Environ. Sci. Technol. 2005, 39, 1698-1706
Dissolution-Induced Contact Angle Modification in Dense Nonaqueous Phase Liquid/Water Systems ORPHIUS I. MOHAMMAD AND TOHREN C. G. KIBBEY* School of Civil Engineering and Environmental Science, The University of Oklahoma, Norman, Oklahoma 73019-1024
The contact angle between DNAPL, water, and aquifer material interfaces influences the spatial distribution of DNAPLs as they infiltrate into the aquifer, and may ultimately influence their remediation. The objective of this work was to evaluate the effects of dissolution on contact angle. Just as physically retracting a sessile drop reduces its contact angle with a surface, it was speculated that dissolution could cause contact angles to be reduced. Long-term dissolution experiments were conducted over the course of days to weeks, examining the dissolution of sessile drops of two DNAPLs, trichloroethylene (TCE) and tetrachloroethylene (PCE), in water and low concentration surfactant solutions, on glass surfaces. Experiments found that dissolution led to a continuous decrease of contact angle measured through the DNAPL drop, in most cases to near 0°, far lower than angles achievable through measurements of receding contact angles for the same systems. Pinning of drop contact diameter was observed in most experiments. A model developed on the basis of the Bashforth-Adams equation to predict the effect of dissolution on contact angle for drops with a pinned contact diameter showed very good agreement with experimental observations.
Introduction Chlorinated organic liquids are typically nonflammable and are widely used in industrial applications (1). Because their densities tend to be higher than that of water, and because they are typically immiscible with water, many chlorinated organic liquids are considered dense nonaqueous phase liquids (DNAPLs). Because of their high densities, DNAPLs tend to migrate downward in aquifers and accumulate at underlying low-permeability layers. Because of their low aqueous solubilities, DNAPLs can persist as long-term sources of contamination. Subsurface contamination by DNAPLs such as chlorinated organic liquids is an extensive problem at contaminated sites around the world (2-5). As DNAPLs infiltrate into the subsurface, both the rate at which they infiltrate and their ultimate configuration are influenced by a number of factors, including the interfacial tension between the DNAPL and water, and the contact angle between the two fluids and the solid surfaces (6, 7). Contact angle is defined as the angle formed between two immiscible fluids in contact with a solid surface. In multiphase flow, the fluid through which the contact angle is less than 90° is said to be the wetting fluid (8). When wetting and nonwetting * Corresponding author phone: (405)325-0580; fax: (405)325-4217; e-mail:
[email protected]. 1698
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fluids are in contact in a soil, interfacial forces work to draw the wetting fluid into the smaller pore throats and corners, displacing the nonwetting fluid. For a nonwetting fluid to resist being displaced by a wetting fluid in a pore, sufficient pressure or gravitational forces must be applied in the nonwetting fluid to overcome the interfacial forces. For a relatively clean DNAPL infiltrating into a saturated sandy aquifer, water will generally be the wetting fluid (6). As the nonwetting fluid, the DNAPL must displace water from pores to infiltrate into the aquifer. The lower the contact angle through the water in the presence of the DNAPL, or the higher the interfacial tension between the two phases, the more strongly the water will resist being displaced from pores. For relatively small DNAPL spills, the DNAPL will ultimately be dispersed until it is in the form of disconnected droplets or blobs at a nonwetting phase saturation known as the residual nonwetting phase saturation (8). Larger spills may also become pooled on low permeability formations (9, 10). Although wettability is defined by the magnitude of the contact angle, that definition is complicated by the fact that contact angle is hysteretic, having different values depending on whether a fluid is advancing or receding over a surface (11, 12). The angle formed when liquid moves out over a new surface is known as the advancing contact angle (θA), and the angle formed when liquid moves off of a previously occupied surface is known as the receding contact angle (θR). Receding contact angles are typically smaller than advancing contact angles (11, 12). The differences between the two angles can result from surface heterogeneity and surface roughness (12). The work described here examines the influence of dissolution in water of two chlorinated organic liquids, trichloroethylene (TCE) and tetrachloroethylene (PCE), on their contact angles on glass surfaces. When a drop is formed on a surface, and then the drop volume is gradually reduced (e.g., with a syringe), the base of the drop often maintains its initial footprint, and the contact line (where the two fluids and the solid meet) remains pinned until the contact angle reaches the receding angle. As volume continues to decrease, the drop footprint will begin to shrink. Because dissolution causes drop volume to decrease, we were interested in determining whether this same behavior would be observed. Although the effects of solution properties (pH, ionic strength, solutes) on contact angles have been widely studied (e.g., 13-18), we are not aware of previously reported work examining the effect of dissolution of DNAPLs on contact angles. The Bashforth-Adams Equation. The Bashforth-Adams equation is a special case of the Laplace equation of capillarity describing the shape of an axisymmetric interface between two fluids as a function of the interfacial tension between the fluids and the density difference between the fluids (11). Among other applications, the equation can be used to predict the shape of a sessile (sitting) or pendant (hanging) drop or bubble given the interfacial tension and density difference with the surrounding fluid and, in the case of sessile drops, the contact angle with the solid surface. In addition, the equation is also the basis for a family of very precise methods for measuring surface and interfacial tension based on image analysis of drop shapes (19-22). The Bashforth-Adams equation is given in eq 1 below (11, 12):
sin φ z 1 + )2+β R1/b x/b b
(1)
where b is the radius of curvature at the apex of the drop, 10.1021/es048810o CCC: $30.25
2005 American Chemical Society Published on Web 02/09/2005
FIGURE 1. Bashforth-Adams dimensionless drop profile corresponding to β ) 1.743. Because the drop is axisymmetric, solution of the Bashforth-Adams equation gives a half profile (i.e., x positive); in this figure, both sides of the profile have been shown for clarity. In the orientation shown, ∆G ) Gdrop - Gsurroundingliquid. To solve for a drop with its apex at the bottom, the orientation of the axes and the sign of ∆G are switched. φ is the angle from the horizontal plane to the tangent to the drop at a point (x, z) on the drop profile, and R1 is the radius of curvature of the profile of the drop (i.e., in the plane of the page for a side view of the drop) at any point along the profile. The parameter β is known as the Bond number or the shape factor and is a ratio of interfacial forces to gravitational forces. The Bond number is given by eq 2:
β)
∆Fgb2 γ
(2)
The Bond number encapsulates the effects of interfacial tension (γ) and density difference (∆F) on the shape of a drop. A positive β produces a sessile drop shape (drop is wider than it is high), while a negative β produces a pendant drop shape (elongated vertically). A β of zero corresponds to a spherical drop. Note that reducing γ will elongate a pendant drop or flatten a sessile drop, but cannot change the sign of β; conversion of a drop from a sessile shape to a pendant shape can only be accomplished with a density change. Figure 1 shows the dimensionless profile of a Bashforth-Adams drop with all important variables. Solution of the Bashforth-Adams equation is achieved by simultaneous solution of eqs 1 and 2 with three additional relationships that can be determined from geometry, eq 3-5 (19):
1 dφ ) R1 ds
(3)
dx ) cos φ ds
(4)
dz ) sin φ ds
(5)
where s is the distance along the profile of the drop from the apex. Solution methods start at the apex of the drop (x ) 0, z ) 0, s ) 0, φ ) 0, dφ/ds ) 1) and integrate along s to calculate the profile of the drop. A number of different methods have been used with success; higher order Runge-Kutta methods have been shown to be a good choice (22). Solution of eqs 1-5 gives a dimensionless drop profile (x/b vs z/b); conversion to an actual drop profile requires a reference length to determine b. In the case of a sessile drop, the contact angle (θ) is also needed to define the actual drop profile, because the theoretical profile is truncated by its contact with the surface (Figure 1). When contact angle is
FIGURE 2. Schematics of the experimental setup. (A) View of the optical cell from the direction of the camera showing the contact angle (θ) and contact diameter (D) as they are defined in this paper. (B) Top view of one entire experimental setup (two parallel setups were used). Diagrams are not drawn to scale. defined through the drop, the contact angle is equal to the value of φ at the intersection between the profile and the surface. For this work, we use the Bashforth-Adams equation in two contexts: first, a model is used to describe the effect of dissolution on contact angle for a drop for which the footprint is pinned to the surface; second, all drop analyses in this paper were conducted via axisymmetric drop shape analysis of images of drop profiles. Details of both uses of the Bashforth-Adams equation are given below.
Materials and Methods Materials. Tetrachloroethylene (PCE) and trichloroethylene (TCE) were the DNAPLs selected for this research work. PCE and TCE were selected as they are widely used chlorinated solvents, and are common contaminants at National Priority List (NPL) sites (5). Both PCE and TCE were purchased from Sigma-Aldrich Chemical Co., Inc. (St. Louis, MO). An alternate TCE was purchased from Fisher Chemical (Fairlawn, NJ) and was used in experiments conducted prior to construction of an automated imaging system (described below). Of the data presented in this paper, only the TCE/anionic surfactant data in Figure 7C made use of the Fisher TCE. TCE/water experiments with the Fisher TCE (data not shown) exhibited trends identical to those of experiments using the SigmaAldrich TCE (e.g., Figure 4). All DNAPLs had stated purities of greater than 99.5% and were used as received. Properties of DNAPLs used in this research work are given in Table 1. Experiments involving surfactants were conducted with one of the following: cetyltrimethylammonium bromide (CTAB) (a cationic surfactant), sodium dodecylbenzenesulfonate (SDBS) (an anionic surfactant), or Tergitol NP9 (an ethoxylated nonionic surfactant). CTAB and SDBS were purchased from Sigma-Aldrich Co. (St. Louis, MO), while NP9 was provided by Dow Chemical Co. (Midland, MI). CTAB had a minimum stated purity of 99%. SDBS was technical VOL. 39, NO. 6, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Properties of DNAPLs Used in Experimentsa molecular weight DNAPL formula (g/mol) TCE PCE a
C2HCl3 C2Cl4
131.39 165.83
aqueous solubility (M)
interfacial tension with density, water, γow G (g/mL) (mN/m)
8.37 × 10-3 1.4642 8.99 × 10-4 1.6227
34.5 47.5
All properties from ref 33.
grade surfactant containing approximately 80% dodecylbenzenesulfonate based on total alkylsulfonate content (monodisperse SDBS is not commercially available). NP9 is a commercial ethoxylated surfactant with greater than 99% active content. Like most ethoxylated surfactants, NP9 contains a broad distribution of ethoxylated components, which results from the manufacturing process. For SDBS and NP9, molar concentrations are based on average molecular weights (348.48 and 616.82 g/mol, respectively). All experiments were conducted at concentrations below surfactant critical micelle concentrations (CMCs). Although surfactant-based remediation applications typically involve concentrations much higher than the CMC (e.g., (23-24)), the purpose of this work was to examine the possible effects of low concentration surfactants either present initially in the subsurface (e.g., through incomplete wastewater treatment), or entering the environment with the DNAPL. The CMCs of CTAB and SDBS have been reported to be 9.2 × 10-4 M (25) and 1.7 × 10-3 M (26) in the absence of added salt, respectively. The CMC of NP9 is estimated to be 9.4 × 10-4 M, based on reported CMCs of homologous Triton NP series surfactants (27). All surfactants were used as received. All experiments reported in this paper were conducted on silicate glass surfaces (24 mm × 40 mm Gold Seal cover glass (Erie Scientific, Portsmouth, NH)). Glass surfaces were selected to represent the surfaces of sandy, low-carbon aquifer materials. Preliminary experiments on mica surfaces found results quantitatively similar to those of experiments on glass slides, so work with mica was not pursued further. Glass slides and other glassware were cleaned prior to use by rinsing in HPLC-grade methanol (Sigma-Aldrich), soaking for 24 h in 1% LIQUI-NOX solution (Alconox, Inc., White Plains, NY) followed by at least 10 rinses in Nanopure water (Barnstead, Dubuque, IA). Cover glass surfaces were not reused. All solutions were prepared using Nanopure water. Dissolution Experiments. Experiments conducted involved long-term (days to weeks) observation of the dissolution of DNAPL sessile drops in aqueous solutions. Experiments were conducted in rectangular optical cells, open to the atmosphere (Figure 2A). Two different optical cells were used: one 5 cm × 5 cm × 5 cm optical glass cell (purchased from Fisher Scientific) and one 4.5 cm × 4.5 cm × 3 cm quartz cell (purchased from Rame´-Hart (Mountain Lakes, NJ)). No differences were observed or expected between the cells, with the exception of slightly different dissolution rates because of the different volumes and air/ water interfacial areas in the cells. Because our purpose was not to examine dissolution rates, no attempt was made to prevent escape of TCE or PCE to the vapor phase through Henry’s Law partitioning. In fact, several experiments (data not shown) were conducted using nitrogen sparging to accelerate dissolution, but the approach was abandoned because of difficulty preventing the nitrogen bubbles from disrupting the drop, and because of foaming in the surfactant solutions. To conduct a dissolution experiment, an optical cell was initially filled with aqueous solution and glass slides were positioned on a stainless steel or aluminum stage within the cell. A sessile drop was then formed manually in the center 1700
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of the glass slide using a syringe with a 30 gauge needle. Drops were generally formed at or near their advancing contact angle, although in some cases (e.g., Figure 4 data) larger drops were initially created and then retracted to desired volume; as such, initial contact angles may be somewhat lower than measured advancing angles would indicate for the same system. Drop volumes used in this work ranged from a few microliters to approximately 100 µL. Following placement of the drop, the camera was focused, and a reference dimension was taken by submerging a vertical precalibrated cylindrical reference directly above the drop. The reference was then removed, and imaging was started, typically within a few minutes of the time the drop was formed. Experiments were conducted in two parallel experimental setups, each like the one shown in Figure 2B. Each setup consists of one 30 W halogen lamp, one groundglass diffuser, an optical cell containing the solution, the glass surface and the DNAPL drop, and a CCD camera. All components except the cameras are height adjustable. The platform on which both setups are constructed can be leveled by adjustment of six height-adjustable feet. Each camera is mounted on a Bogen-Manfrotto (Ramsey, NJ) model 410 geared head, allowing fine angle adjustments to be made. Cameras used were: one Hitachi (Woodbury, NY) KP-M2 camera, and one Pulnix (Sunnyvale, CA) TM-7CN camera. Both cameras are 525 line, 1/2 in. CCD, monochrome cameras. Both cameras were equipped with Computar TEC-55 telecentric lenses with 2× extenders (Computar Optics, Inc., Hudson, NH). Green filters were used to improve image sharpness. Imaging was computer-controlled using software written for the purpose. To prevent heating of samples over the long duration of experiments, halogen lights were controlled by computer-controlled relays, which illuminated them only when images were taken. Images were taken at time intervals ranging from a few seconds at the start of each experiment, to 30 min after approximately 1 day. More rapid imaging at the start was intended to capture initial rearrangement of the drop as the interfacial region of the water and DNAPL became mutually saturated and (where appropriate) surfactant adsorbed at interfaces. Although temperature was not controlled in experiments, the laboratory where experiments were conducted typically maintains a temperature ranging from approximately 20 to 22 °C. Room lights were left on for the duration of experiments to improve temperature stability. Note that small fluctuations in temperature could not cause the pinning behavior observed in the experiments presented here, although they could possibly contribute to drop slipping (e.g., Figure 9). Selected experiments presented here were conducted manually before the automated system was completed (Figures 7C and 8). All procedures were the same as for automated measurements, except fewer images were collected. The receding contact angle of TCE in water was determined using a J-shaped needle, with its tip inserted upward through a drilled hole in a glass slide. A TCE drop was formed and then taken through a sinusoidal volume range (approximately 30-220 µL, at a rate of 1 µL/s) using an I.T. Concept Tracker system (ThetaDyne Corp., Charlottesville, NC). Contact angles were taken as the value of the BashforthAdams φ corresponding to the intersection of the theoretical profile and the surface. Similar analyses conducted manually produced very similar results, to within a few degrees. Sessile Drop Analysis. Contact angle, drop volume, and interfacial tension were measured using axisymmetric drop shape analysis (19-22). Edge detection made use of the Sobel edge operator (19), and drop profiles were fit using a fourthorder Runge-Kutta solution of the Bashforth-Adams equation, and nonlinear regression fits based on the NelderMead downhill-simplex algorithm (28). Automated software written for this work allowed batches of hundreds of images
to be analyzed without user intervention. Nonlinear fits were conducted by minimizing the error between the BashforthAdams equation and up to 700 points (depending on drop size) from both sides of the drop profile. Although this number of points would be unnecessarily large for conventional analyses, the use of high-resolution images with many data points improved fits for very flat drops, which are known to yield difficult analyses (22). Fits started with initial estimates of β, b, and the coordinates of the drop apex, determined from the basic dimensions of the drop. Regressions varied these parameters in addition to the angle of the drop (to allow for slight deviations from vertical, and improve fits). Contact angles were taken as the value of φ corresponding to the intersection of the profile and the surface. Note that all contact angles in this work are reported through the DNAPL drop (Figure 1). One of the difficulties of sessile drop analysis, particularly for long-term experiments such as those conducted here, is that sessile drops are more likely to become asymmetric than would be the case with pendant drops, and as such violate the assumptions of the Bashforth-Adams equation (29). This can lead to errors in calculated interfacial tensions and volumes and can be a particular problem for drops whose contact angles are less than 90°. For the experiments reported here, all drops were very nearly symmetrical within the plane of the profile being imaged, typically with no more than a few degrees difference between contact angles on each side as measured manually. Implications of possible asymmetry on observed results are discussed in the context of experimental results, below. Dissolution Model. As a part of the work described below, a model was developed to predict the shapes of dissolving drops for which their contact diameter remains constant, based on solution of the Bashforth-Adams equation. The model requires specification of a contact diameter (D), interfacial tension (γ), and density difference (∆F), and then calculates the volume of a theoretical drop for a range of contact angles, from 1° up to a specified maximum. The solution for the model is the same as for the drop shape analysis as described above, but the specified drop diameter is used as reference length. For each contact angle, θ, the solution is iterated by setting:
{ /(bx) }
bi ) D
i
φ)θ
(6)
calculating β from eq 2, and then solving the BashforthAdams equation at φ ) θ to determine (x/b)φ)θi+1, which is used in eq 6 to determine bi+1. Iteration continues until the value of β converges for the current θ value, and then θ is increased and the procedure is repeated.
Results and Discussion Early in the course of experiments conducted for this work, it was observed that dissolving drops tended to retain their initial contact diameters during dissolution for a wide range of systems; that is, the original footprint of the drop on the surface did not change during dissolution. This is illustrated in Figure 3, which shows images of a drop of TCE dissolving in Nanopure water over approximately 6.5 days. Although a small difference in contact diameter is reported (5.48 mm initially, 5.63 mm after approximately 6.5 days), the difference is more the result of the inability to identify the location of the base of the drop with sub-pixel accuracy, and the very flat profiles of nearly-dissolved drops, which are both difficult to fit, and for which a small vertical error in identification of the base corresponds to a large error in the diameter. For example, for the bottom drop in Figure 3, a 1 pixel error in identifying the base would correspond to approx a 0.1 mm error in the contact diameter. Despite the slight variations
FIGURE 3. Dissolution of TCE on glass in Nanopure water over approximately 6.5 days (155 h). Time (t), contact angle (θ), drop volume (V), and contact diameter (D) are indicated. in measured values, it is apparent from Figure 3 that the drop is essentially pinned in place; its contact diameter remains essentially constant. Note that, although this result has been observed for different DNAPLs in a range of solutions, preliminary experiments examining volatilization of liquids in air (data not shown) did not observe constant contact diameters, although contact angles were still observed to decrease during volatilization. Figure 4 provides further quantitative analyses of the experiment corresponding to the images shown in Figure 3. Figure 4A shows the contact angle of the TCE drop (measured through the drop) versus the drop volume, taken from approx 430 images collected over approximately 6.5 days. Vertical arrows in Figure 4 indicate the data points corresponding to images in Figure 3. The dashed line indicates the receding contact angle measured in separate experiments (described in the Materials and Methods section). One of the most interesting observations of this work is that dissolution tended to cause contact angles to decrease to angles far lower than measured receding contact angles. The reason for this is unknown, but it is possible the difference is due to the difference in rates of volume change between drop retraction and dissolution. As mentioned earlier, the receding contact angle was measured by retracting a drop at a rate of 1 µL/s; that result did not appear to be particularly rate dependent, as faster rates, and even manual measurements, produced nearly the same contact angle. However, dissolution of the drop causes the volume to decrease at approximately 1 µL/h VOL. 39, NO. 6, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 4. Dissolution of TCE on glass in Nanopure water over approximately 6.5 days (155 h). (A) Contact angle versus drop volume. Vertical arrows indicate images in Figure 3. Dashed line indicates measured receding contact angle, θR. (B) Interfacial tension and elapsed time versus volume. initially (and slower as dissolution progresses and the dissolved concentration increases), a rate that is approximately 1/3600th of the rate achieved in the receding angle experiments. It is conceivable that the rapid retraction of the drop volume may introduce sufficient energy to overcome the forces that pin the drop, while the much slower volume change caused by dissolution may not. The slower volume change caused by dissolution may also allow additional time for interface aging (discussed below). It should be noted that at a volume of approximately 5 µL and a contact angle of approximately 15° (to the left of the leftmost data point shown in Figure 4A), the base of the drop slipped to approximately 3.3 mm, the contact angle increased, and the drop became asymmetric preventing further analyses. However, further imaging of the asymmetric drop showed that, as it dissolved, its contact angle decreased all of the way to 0°. That is, there was apparently no receding contact angle for this system from a practical standpoint. This result was consistent across all experiments where we allowed drops to dissolve completely. Whether or not there was a slip in the drop footprint prior to complete dissolution may depend on the initial diameter of the drop, but more work would be needed to confirm that. Figure 4B shows both the interfacial tension of the drop during dissolution and the time each image was collected as a function of drop volume. The interfacial tension shows an initial glitch as the interfacial regions of the two phases become mutually saturated (less obvious in these data than later experiments, due to a 25 min delay in the start of imaging after the drop was formed), and then the interfacial tension shows a continuous gradual decrease with decreasing drop volume. The interfacial tension near the start of the experiment (34.8 mN/m after a 3 h equilibration period) is 1702
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consistent with reported values for TCE in water (34.5 mN/ m), but after 1 day the interfacial tension dropped to approximately 30.8 mN/m, and continued to drop throughout the experiment. This behavior has been observed in all systems studied and may result from one of three factors. One possible explanation is increasing drop asymmetry with dissolution may produce erroneous interfacial tension values, as drops no longer fit the assumptions of the BashforthAdams equation. Although the profiles imaged for this work appear to be highly symmetric, top views were not imaged, so any three-dimensional asymmetry would not have been observed. Preliminary experiments applying the BashforthAdams solution to intentionally asymmetric drops found that lower interfacial tensions were generally predicted for highly nonaxisymmetric drops, even when a very good fit to the profile could be achieved. However, more work would be needed to determine if the magnitude of the error would be sufficient to explain our observed decrease. A second possible explanation is the long-term aging of the interface and gradual adsorption of trace impurities in the DNAPLs used. Although high purity chemicals were used, even a small quantity of a slowly adsorbing impurity could produce measurable interfacial tension reductions. (Impurities from other sources (the atmosphere, water) were eliminated as possibilities through a number of control experiments (sealed optical cells, different water sources) which exhibited the same behavior as Figure 4B.) A third possibility is that a pinned drop may be overconstrained from the standpoint of the Bashforth-Adams equation. That is, by decreasing the volume of a drop while it’s perimeter remains pinned, stresses such as line tension (30-32) may become more important, producing an erroneous result. Kwok et al. (29) studied the low rate expansion of drops of 30 liquids on a nonpolar surface in air and observed slip/ stick behavior for all but 9 of them, in that drop diameters would remain pinned (i.e., the drop footprint would stick to the surface) as contact angle would increase, and then the drop diameter would expand suddenly (slip) to a new diameter and the contact angle would decrease. Many of the liquids exhibited substantial changes in measured surface tension as drops increased in size, with large jumps in surface tension frequently accompanying slipping drop diameters. The authors attributed the result to drop asymmetry. Interestingly, we have observed that collecting a partially dissolved drop in a syringe and reforming the same drop in the same solution typically led to an increase in measured interfacial tension to near the initial interfacial tension. This result could be consistent with all three possible explanations described above, as reforming the drop would eliminate asymmetries produced by dissolution, would create a new interface, and would relieve any stresses in the drop interfaces. Further interpretation of the causes of the decrease in interfacial tensions would require collection of simultaneous top and profile views (and/or multiple profiles) to quantify symmetry. Another observation that can be made from Figure 4B is that below a volume of approximately 10 µL, measured interfacial tension values exhibit considerable scatter. Although the interfacial tensions reported at higher volumes may or may not be accurate for reasons discussed above, they are highly repeatable. At low volumes, however, two factors hinder measurement of interfacial tension. First, very flat drops with low contact angles can be difficult to fit using drop profile analysis (22). Second, as drop volume decreases, the surface area-to-volume ratio increases, decreasing the influence of gravity. For a very small drop, large variations in interfacial tension produce very small variations in drop shape, making it difficult to precisely identify interfacial tension from the profile of a small drop. As such, for all
FIGURE 6. Contact angle versus normalized volume, V/V180, where V is drop volume and V180 is the volume of the drop at 180°. Curves are plotted for a range of values of the alternate Bond number, β*.
FIGURE 5. Model-predicted contact angle (θ) versus volume for drops of a fluid with the density of TCE in water, shown for a range of interfacial tensions (γ). (A) Small drop, with D ) 2 mm. (B) Large drop, with D ) 10 mm. analyses in subsequent figures where interfacial tensions are presented, we show interfacial tension data only down to a volume of 10 µL. It should be noted that, although error in measured interfacial tension does correspond to error in measured drop volume, the two are not proportional. For example, the profile of a 1 µL drop of TCE in water with a 10° contact angle and a 10 mN/m interfacial tension is almost indistinguishable from that of the same drop with a 100 mN/m interfacial tension. The fact that the profiles are virtually the same means that even if the fit determines that a 10 mN/m liquid has an interfacial tension of 100 mN/m, integration of the profile will still produce a nearly-exact volume. Similarly, errors in calculated volumes resulting from mild asymmetry are likely to be relatively small in magnitude as long as the rotated profile is a reasonably close match to the profile of the actual drop, even if calculated interfacial tensions are not accurate. Based on the observation of drops remaining pinned during dissolution, a numerical model was developed on the basis of the Bashforth-Adams equation to examine the theoretical effect of dissolution of a pinned drop on contact angle. Details of the model and its solution are given in the Materials and Methods section. Figure 5 shows model predictions for two drops with the density of TCE in water, for a number of interfacial tensions. Both figures correspond to dissolution of drops with an initial contact angle of 130°, and fixed contact diameters. Figure 5A corresponds to dissolution of a drop with a 2 mm contact diameter (a small drop), while Figure 5B corresponds to dissolution of a drop with a 10 mm contact diameter (a large drop). Because contact diameter is fixed, the volume of each drop at a particular
contact angle varies with interfacial tension, with smaller interfacial tensions corresponding to flatter drops that have lower volumes. From Figure 5A and B, it is apparent that, for a particular liquid, the change of contact angle of a large drop with dissolution is a strong function of interfacial tension, with lower interfacial tensions producing a near linear relationship between contact angle and volume. Smaller drops, or larger drops with higher interfacial tensions, show a nonlinear relationship between contact angle and volume, with large initial changes in volume having little effect on contact angle, but small changes in volume having a much greater effect on contact angle as the drop becomes smaller. It should be noted that the preceding discussion is somewhat of a simplification of the situation, and the comparison between small and large drops is only strictly true if the two drops have the same densities and interfacial tensions. This is because drop shape is primarily a function of the Bond number, β, which encapsulates the effects of both the density difference (gravitational forces) and the interfacial tension (interfacial forces) of the two drops. To convert the problem to dimensionless form, we define an alternate Bond number, β*, whose characteristic length is taken as the contact diameter of the drop, D:
β* )
∆FgD2 γ
(7)
Figure 6 shows the problem in dimensionless form, with each curve corresponding to the expected influence of dissolution on contact angle for a particular alternate Bond number, β*. In the figure, volume (V) is normalized to the volume of a drop with a contact angle of 180° (V180). To illustrate that the trends in Figure 5A and B are not unique to small and large drops, respectively, note that a small drop of TCE with a contact diameter of 2.1 mm and an interfacial tension of 0.2 mN/m (a very feasible interfacial tension value in the presence of some surfactants, such as sulfosuccinates) would exhibit a β* value of approximately 100, and so would follow the β* ) 100 curve in Figure 6. Similarly, a moderately large 5 mm drop of chlorobenzene (F ) 1105.8 kg/m3; g ) 37.41 mN/m (33)) would exhibit a β* value of approximately 0.7, and so would follow a curve between the 0.1 and 1.0 curves in Figure 6. It should be noted that the higher values of β* shown in Figure 6 correspond to very flat drops. Although the Bashforth-Adams Bond number (β) varies along the curves shown in Figure 6 (because b is not constant as drop volume increases), a β* value of 400 corresponds to β values on the VOL. 39, NO. 6, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 8. Dissolution of PCE in Nanopure water and 1.2 × 10-4 M CTAB solution. Model predictions are shown, based on the reported interfacial tension of pure PCE (47.48 mN/m). The small size of drops precludes accurate interfacial tension measurements.
FIGURE 7. The effect of dissolution on contact angle, showing contact angle (θ) and measured interfacial tension (γ) as a function of volume. Model predictions corresponding to the indicated interfacial tension (γ) values are shown. (A) TCE in Nanopure water. (B) TCE in 8.4 × 10-5 M NP9 solution. (C) TCE in 2.2 × 10-4 M SDBS solution. order of 104 over much of the contact angle range, indicating extremely flat drop profiles. Although β* values larger than 400 are possible, creating a stable, axisymmetric drop with a higher β* value would be difficult from an experimental standpoint. One final interesting trend that can be noted in Figure 6 is that for the flattest drops (i.e., the highest β* values), small changes in volume actually correspond to large changes in contact angle. This result may have implications for the use of ultralow interfacial tensions for mobilization of entrapped DNAPLs, because ultralow interfacial tensions will tend to produce high β* values. Figure 7 shows application of the dissolution model to dissolution of sessile drops of TCE in three different solutions. Figure 7A shows TCE in water (data from Figure 3), Figure 7B shows TCE in 8.4 × 10-5 M NP9, and Figure 7C shows TCE 1704
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in 2.2 × 10-4 M SDBS. Data shown in Figures 7A, B, and C correspond to dissolution over approximately 6.5, 7.2, and 6.0 days, respectively. In Figures 7A and B, 9 of every 10 contact angle-volume data points collected have been omitted to prevent obscuring the model predictions with the data points. Unlike the data in Figures 7A and B, the data in Figure 7C were collected manually (see Materials and Methods), so all points are shown. All interfacial tension data for volumes larger than 10 µL are shown (symbols have been included in the interfacial tension data in Figure 7C, because fewer data points exist). Figures 7B and C show a distinct initial drop in interfacial tension as the interfacial region of the drops and surrounding solution equilibrates. This rapid interfacial tension drop also corresponds to an initial increase in contact angle and contact diameter. All model predictions shown are based on the drop contact diameter taken from after the initial equilibration/ rearrangement period, which is typically complete within 1.0-1.5 h after the drop is initially formed. (As mentioned above, the data in Figure 7A (also Figure 4) show the effect to a much lesser extent, due to a delay in the start of imaging.) After the initial decrease in interfacial tension, the measured interfacial tension continues to gradually decrease for all three systems, as noted in the discussion of Figure 4, above. From the figures, it is apparent that the model does a very good job of predicting the contact angle/volume dissolution behavior for all three systems, including the effects of changing interfacial tension. It should be noted, however, that this cannot necessarily be taken as evidence that interfacial tension is actually dropping (as opposed to an artifact of asymmetry or other factors, as discussed above), because the interfacial tension, contact angle, and volume are all determined from the same image analyses, so may all be influenced in a parallel way by drop asymmetry. Nevertheless, an important observation that can be made from the figure is that in most cases assuming interfacial tension remains constant should produce very reasonable predictions of the effect of dissolution on contact angle, because the predicted curves corresponding to different interfacial tensions converge as volume decreases. Figure 8 shows the effect of dissolution on contact angle for two small drops of PCE, one in water and one in 1.2 × 10-4 M CTAB solution. It is apparent from the figure that the CTAB solution had adsorbed substantially to the glass surface prior to the introduction of PCE, causing the PCE to be the wetting phase. Nevertheless, in both cases, the model provides a very good prediction of the effects of dissolution on contact angle. Both model predictions shown are based
FIGURE 9. Dissolution of TCE in Nanopure water, showing the effects of slip/stick behavior. Model predictions are shown for segments where drop contact diameter remains constant. on the literature value for the interfacial tension of pure PCE (47.48 mN/m). Although the interfacial tension of PCE in the CTAB solution is likely much lower, perhaps on the order of 20 mN/m (the drops in Figure 8 were too small for meaningful interfacial tension measurements), the fact that the drops are small means that model predicted curves of contact angle versus volume are very insensitive to interfacial tension (Figure 5). Although drops of PCE do remain pinned during dissolution, and as such follow model-predicted trends, more work is needed examining the dissolution of larger PCE drops. One of the challenges of working with PCE is that its low solubility (approximately an order of magnitude lower than that of TCE) means that the driving force for dissolution is lower, the aqueous solution becomes saturated after a much smaller volume has dissolved, and dissolution proceeds very slowly. Future work with PCE and other low solubility liquids may consider the use of flow-through systems, to allow larger volumes of solution to contact the drop. While most dissolution experiments have shown continuous decreases in contact angle with dissolution down to very small volumes, some have exhibited slip at seemingly random points, possibly due to surface heterogeneity or unnoticed external disruption (e.g., vibration, temperature change, etc.). Figure 9 shows an experiment examining the dissolution of TCE in water. Like the experiments in previous figures, the data in Figure 9 show an initial decrease in interfacial tension and a corresponding drop rearrangement, followed by a longer-term gradual decrease in measured interfacial tension. Unlike previous experiments, however, the contact diameter of the drop in Figure 9 suddenly decreased at a volume of approximately 13 µL, and the contact angle jumped from 74.8° to 107.8°. In terms of the actual drop rearrangement on the surface, the decrease in contact diameter corresponded to the slip of one side of the drop while the other side remained pinned. Following the initial slip, the drop remained pinned down to a volume of approximately 9 µL (13 h later), began to slip again, and then eventually was pinned again from a volume of approximately 4 µL (approximately 40 h after the initial slip). At its final contact diameter, the drop dissolved completely without slipping further. Because the drop images remained close to symmetrical during the entire dissolution process, analyses of volume and contact angle were possible down to a volume
of 0.34 µL and a corresponding contact angle of 6.7°. Although further drop images were too flat for analysis with the software, visual observation of drop images below that volume shows eventual disappearance of the drop from the surface without any further slip and approach a 0° receding contact angle. Implications for Environmental Systems. In subsurface environmental systems, DNAPL drops are unlikely to be positioned on flat surfaces as they are in this work, but are more likely to be entrapped in aquifer pores. Within an aquifer pore, the DNAPL is likely to be the nonwetting phase, at least initially. However, if dissolution reduces the contact angle between the DNAPL and the aquifer material surface, as was observed in this work, the apparent wettability of the system may gradually change over time, with the DNAPL exhibiting a very small contact angle with the aquifer material surface. To mobilize newly entrapped DNAPL as a separate phase, the receding contact angle and corresponding interfacial forces will resist DNAPL motion. If the DNAPL has dissolved and its contact angle with the surface has approached zero, then additional hydrostatic force will be needed to mobilize the DNAPL. This scenario may lead to flow bypassing of smaller pores, and longer remediation times. Future experiments examining dissolution from capillaries, and the effects on corresponding forces needed to cause them to drain, would provide useful insight into this possible scenario. Additional experiments examining the effects of high concentration surfactants likely to be used in remediation applications would also be useful. One preliminary experiment we conducted with TCE in a high concentration SDBS solution (data not shown) showed some slipping in the drop footprint with dissolution, but nevertheless found a continuous decrease in contact angle with dissolution. More work would be needed to understand this behavior and to determine the surfactants and conditions likely to produce it.
Acknowledgments This material is based upon work supported by the National Science Foundation under Grant No. BES-0092995.
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Received for review July 29, 2004. Revised manuscript received December 17, 2004. Accepted December 21, 2004. ES048810O
