coated glass slide in the DIUF water at the equilibrium state as produced on a laser printer, where q= 56.88°, R = 0.2429 cm and Vo =0.0130 cm3.
gles that can be used directly in both the classical and the modified Young equations, Eqs. (4) and (5). After each oil drop resides on the FC725 solid surface in water and its digital image is well focused, its instantaneous image is acquired sequentially and stored automatically in computer memory. All these stored images can be retrieved, processed and analyzed at a later time. A typical digital image of the sessile silicone oil drop on the FC725 surface in the DIUF water at the equilibrium state is given in Fig. 2. This image clearly shows the profiles of the oil drop and the solid surface in the DIUF water. For such an oil drop image, a standard grid image is used to calibrate the drop image and correct possible optical distortion. Then the ADSA program for the sessile drop case is executed to determine the instantaneous contact angle of the oil drop. The output of this program also includes the base radius R of the oil drop, its volume Vo and its surface area Aow. In this work, the measured equilibrium contact angles are in the range of q= 55–64°. Accordingly, the equilibrium base radius ranges roughly from 0.47 to 0.02 cm and the drop volume varies approximately from 0.100 to 0.001 cm3. Here, only the measured equilibrium contact angle q, the equilibrium base
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radius R of the oil drop, and the interfacial tension kow are required in order to determine the line tension of the solid – oil – water system from Eq. (4). All contact angle measurements are conducted at 22°C.
3. Results and discussion In the contact angle measurements, it has been observed that the silicone oil drop immediately begins to spread on the FC725 surface once it reaches and makes contact with the solid surface. Such drop spreading proceeds for some time until the so-called equilibrium state is reached. To characterize the spreading process, two parameters, the dynamic contact angle qd(t) and the instantaneous base radius r(t) of the sessile oil drop are measured sequentially. The typical measured results are plotted in Fig. 3(a) for qd(t) and Fig. 3(b) for r(t) of the silicone oil drop whose digital image at the equilibrium state is shown in Fig. 2. As marked by the error bars in Fig. 3(a), the overall accuracy of the contact angles measured by the ADSA technique is known to be
221
0.1°. It is noticed from the figure that the dynamic contact angles measured 40 min after the oil drop is deposited onto the solid surface can be considered nearly identical and thus approximated as the equilibrium contact angle q. Also as clearly marked by the error bars in Fig. 3(b), the instantaneous base radii measured after 40 min are essentially the same and can be approximated as the equilibrium base radius R. Furthermore, it is found in experiment that smaller silicone oil drops spread more slowly and thus take longer time to reach their equilibrium shapes. This finding is consistent with the previous theoretical predictions [30,31]. Since the slow spreading process has been identified for the silicone oil drops on the FC725 solid surface in the DIUF water, in this study, usually a period of more than 40 min is allowed for the spreading process to reach its equilibrium state. Physically, the equilibrium contact angle q depends on the drop size due to the line tension effect. In order to study the contact angle –drop size dependence of the solid –oil –water system, hereafter only the equilibrium contact angle q and the equilibrium base radius R for the silicone oil drops of different sizes will be discussed.
Fig. 3. (a) Variation of the dynamic contact angle qd(t) with time during the spreading process of a sessile silicone oil drop on the FC725 solid surface in the DIUF water. (b) Variation of the instantaneous base radius r(t) with time during the spreading process of a sessile silicone oil drop on the FC725 solid surface in the DIUF water.
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Fig. 4. (a) Variation of the equilibrium contact angle q of silicone oil drop on the FC725 solid surface in the DIUF water with its equilibrium base radius R. (b) Experimental data in terms of cos q vs. 1/R for the silicone oil drop on the FC725 solid surface in the DIUF water, where the line tension | and the contact angle q are determined from Eq. (4) with the equilibrium contact angle q and the equilibrium base radius R measured by using the ADSA technique.
Fig. 4(a) shows variation of the equilibrium contact angle of the silicone oil drop with the drop size. It is seen from this figure that the measured equilibrium contact angle decreases by
approximately 7.3° as the equilibrium base radius of the sessile oil drops increases from 0.0205 to 0.4684 cm. These experimental data are further plotted in Fig. 4(b) in terms of cos q versus 1/R. In this plot, the least-squares linear curve-fitting to these data points is represented by the solid straight line whose gradient and intercept are equal to the ratio − |/kow and cos q , according to Eq. (4). Thus, the line tension for the silicone oil drop on the FC725 solid surface in the DIUF water is determined to be | = 0.82 mJ m − 1, and q = 56.6°. In addition, the correlation coefficient of the least-squares linear curve-fitting is found to be 0.86. Therefore, the linear relationship between cos q and 1/R as expressed by Eq. (4) is statistically supported by the present experimental data. It should be noted that, theoretically, Eq. (4) is valid only for an ideal solid surface. As was discussed earlier, the solid surfaces used in this study still have small contact angle hysteresis, which may be caused by small surface heterogeneity. It has also been shown elsewhere [20,21] that the advancing contact angle measured on a real solid surface represents the equilibrium properties of the dominant materials of a smooth but nonhomogeneous surface and can be used in the classical and modified Young equations. Thus the line tension determined from Eq. (4) with the measured advancing equilibrium contact angles represents the property of the coating material, the FC725 in the present case. The observed contact angle changes are attributed to the line tension effect. Nevertheless, since the solid surface used in this study has small contact angle hysteresis, interpretation of the contact angle data by using Eq. (4) may not give the true line tension. Hence, the line tension value reported here may be more strictly referred to the ‘pseudo-line tension’ value [32]. In addition, the line tension of the present solid –oil –water system is positive and close to those of n-alkane liquid drops on the FC721 and FC725 solid surfaces in air measured by the ADSA technique [11,12] and by the ACPAC technique [17,18], respectively. As was defined before, the positive line tension will always tend to minimize the three-phase contact circle and enlarge the contact angle. Eq. (4) indicates that, the smaller
Y. Gu / Colloids and Surfaces A: Physicochem. Eng. Aspects 181 (2001) 215–224
Fig. 5. Digital image of a small silicone oil drop on the FC725 solid surface in the DIUF water as produced on a laser printer. The equator diameter and base radius of the silicone oil drop on the solid surface are measured to be = 115 mm and R =21 mm.
the oil drop is, the stronger the line tension effect will be. This fact has been verified by the experimental observation for some extremely small oil drops. As shown in Fig. 5, for example, a very small silicone oil drop is observed to keep its almost spherical shape for a few hours in the DIUF water. Its equator diameter and base radius on the FC725 solid surface are measured to be = 115 mm and R =21 mm, respectively. If the silicone oil drop shown in this figure is assumed to be a truncated sphere, its geometric contact angle is calculated to be qgeo =158.6°. This geometric contact angle is in a reasonable agreement with the contact angle value, qpre =131.8°, which is predicted from Eq. (4) with the known values of |= 0.82 mJ m − 1, q =56.6°, kow =32.08 mJ m − 2, and R =21 mm. Hence, the large contact angle is caused by the pronounced line tension effect on the small oil drop ( : 100 mm).
4. Summary A natural sedimentation method is employed to deposit oil drops onto a solid surface in an aqueous phase. This deposition method avoids all the appreciable mechanical disturbance and vibra-
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tions during the formation of the sessile drops and thus ensures the measured contact angles to be advancing contact angles. In addition, the natural sedimentation method can generate liquid drops in a large range of drop size to facilitate the studies of the drop size dependence of contact angles. Using this method, the contact angle – drop size dependence of silicone oil drops on the FC725 surface in the pure DIUF water is studied. Such dependence is then explained in terms of the line tension effect using the modified Young equation. The line tension of the solid –oil –water system is determined to be |= 0.82 mJ m − 1, which is close to those of similar solid –oil –air systems. For extremely small sessile oil drops (:100 mm), the strong line tension effect enables them to have nearly spherical shapes on the hydrophobic solid surface in an aqueous phase.
Acknowledgements The author wishes to thank Dr Dongqing Li at the University of Alberta for technical discussion and valuable suggestions and acknowledge the financial support of the Izaak Walton Killam Memorial Scholarship at the University of Alberta and the research grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada. The author also thanks two anonymous reviewers for their helpful comments.
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Drop size dependence of contact angles of oil drops on a solid surface in water Yongan Gu * Faculty of Engineering, Uni6ersity of Regina, Regina, Sask., Canada S4S 0A2 Received 31 May 2000; accepted 26 October 2000
Abstract Contact angle is a fundamental quantity in colloid and surface science. Of all the methods employed to measure the contact angles, direct measurement from sessile drops is probably the most popular approach. However, it has long been found that the measured contact angle is not unique for a given solid– liquid– fluid system. There are two types of contact angle multiple-value phenomena — the drop size dependence of contact angles and the contact angle hysteresis. In the literature, the contact angle dependence on the liquid drop size for the solid– liquid– vapour systems has been studied extensively. In this paper, the contact angle dependence on the oil drop size for a solid– oil– water system is measured by applying the axisymmetric drop shape analysis (ADSA) technique. More specifically, a natural sedimentation method is employed to deposit drops of a silicone oil with a density slightly higher than that of water onto the hydrophobic FC725 coated glass slide in the deionized ultra filtered (DIUF) water. It has been observed that the measured equilibrium contact angle decreases by approximately 7.3° as the equilibrium base radius of the silicone oil drop increases from 0.0205 to 0.4684 cm. According to the modified Young equation, the measured contact angle changes are then interpreted in terms of the so-called line tension effect. The line tension of the solid– oil– water system is found to be 0.82 mJ m − 1, which is very close to those for similar solid– oil– air systems. Unlike other conventional drop formation methods, the natural sedimentation method used in this study can eliminate all the appreciable mechanical disturbance and vibrations. Furthermore, this deposition can generate liquid drops in a much larger range of drop size such that the line tension effect becomes much more pronounced. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Contact angle; Sessile drop method, line tension; Solid– oil– water systems; Modified Young equations; ADSA technique
1. Introduction Accurate contact angle measurement of an oil drop on a solid surface in an aqueous phase is of * Tel.: +1-306-5854630; fax: + 1-306-5854855. E-mail address: [email protected] (Y. Gu).
interest in colloid science and interfacial phenomena. The wettability of the solid –oil –water system also plays an important role in a number of environmental, biological and industrial processes. There have been several techniques available for this purpose and some detailed descriptions of these methods can be found in the
0927-7757/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 ( 0 0 ) 0 0 8 0 4 - 9
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literature [1 – 5]. Of all the existing experimental methods, the sessile drop method is probably the most widely used contact angle measurement technique. In the sessile drop method, the contact angle is determined directly by aligning a tangent with the drop profile at the point of the solid –liquid –fluid three-phase contact circle on the solid surface. In addition to its simplicity, this method requires only small quantities of liquid sample and solid surface. However, usually an accuracy of 92° is claimed for the simple sessile drop method using a telescope equipped with a goniometer eyepiece. Alignment of the tangent is dependent on the operator’s skill and hence subjective. In recent years, Neumann and co-workers have developed a sophisticated sessile drop method, the axisymmetric drop shape analysis (ADSA) technique [6 – 8]. The ADSA technique can measure both the contact angles and the surface/interfacial tensions. The accuracy of the ADSA technique is approximately 0.1° for the contact angle measurements and 0.05 mJ m − 2 for the surface/interfacial tension measurements. It has long been found that, contrary to the prediction of the classical Young equation, the contact angle measured with the sessile drop method is not unique for a given solid –liquid – fluid system. This is often referred to as the contact angle multiple-value problem. Generally, there are two kinds of contact angle multiplevalue phenomena — the contact angle hysteresis and the drop size dependence of contact angles. Although the contact angle hysteresis phenomenon has been studied extensively, the phenomenon of the drop size dependence of contact angles is not fully investigated yet. Some recent progress on the contact angle dependence on the liquid drop size for the solid – liquid – air systems is reviewed in detail elsewhere [9]. In particular, it has been observed in experiment that for a given solid –liquid – air system, the contact angle can decrease up to 3 – 10° as the equilibrium base radius of the sessile liquid drop on the solid surface increases from 1 to 5 mm [10 – 12]. Physically, the contact angle dependence on the liquid drop size can be understood in terms of the so-called line tension effect, which is caused by the tension of the three-phase contact line. The
line tension concept was first described by Gibbs [13] and subsequently developed by many other researchers, particularly in the generalized theory of capillarity by Boruvka and Neumann [14]. In surface thermodynamics, in analogy to the surface/interfacial tension for a two-dimensional interface, the line tension of a three-phase equilibrium system can be defined as the free energy per unit length of the three-phase contact line [13,14]. Alternatively, it can be defined as the force operating in a one-dimensional three-phase contact line and tending to minimize its length in much the same way as the surface/interfacial tension always tends to minimize the interface area [14]. For a sessile liquid drop on an ideal solid surface in air, the mechanical equilibrium condition at any point along the three-phase contact circle can be expressed by the modified Young equation [14]: cos q= cos q −
| 1 , klv R
(1)
where cos q =
ksv − ksl , klv
(2)
q is the equilibrium contact angle corresponding to a finite base radius R of the three-phase contact circle; q the equilibrium contact angle corresponding to an infinitely large drop (i.e. R= ); klv, ksv and ksl are the surface tensions of the liquid –vapour interface, the solid –vapour interface, and the interfacial tension of the solid –liquid interface, respectively; and | is the line tension of the three-phase contact circle. Eq. (2) is the well-known classical Young equation, which indicates that for a given solid –liquid –vapour system, q is a constant solely dependent on its surface/interfacial tensions, klv, ksv and ksl. The modified Young equation, Eq. (1), relates the line tension | to the contact angle q and the base radius R of the three-phase contact circle. The line tension | and the equilibrium contact angle q of an infinitely large drop can be determined by measuring the drop size dependence of contact angles and plotting the experimental data in terms of cos q versus 1/R. The best curve-fitting technique can be employed to fit the data points
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to a straight line. According to Eq. (1), the slope and the intercept of the straight line are equal to − |/klv and cos q , respectively. Thus, the line tension | can be calculated from the slope if the liquid surface tension klv is given. Using the leastsquares curve-fitting technique and the ADSA technique, the line tension values for dodecane and ethylene glycol on three hydrophobic surfaces were found to be positive and of the order of 1 mJ m − 1 [11]. More recently, Duncan et al. [12] studied the drop size dependence of the contact angles of several n-alkane liquids on the FC721 coated surface again using the ADSA technique. A similar pattern of contact angle change with drop size was observed and the line tensions were all positive and of the order of 1 mJ m − 1. So far most experimental studies on the contact angle –drop size dependence have been conducted on the horizontal flat solid surfaces using the sessile drop method, such as the ADSA technique. Recently, Lin and Li [15] derived another form of the modified Young equation for the case where the three-phase line is in contact with an inclined solid surface. They incorporated the local inclination angle i of the inclined solid surface in the form of cos i into the line tension term in Eq. (1). For a solid – liquid – vapour system in which the shape of the solid surface is of revolution such as a cone or a cylinder, the modified Young equation can be written as [15]: cos q =cos q −
| cos i , klv Rc
(3)
where Rc is the radius of the three-phase contact circle on the conic or cylindrical solid surface. Obviously, for a horizontal flat surface, i= 0°, Eq. (3) will reduce to Eq. (1). For a vertical cylinder or flat plate as used in the Wilhelmy plate technique [3 – 5,16], i =90°, Eq. (3) then becomes the classical Young equation, Eq. (2), and the line tension term is absent from Eq. (3) in such a case. Later on, a new experimental technique was developed to measure the contact angle by analysis of the capillary profile around a cylinder (ACPAC) [17 –19]. The contact angles measured with the ACPAC technique were found to increase by approximately 4 – 6° as the term cos i/Rc increases from −2.0 to 10.0 cm − 1. According to
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Eq. (3), these contact angle data were then interpreted in terms of the line tension effect. The line tensions of four n-alkane liquids on the FC725 coated solid surface were determined to be positive and of the order of 1 mJ m − 1 [17], close to those published data for the FC721-decane and the FC721-dodecane systems [11,12]. A thorough literature search indicates that, however, no effort has been made yet to determine the drop size dependence of contact angels for any solid –liquid –liquid system, such as oil drops on a solid surface in an aqueous phase. Hence, the purpose of this paper is to study the contact angle dependence on the drop size in a solid –oil –water system using the ADSA technique and then to interpret the measured contact angle data in terms of the line tension effect. For such a solid –oil –water system, Eqs. (1) and (2) can be rewritten as: cos q= cos q −
| 1 , kow R
(4)
and cos q =
ksw − kso , kow
(5)
where, the subscripts o and w represent the oil phase and the water phase, respectively. With the measured contact angle dependence on the oil drop size, the same strategy as was described previously can be employed to determine the line tension of the solid –liquid –liquid system.
2. Experimental
2.1. Apparatus A block diagram of the apparatus used in the present experiment is shown in Fig. 1. In the set-up, a glass slide (2.5× 2.5 cm) pre-coated with the FC725 material is placed on the bottom of a square glass test cell (4.0× 4.0× 4.0 cm3), which is half filled with water. The glass slide can be set horizontally by properly leveling the test cell. The square glass test cell is placed between a light source and a microscope (a Leica Wild M3B microscope mounted with a Cohu 4910 CCD
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monochrome camera). The small oil drops in the oil-in-water mixtures are introduced into the water phase through a syringe. Due to their slightly higher density than that of the aqueous phase, the oil drops sink down slowly by natural sedimentation and eventually gently reside on the FC725 surface. After an oil drop is well focused, its instantaneous image is taken and the corresponding video signal is transmitted to a videopix digital processor, which performs the frame grab and digitization of the image. The entire experimental set-up is put on a vibration-free table. A SunSparc20 work station is used to acquire the digital image of the oil drop from the videopix and perform the subsequent image analysis, digitization and computation. In this study, the ADSA technique for the sessile drop case is used to measure the contact angles. The ADSA technique accomplishes the measurements by finding the best fit of the Laplace equation of capillarity to the real drop profile, which is obtained by digitizing the drop image. In comparison to other existing contact angle measurement methods, the ADSA technique is accurate, fully automatic and completely free of operator’s subjectivity. More technical details of the ADSA technique can be found in the literature [6 – 8]. The major principle of ADSA is summarized as follows. Theoretically, the equilibrium shape of a moderately curved liquid –fluid
interface should obey the governing Laplace equation of capillarity. On the other hand, ADSA acquires the actual drop profile from the digitized drop image. Then ADSA creates an objective function, which represents the discrepancy between the theoretically calculated Laplacian curve and the physically observed drop profile. ADSA optimizes the objective function numerically using the contact angle as an adjustable parameter. Once the objective function is optimized, i.e. the best fit of the Laplacian curve to the real drop shape is achieved, the contact angle is determined. Besides the digital image of liquid drop profile, the only additional input datum required by the ADSA program is the density difference between the liquid phase and the surrounding fluid phase, i.e. Dz = zo − zw between the oil phase and the aqueous phase in the present case.
2.2. Solid–oil–water system The oil phase used in the contact angle measurements is silicone oil No. 1 with density of zo = 1050 kg m − 3 and viscosity of vo = 172.7 mPa s (Aldrich Chemical Co.). Its surface tension against the air is kov = 26.8890.09 mJ m − 2 at 22°C. All the surface/interfacial tensions reported in this paper are measured using the ADSA technique for the pedant drop case [6–8]. This silicone oil is chosen as the oil phase because it is slightly
Fig. 1. Schematic diagram of the experimental set-up for using the ADSA technique to measure the drop size dependence of contact angles in a solid–oil–water system.
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heavier than water. Such oil drops will settle down slowly and eventually form small sessile drops on the FC725 solid surface in an aqueous phase. The aqueous phase is pure deionized ultra filtered (DIUF) water (Fish Scientific, Canada). The DIUF water has a density of zw = 998 kg m − 3, a conductivity of uw =1.21 ×10 − 4 S m − 1 and an equilibrium pH of 6.5. Its surface tension against the air is kwv =72.66 9 0.08 mJ m − 2 and its interfacial tension against the silicone oil No. 1 is kow = 32.08 90.10 mJ m − 2 at 22°C. Prior to the experimental use, the microscope glass slides were coated with a flurochemical surfactant coating material, FC725 (3M Product). This hydrophobic coating material enables oil drops to form acute contact angles on the glass slide in water. The FC725 solid surface is prepared using a dip-coating method [18]. The quality of the FC725 surfaces is examined carefully. First, it is known from the 3M Product Selection Guide that this fluorochemical surfactant coating material is very stable, even in many extremely aggressive chemical environments. The FC725 coating material is insoluble in organic liquids such as the silicone oil tested in this study. Secondly, the average roughness of the dip-coated FC725 surfaces as measured by using a Tencor Surface Profilometer (TSP) is less than 250 A, . In the previous paper [18], the contact angle hysteresis was measured to be within 5 – 7° for four n-alkane liquids on the FC725 surface in air. Similar contact angle hysteresis was found for two silicone oil – DIUF water interfaces on the same solid surface [19]. It should be pointed out that, although the solid surfaces used in this study are very smooth, they may still have a very small percentage of heterogeneity probably due to impurities of the coating material and dust in air. This might be the cause of the observed contact angle hysteresis. It has been shown elsewhere [20,21] that the advancing contact angle on a smooth but heterogeneous solid surface represents the equilibrium properties of the dominant material of the surface, whereas the receding contact angle more reflects the property of the impurity of the surface. Therefore, hereafter only the advancing contact angles of the silicone oil drops on the FC725 surface in the DIUF water are of concern.
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2.3. Formation of sessile oil drops on the FC725 surface in water Because of the small density difference between the oil and the aqueous phases, it is easy to make the oil-in-water mixtures. In experiment, the silicone oil-in-water (O/W) mixtures are prepared by adding 2 ml sample of the silicone oil into 200 ml of the DIUF water while a small stirrer (GiffordWood Homogenizer, Greerco Corp.) is kept stirring. Stirring is continued for 10 min after addition of the oil phase. The silicone oil drops are dispersed gradually in the aqueous phase, and eventually the O/W mixtures are formed. In this study, small sessile oil drops on the FC725 solid surface in the DIUF water are formed according to the following procedure. First, the square glass test cell is half filled with the DIUF water. Then the prepared silicone oilin-water mixtures are gently injected into the aqueous phase through a syringe. Since the oil phase is slightly heavier than the aqueous phase, the small oil drops will sink by natural sedimentation through the aqueous phase and ultimately form small sessile oil drops on the solid surface in water. Large sessile oil drops (R\ 0.1 cm) on the solid surface in water are generated in a similar way. Instead of injecting the oil-in-water mixtures into the DIUF water, the pure silicone oil is introduced directly into the test cell through a syringe. Because the size of the oil drop generated by this method depends on the size of syringe needle only, the oil drop size can be adjusted purposely by choosing different size of the syringe needle. Once the oil drop generated by the syringe becomes heavy enough, it leaves the tip part of the syringe needle, falls down through the aqueous phase by natural sedimentation and finally gently resides on the solid surface. It has long been realized that using a syringe either to form a liquid drop at its tip and then to deposit the drop directly onto a solid surface, or to add more liquid into an already formed liquid drop will inevitably cause severe mechanical disturbance and vibrations to the liquid –fluid interface and the three-phase contact line. This type of disturbance, in combination with the surface roughness and heterogeneity, can alter the pattern
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and the order of magnitude of the contact angle – drop size dependence and thus influence both the ‘sign’ and ‘value’ of the line tensions [22 –26]. However, in this study, due largely to the small density difference between the silicone oil and water as well as the small separation distance (falling height) between the syringe tip and the solid surface, the natural sedimentation deposition method virtually eliminates all the appreciable mechanical disturbance and vibrations during the formation of the sessile drops. This ensures the equilibrium state of the measured advancing contact angles and hence makes the experimental results more reliable. Furthermore, this deposition method can readily generate liquid drops whose size ranges from a few hundred micrometers to a few millimeters. In comparison to other conventional drop formation methods, the natural sedimentation method makes it possible to study the drop size dependence of contact angles in an even larger range.
2.4. Contact angle measurements In experiment, it is observed that, once a silicone oil drop makes contact with the FC725 solid surface in water, it begins to spread on the solid substrate. The spreading process of oil drop can be well characterized by its quickly decreased dynamic contact angle and its slowly increased base radius. As was indicated in the literature [19,27 –29], it takes time for possible adsorption of the dissociated ions in the aqueous phase onto the O/W interface to reach an equilibrium state. It has been observed in this study that variations of the dynamic contact angles measured 40 min after oil drops are deposited are roughly within 0.1°, equaling to an overall accuracy of the contact angles measured by the ADSA technique for the sessile drop case. Hence, the contact angle of an oil drop measured 40 min after it touches the solid surface in water can be considered as its equilibrium or static contact angle. During the measurements, for each oil drop, its digital image is acquired continuously until about 60 min after it is deposited. It should be emphasized that these equilibrium advancing contact angles are the Young contact angles [20,21], i.e. the contact an-
Fig. 2. Digital image of a sessile silicone oil (No. 1) drop on a FC725 coated glass slide in the DIUF water at the equilibrium state as produced on a laser printer, where q= 56.88°, R = 0.2429 cm and Vo =0.0130 cm3.
gles that can be used directly in both the classical and the modified Young equations, Eqs. (4) and (5). After each oil drop resides on the FC725 solid surface in water and its digital image is well focused, its instantaneous image is acquired sequentially and stored automatically in computer memory. All these stored images can be retrieved, processed and analyzed at a later time. A typical digital image of the sessile silicone oil drop on the FC725 surface in the DIUF water at the equilibrium state is given in Fig. 2. This image clearly shows the profiles of the oil drop and the solid surface in the DIUF water. For such an oil drop image, a standard grid image is used to calibrate the drop image and correct possible optical distortion. Then the ADSA program for the sessile drop case is executed to determine the instantaneous contact angle of the oil drop. The output of this program also includes the base radius R of the oil drop, its volume Vo and its surface area Aow. In this work, the measured equilibrium contact angles are in the range of q= 55–64°. Accordingly, the equilibrium base radius ranges roughly from 0.47 to 0.02 cm and the drop volume varies approximately from 0.100 to 0.001 cm3. Here, only the measured equilibrium contact angle q, the equilibrium base
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radius R of the oil drop, and the interfacial tension kow are required in order to determine the line tension of the solid – oil – water system from Eq. (4). All contact angle measurements are conducted at 22°C.
3. Results and discussion In the contact angle measurements, it has been observed that the silicone oil drop immediately begins to spread on the FC725 surface once it reaches and makes contact with the solid surface. Such drop spreading proceeds for some time until the so-called equilibrium state is reached. To characterize the spreading process, two parameters, the dynamic contact angle qd(t) and the instantaneous base radius r(t) of the sessile oil drop are measured sequentially. The typical measured results are plotted in Fig. 3(a) for qd(t) and Fig. 3(b) for r(t) of the silicone oil drop whose digital image at the equilibrium state is shown in Fig. 2. As marked by the error bars in Fig. 3(a), the overall accuracy of the contact angles measured by the ADSA technique is known to be
221
0.1°. It is noticed from the figure that the dynamic contact angles measured 40 min after the oil drop is deposited onto the solid surface can be considered nearly identical and thus approximated as the equilibrium contact angle q. Also as clearly marked by the error bars in Fig. 3(b), the instantaneous base radii measured after 40 min are essentially the same and can be approximated as the equilibrium base radius R. Furthermore, it is found in experiment that smaller silicone oil drops spread more slowly and thus take longer time to reach their equilibrium shapes. This finding is consistent with the previous theoretical predictions [30,31]. Since the slow spreading process has been identified for the silicone oil drops on the FC725 solid surface in the DIUF water, in this study, usually a period of more than 40 min is allowed for the spreading process to reach its equilibrium state. Physically, the equilibrium contact angle q depends on the drop size due to the line tension effect. In order to study the contact angle –drop size dependence of the solid –oil –water system, hereafter only the equilibrium contact angle q and the equilibrium base radius R for the silicone oil drops of different sizes will be discussed.
Fig. 3. (a) Variation of the dynamic contact angle qd(t) with time during the spreading process of a sessile silicone oil drop on the FC725 solid surface in the DIUF water. (b) Variation of the instantaneous base radius r(t) with time during the spreading process of a sessile silicone oil drop on the FC725 solid surface in the DIUF water.
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Fig. 4. (a) Variation of the equilibrium contact angle q of silicone oil drop on the FC725 solid surface in the DIUF water with its equilibrium base radius R. (b) Experimental data in terms of cos q vs. 1/R for the silicone oil drop on the FC725 solid surface in the DIUF water, where the line tension | and the contact angle q are determined from Eq. (4) with the equilibrium contact angle q and the equilibrium base radius R measured by using the ADSA technique.
Fig. 4(a) shows variation of the equilibrium contact angle of the silicone oil drop with the drop size. It is seen from this figure that the measured equilibrium contact angle decreases by
approximately 7.3° as the equilibrium base radius of the sessile oil drops increases from 0.0205 to 0.4684 cm. These experimental data are further plotted in Fig. 4(b) in terms of cos q versus 1/R. In this plot, the least-squares linear curve-fitting to these data points is represented by the solid straight line whose gradient and intercept are equal to the ratio − |/kow and cos q , according to Eq. (4). Thus, the line tension for the silicone oil drop on the FC725 solid surface in the DIUF water is determined to be | = 0.82 mJ m − 1, and q = 56.6°. In addition, the correlation coefficient of the least-squares linear curve-fitting is found to be 0.86. Therefore, the linear relationship between cos q and 1/R as expressed by Eq. (4) is statistically supported by the present experimental data. It should be noted that, theoretically, Eq. (4) is valid only for an ideal solid surface. As was discussed earlier, the solid surfaces used in this study still have small contact angle hysteresis, which may be caused by small surface heterogeneity. It has also been shown elsewhere [20,21] that the advancing contact angle measured on a real solid surface represents the equilibrium properties of the dominant materials of a smooth but nonhomogeneous surface and can be used in the classical and modified Young equations. Thus the line tension determined from Eq. (4) with the measured advancing equilibrium contact angles represents the property of the coating material, the FC725 in the present case. The observed contact angle changes are attributed to the line tension effect. Nevertheless, since the solid surface used in this study has small contact angle hysteresis, interpretation of the contact angle data by using Eq. (4) may not give the true line tension. Hence, the line tension value reported here may be more strictly referred to the ‘pseudo-line tension’ value [32]. In addition, the line tension of the present solid –oil –water system is positive and close to those of n-alkane liquid drops on the FC721 and FC725 solid surfaces in air measured by the ADSA technique [11,12] and by the ACPAC technique [17,18], respectively. As was defined before, the positive line tension will always tend to minimize the three-phase contact circle and enlarge the contact angle. Eq. (4) indicates that, the smaller
Y. Gu / Colloids and Surfaces A: Physicochem. Eng. Aspects 181 (2001) 215–224
Fig. 5. Digital image of a small silicone oil drop on the FC725 solid surface in the DIUF water as produced on a laser printer. The equator diameter and base radius of the silicone oil drop on the solid surface are measured to be = 115 mm and R =21 mm.
the oil drop is, the stronger the line tension effect will be. This fact has been verified by the experimental observation for some extremely small oil drops. As shown in Fig. 5, for example, a very small silicone oil drop is observed to keep its almost spherical shape for a few hours in the DIUF water. Its equator diameter and base radius on the FC725 solid surface are measured to be = 115 mm and R =21 mm, respectively. If the silicone oil drop shown in this figure is assumed to be a truncated sphere, its geometric contact angle is calculated to be qgeo =158.6°. This geometric contact angle is in a reasonable agreement with the contact angle value, qpre =131.8°, which is predicted from Eq. (4) with the known values of |= 0.82 mJ m − 1, q =56.6°, kow =32.08 mJ m − 2, and R =21 mm. Hence, the large contact angle is caused by the pronounced line tension effect on the small oil drop ( : 100 mm).
4. Summary A natural sedimentation method is employed to deposit oil drops onto a solid surface in an aqueous phase. This deposition method avoids all the appreciable mechanical disturbance and vibra-
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tions during the formation of the sessile drops and thus ensures the measured contact angles to be advancing contact angles. In addition, the natural sedimentation method can generate liquid drops in a large range of drop size to facilitate the studies of the drop size dependence of contact angles. Using this method, the contact angle – drop size dependence of silicone oil drops on the FC725 surface in the pure DIUF water is studied. Such dependence is then explained in terms of the line tension effect using the modified Young equation. The line tension of the solid –oil –water system is determined to be |= 0.82 mJ m − 1, which is close to those of similar solid –oil –air systems. For extremely small sessile oil drops (:100 mm), the strong line tension effect enables them to have nearly spherical shapes on the hydrophobic solid surface in an aqueous phase.
Acknowledgements The author wishes to thank Dr Dongqing Li at the University of Alberta for technical discussion and valuable suggestions and acknowledge the financial support of the Izaak Walton Killam Memorial Scholarship at the University of Alberta and the research grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada. The author also thanks two anonymous reviewers for their helpful comments.
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