J Appl Physiol 97: 704-715, 2004.
First published April 2, 2004; doi:10.1152/japplphysiol.00089.2003
8750-7587/04 $5.00
INNOVATIVE METHODOLOGY
Constrained sessile drop as a new configuration to measure low surface tension in lung surfactant systems
Laura M. Y. Yu,1
James J. Lu,1
Yawen W. Chan,1
Amy Ng,2
Ling Zhang,1
Mina Hoorfar,1
Zdenka Policova,1
Karina Grundke,3 and
A. Wilhelm Neumann1
1Department of Mechanical and Industrial Engineering, University of Toronto, Toronto M5S 3G8; 2Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 3E5; and 3Institut für Polymerforschung Dresden, 01069 Dresden, Germany
Submitted 29 January 2003
; accepted in final form 23 March 2004
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ABSTRACT
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Existing methodology for surface tension measurements based on drop shapes suffers from the shortcoming that it is not capable to function at very low surface tension if the liquid dispersion is opaque, such as therapeutic lung surfactants at clinically relevant concentrations. The novel configuration proposed here removes the two big restrictions, i.e., the film leakage problem that is encountered with such methods as the pulsating bubble surfactometer as well as the pendant drop arrangement, and the problem of the opaqueness of the liquid, as in the original captive bubble arrangement. A sharp knife edge is the key design feature in the constrained sessile drop that avoids film leakage at low surface tension. The use of the constrained sessile drop configuration in conjunction with axisymmetric drop shape analysis to measure surface tension allows complete automation of the setup. Dynamic studies with lung surfactant can be performed readily by changing the volume of a sessile drop, and thus the surface area, by means of a motor-driven syringe. To illustrate the validity of using this configuration, experiments were performed using an exogenous lung surfactant preparation, bovine lipid extract surfactant (BLES) at 5.0 mg/ml. A comparison of results obtained for BLES at low concentration between the constrained sessile drop and captive bubble arrangement shows excellent agreement between the two approaches. When the surface area of the BLES film (0.5 mg/ml) was compressed by about the same amount in both systems, the minimum surface tensions attained were identical within the 95% confidence limits.
constrained sessile drop; sharp knife edge; ultra-low surface tension; film leakage; spread dipalmitoyl phosphatidylcholine film
LUNG SURFACTANT PLAYS A CRUCIAL role in respiration. Its primary function is to reduce the surface tension at the air-liquid interface in alveoli during respiration. The reduction in surface tension lowers the energy required to inflate the lungs during breathing. As a result of surface tension changing during respiration, the alveoli are also protected against collapse and overdistention of the lungs (19, 20). The work of Avery and Mead (2) identified a deficiency of lung surfactant in the alveolar cavity of newborn babies as the primary cause of neonatal respiratory distress syndrome. Lung surfactant lining the inner surface of the alveoli is a complex mixture of lipids and proteins. It is comprised of 
85–90% phospholipids, 4–7% neutral lipid, and 6–8% surfactant proteins (21). The phospholipid fraction is in turn made up of 30% dipalmitoyl phosphatidylcholine (DPPC), a saturated phospholipid, and 70% of other monosaturated and unsaturated phospholipids (9, 21, 23). DPPC is the main contributor to a film capable of attaining near-zero surface tension at the air-liquid interface in the alveoli during respiration (10, 11). There are also four surfactant-associated proteins (SP), denoted as SP-A, SP-B, SP-C, and SP-D. One of the functions of SP-A is to enhance surface adsorptivity (16), and it is also involved in the pulmonary defense system together with SP-D (10, 14, 23). The function of SP-B and -C is to enhance the surface film characteristics during dynamic compression and expansion (10, 14, 23).
Because of the biological significance of lung surfactant in respiratory mechanics, its interfacial properties and characteristics have been of special interest to researchers since its discovery by von Neergaard in 1929 (31). An early method of measuring surface tension in lung surfactant was the Langmuir-Wilhelmy (L-W) film balance. Although near-zero surface tension measurements during dynamic compression and expansion of the surfactant film had been recorded by using the L-W film balance by some of the earlier researchers in lung surfactant (12, 15, 22), the methodology suffers from a drawback. The barrier would create waves in the trough if the surfactant film were dynamically compressed and expanded at frequencies comparable to human breathing (24). To circumvent the problems, Adams and Enhörning (1) developed the pulsating bubble surfactometer, in which an air bubble formed at the end of a plastic capillary is pulsating in the fluid and pressure changes across the air-liquid interface are recorded. Surface tension is then assessed by use of the Laplace equation of capillarity for spherical surfaces (8). However, the assumption of spherical surfaces can become invalid and introduce errors, particularly at low surface tension at which the spherical shape of the bubble cannot be maintained (24). The effect of gravity on bubble deformation at low tension and other factors such as inertial effects and dilatational viscosity were extensively studied by Chang and Franses (4).
Another major drawback of the pulsating bubble surfactometer is that it is unable to prevent film leakage (24, 28, 29). Film leakage occurs for thermodynamic reasons: When surface tension has reached a sufficiently low value, the surface film will spread onto nearby solid surfaces to minimize the overall free energy of the system (24, 29), but this is not a problem in Teflon-lined L-W balance (6). Further discussion of these points can be found in Refs. 6, 13, 28, 29.
To circumvent the film leakage problem, Schürch and colleagues (25, 28, 30) developed the captive bubble (CB) arrangement in which an air bubble is directly injected into the chamber filled with lung surfactant. The bubble remains separated from the ceiling of the chamber by a liquid film. Consequently, the closed continuous surface of the air bubble prevents the adsorbed surfactant film from the inadvertent leakage of spreading. The CB in conjunction with axisymmetric drop shape analysis (ADSA) was used extensively in our laboratory to study dynamic surface tension of lung surfactant. Although the CB arrangement avoids the problem of leakage, it becomes inapplicable at high surfactant concentrations because of opaqueness (produced by the scattering of light from surfactant aggregates) of the lung surfactant preparation at high concentrations (>1.0 mg/ml). Therefore, studies have been limited to low surfactant concentrations, one order of magnitude below the physiological concentration. Although the CB chamber is limited to low surfactant concentration, it is presently used extensively in our laboratory for gas-transfer studies across lung surfactant films (32). In fact, the CB arrangement is presently the only effective methodology to study dynamic surface tension and pressure changes across an interfacial film simultaneously. Codd et al. (7) developed a new spreading technique used in conjunction with the CB that allows studying surface activity of lung surfactant at physiological concentrations and small volume. Putz et al. (26) also developed another spreading technique that allows spreading of lung surfactant components at the air-water interface of an air bubble inside the CB chamber. There is an alternative setup, the pendant drop arrangement, which has been used in our laboratory for similar purposes (29). The main advantage of this setup is that it is not limited by surfactant concentrations, in addition to the simplicity of the setup, which allows a large throughput of experiments. Therefore, lung surfactant concentrations can be studied under physiologically relevant conditions. However, the setup also suffers from the film leakage problem.
The purpose of this paper is to present a new configuration for measuring low surface tension that circumvents both the concentration and film leakage restrictions by using a sharp knife edge in a constrained sessile drop (CSD) arrangement. In conjunction with ADSA, the CSD arrangement can be used to study the static and dynamic properties of lung surfactant at any concentration and a wide range of dynamic frequency, including relevant physiological conditions. A further advantage is that microliter quantities of liquid are needed.
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MATERIALS AND EXPERIMENTAL METHODS
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Organic liquids and surfactant materials.
Dodecane (99% purity) and cyclohexane (99.9+% purity, HPLC grade) were both purchased from Sigma-Aldrich Chemicals. The surface tensions of these liquids were measured and compared with literature data.
Bovine lipid extract surfactant (BLES) was used in all experiments. BLES was generously donated for research purposes by BLES Biochemical (London, ON, Canada). BLES samples were supplied at a concentration of 27 mg/ml and were used without further treatment. The surfactant composition of BLES consists of 98% by weight phospholipids and 2% by weight proteins. The phospholipid components are 45% DPPC, 35% unsaturated phosphatidylcholine, 12% phosphatidylglycerol, 2% phosphatidylethanolamine, 1% phosphatidylinositol, 1% lysophosphatidylcholine, and 2% sphingomyelin. The low-molecular-weight, hydrophobic surfactant-associated proteins SP-B and SP-C are present, whereas the high-molecular-weight, hydrophilic surfactant-associated proteins SP-A and SP-D are absent. All BLES samples were divided into small vials and stored in the freezer at –20°C until use.
DPPC was purchased from Sigma Chemical and stored at –20°C until the day of the experiment. It was used in our stability experiment to test whether the sharp edge is able to prevent leakage.
Design of the CSD holder (pedestal).
The main disadvantage of the pendant drop is its inability to operate at very low surface tension because of film leakage and the failure of the original CB to function at high surfactant concentration. The CSD (sitting on a "pedestal") avoids these two limitations. A horizontal sharp knife-edge circular boundary is employed in the pedestal design to prevent film leakage at low surface tension (i.e., <5 mJ/m2) as shown in the schematic diagram of Fig. 1. The pedestal is machined from stainless steel (SS316) with its outer and inner diameter being 2.5 and 0.5 mm, respectively. The angle from the base of the pedestal to the neck is 60°. This angle is important to prevent the sessile drop from sliding over the sharp edge. The top surface and the sides of the pedestal did not need to be treated with any coating to alter its wetting properties or as a secondary protection against film leakage. Digitized profiles of two pedestals were compared with an ideal profile. Sobel edge detection in Matlab (version 6.1) was used to obtain a profile of the pedestal. After edge detection, the profile was converted into pixel coordinates followed by noise reduction for further mathematical manipulation. Two straight lines were fitted to the horizontal and diagonal edge by use of the pedestal profile obtained after noise reduction. Figure 2A is a profile of a section on the "good" pedestal along its sharp edge. In the subsequent experiments, there was no leakage with this pedestal (see RESULTS AND DISCUSSION). The distance between each pixel is 0.011 mm. The point at which the two straight lines meet would indicate a perfect edge. Scanning electron micrographs of the pedestal shown in Fig. 2A are shown in Fig. 2, B and C. As shown in Fig. 2B, the edges are fairly smooth. When the pedestal was tilted at 60°, as shown in Fig. 2C, the side edge of the pedestal also shows no sign of jaggedness that could result in film leakage. Figure 3A shows a linear fitting to a poor-quality pedestal showing considerable curvature at the edge. Figure 3, B and C, is the corresponding scanning electron micrograph images taken at the same angles as those in Fig. 2, B and C.
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Fig. 1. Schematic of a sessile drop formed on the surface of the pedestal. The sharp knife edge of the pedestal prevents film leakage.
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Fig. 2. A: plot of the linear fittings to the edge of the pedestal to demonstrate the sharpness of the pedestal with a well-defined sharp edge compared with the pedestal with an ideal sharp edge as indicated by the intersection of 2 fitted straight lines. The distance between each pixel is 0.0111 mm. Also shown are scanning electron micrograph images (SEM) of the pedestal with a well-defined edge when viewed from the top (B) and when tilted by 60° from the horizontal plane (C).
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Fig. 3. A: plot of the linear fittings to the edge of the pedestal to demonstrate the sharpness of the pedestal with a poor knife edge compared with the pedestal with an ideal sharp edge as indicated by the intersection of 2 fitted straight lines. The distance between each pixel is 0.011 mm. Also shown are SEM images of the pedestal with a poor knife edge when viewed from the top (B) and when tilted by 60° from the horizontal plane (C).
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Experimental method and procedure.
The novel sessile drop configuration was used in conjunction with ADSA, which allows the setup to be fully automated. Image acquisition of the experimental drops runs automatically without intervention from the operator after the motor, controlled by an appropriately programmed controller, is started, as described in the next paragraph. ADSA was used to calculate surface tension from the experimental drop profiles. It is a technique for determining liquid-fluid interfacial tensions from the shape of axisymmetric menisci (17). The strategy employed in the technique is to minimize the deviation between the theoretical Laplacian curve and the experimental drop profile, which is extracted from the digitized image by a modified Sobel edge-detection technique. The best match yields the surface tension of the sessile drop with an accuracy of ±0.01 mJ/m2. Surface tension, surface area, volume, and the curvature at the apex of the drop are all output of ADSA. The quality of the fit between the theoretical Laplacian curve and the experimental drop profile was determined by computing the normal distance between the points on the theoretical Laplacian curve and the experimental curve. Thus ADSA determines the quality of the fit (or accuracy) by defining an error function, by minimizing the least square difference between the points on theoretical and experimental profile. Detailed developments of ADSA and its mathematical procedures have been described elsewhere (5, 27).
Figure 4 shows a complete schematic diagram of the CSD arrangement. A fiber-optic light source (Intralux 5000, Volpi) is used. Frosted diffusers together with a blue filter are used to ensure a uniformly lit background. The location and quality of the light source are critical to ensure optimum quality of the image. A high-performance charge-coupled device monochrome camera (COHU) is mounted on a microscope (Wild Heerbrugg type 400076). Images of the sessile drop are taken by using a Sunvideo analog frame grabber that can acquire images up to a rate of 20 frames/s. Images of the drop are digitized on the basis of 256 gray levels for each pixel and image resolution of 320 x 240 pixels. A SPARCstation 10 computer (Sun Microsystems) is used to store the acquired images and perform image analysis and computation. Surface tension and surface area of the sessile drop during dynamic cycling are recorded continuously by using a motor-driven syringe to change the volume of the sessile drop continuously. The rate of image acquisition in all experiments was 20 images/s. The syringe was filled with the test liquid, mounted onto the stepper-motor (Stepper Mike, Oriel), and connected to the pedestal via Teflon tubing. The drop was compressed and expanded, by changing drop volume by moving the syringe plunger back and forth by the appropriately programmed motor. The motor controller (Oriel) allowed the rate of volume change to be adjusted over a large range. Therefore, the overall arrangement can be operated in the periodicity of human breathing, and the surface tension response can be monitored simultaneously. Throughout the experiment, the sessile drop is covered with a glass cuvette (Hellma) to prevent contamination from the environment. A water bath (model RTE-111, Neslab) is used to maintain the desired temperature within the cuvette by controlling the temperature of the base of the supporting holder.
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Fig. 4. Schematic diagram of the constrained sessile drop (pedestal) setup. CCD, charge-coupled device.
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Before the start of each experiment, an image of a calibration grid is acquired and used as a calibrating scale for the drop image, as well as a correction for optical distortion. Next, an image of the pedestal before drop formation is acquired and digitized. The two edge points from the left and right edge of the pedestal are chosen and used as input. These two coordinates serve as a baseline for the sessile drop. First, a sessile drop of the test liquid is formed by using the motor. The motor controller is programmed appropriately to form a drop of 4–4.5 µl. As liquid is being pumped into the initially small drop, the drop front advances over the top surface until it covers the entire circular surface. The sharp knife edge prevents the drop from spreading over the edge of the pedestal. After drop formation, adsorption is allowed for 1 min, which is sufficient for high concentration of BLES because the equilibrium surface tension of 23–25 mJ/m2 is reached almost instantaneously. The motor controller is then switched to the program for the dynamic cycling experiment. At the end of each run, the sessile drop is removed by use of a syringe mounted on a micromanipulator.
Surface tensions of dodecane and cyclohexane were measured and compared with their respective literature values to study the applicability of ADSA to the CSD technique. Fifty images were acquired on the static drop during a 10-s period.
On the day of the experiment, BLES was allowed to thaw and warm up for at least 0.5 h after it was taken from storage at –20°C. It was then diluted to the desired concentration with a physiological salt solution. The final pH of the BLES preparation was measured to be 5.6. The suspension was mixed thoroughly by vortexing (Vortex-Genie, Fisher Scientific). The salt solution was made up of 0.6% by weight NaCl (Sigma) and 1.5 mmol/l CaCl2 (Sigma). The pH of the salt solution was 5.3.
The stability of a spread DPPC film was studied at 37°C in conjunction with ADSA to test the ability of the sharp edge to prevent film leakage. DPPC was allowed to thaw for at least 1 h after being taken from storage at –20°C. DPPC was dissolved in a 9:1 heptane-ethanol mixture to prepare a concentration of 0.02 mg/ml. Heptane was used as a spreading solvent to deposit DPPC on the surface of a saline sessile drop by means of a 5-µl microsyringe (Hamilton). The 5-µl microsyringe was mounted horizontally on a micromanipulator. After a saline drop was formed on the pedestal, the microsyringe was lowered to a position just above the apex of the saline drop. The volume of DPPC solution spread on the surface of the drop was 1.5 µl. The sessile drop was then compressed at a rate of 5.5 µl/min to 30% of its original surface area. The drop was held at the compressed state for a duration of 10 min to test for film leakage at the sharp knife edge.
At the end of the experiment, the pedestal, syringes, and plastic connectors were cleaned in an ultrasonicator bath (Bransonic 52) five times for 15-min duration each. The cleaning solvents used in each of the five sonication procedures are listed in sequence in Table 1. The Teflon tube and other glassware were soaked in chromic acid overnight and cleaned with demineralized and distilled water. All cleaned equipment was then dried under a heat lamp.
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RESULTS AND DISCUSSION
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The applicability of ADSA to the CSD configuration was determined by measuring the surface tension of dodecane and cyclohexane. The average values of surface tension and the 95% confidence limits are given in Table 2. The surface tension of dodecane agrees with the literature value within the 95% confidence limit. However, for cyclohexane, the reported surface tension has a 1% error compared with the literature value. One possible reason for the 1% higher value may be evaporation and hence cooling of the surface of the cyclohexane drops.
Preliminary work performed using the CSD arrangement at 23°C shows results with no evidence of film leakage when a BLES film at 5.0 mg/ml was compressed at a relatively slow rate of compression and expansion, as shown in Fig. 5. The results clearly demonstrate that there is no evidence of film leakage during dynamic cycling of the BLES film under these conditions, and ultra-low surface tension is recorded. As apparent in Fig. 5, the volume of the drop is only a few microliters, an added advantage of the new design. Figure 6 is an enlargement of the rectangular region of Fig. 5 showing the surface tension response during the first compression cycle. Figure 6 clearly shows a pattern of film collapse as indicated by the three peaks, showing sudden increase and steady decrease in surface tension in each case. The most important point to be noted in Fig. 6 is that a surface tension as low as 0.23 ± 0.01 mJ/m2 was recorded during the first compression cycle.
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Fig. 5. Dynamic experiment of bovine lipid extract surfactant (BLES; 5.0 mg/ml) at 23°C. Also shown is period of 20 s using the constrained sessile drop arrangement.
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Fig. 6. Enlargement of boxed region in Fig. 5. The first compression cycle of BLES (5.0 mg/ml) at 23°C shows patterns of film collapse.
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To conform completely to physiological conditions, lung surfactant studies at 37°C and a period of 3 s were also performed with a first generation setup at a compression ratio of 18%. A typical result is shown in Fig. 7. Figure 8 is a plot of surface tension vs. relative surface area of the first compression cycle shown in Fig. 7. A surface tension of 1 mJ/m2 was obtained in the initial cycle as shown in both Figs. 7 and 8, which agrees with previously performed experiments (3, 6). Figure 9 shows the curves of surface tension and volume both plotted against time for the first two compression cycles of Fig. 7. It is clearly shown in this figure that, when surface tension is reduced to 1 mJ/m2, the volume-vs.-time curve is smooth with no sudden decrease, which would suggest film leakage. Figure 10 shows a typical output of ADSA when a poor-quality pedestal was used (see Fig. 3A) and film leakage occurred. Clearly, there is a sudden decrease in the volume vs. time. The surface tension in that cycle also shows a higher surface tension compared with the previous compression cycles. Figure 11 is a series of images captured during the first dynamic cycle of BLES (5.0 mg/ml) at 3 s/cycle and 37°C. These images also support the conclusion that the sharp edge prevents film leakage when low tension is attained (see Fig. 11, E–G). A concentration restriction due to opaqueness of the dispersion at higher surfactant concentration, obviously, does not exist, because imaging of the sessile drop is through the air phase and not the liquid phase as in the CB arrangement (see Fig. 11).
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Fig. 7. Dynamic experiment of BLES (5.0 mg/ml) at 37°C, period of 3 s, using the constrained sessile drop arrangement.
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Fig. 10. Dynamic experiment of BLES (5.0 mg/ml) at 37°C, period of 5 s, using the constrained sessile drop arrangement (with the pedestal profile shown in Fig. 3, B and C) showing the occurrence of film leakage.
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The fast dynamic study performed on the small sessile drop may raise a concern that the fast cycling may distort the Laplacian surface and ADSA would fail to provide accurate surface tension measurement. It is evident from Fig. 11 that the Laplacian surface is not distorted because of the fast compression and expansion of the sessile drop. To demonstrate the applicability of ADSA in calculating surface tension of dynamic drops, the theoretical Laplacian fittings to the experimental profile of a static sessile drop and one taken during dynamic cycling using ADSA (see Fig. 12, A and B, respectively) were performed. Figure 12, A and B, were chosen such that their volume and surface tension values are approximately the same. Table 3 summarizes the output of ADSA obtained for both the static and dynamic sessile drops. The error function values obtained for the static and the dynamic sessile drop are similar and very small. Thus the validity of ADSA to calculate the surface tension from the experimental drop shapes is not compromised under fast dynamic conditions.
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Fig. 12. Experimental drop images taken during static (A) and dynamic (B) cycling conditions with approximately the same drop volume.
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To increase confidence in the novel CSD arrangement for measuring low surface tension, results were compared with those obtained with the CB. Because of liquid opaqueness at higher surfactant concentration in the CB arrangement, experiments were performed using a BLES concentration of 0.5 mg/ml with both setups at 37°C and a period of 3 s. Figure 13 shows the surface tension response as a function of time. Surface tension values measured by using the CB and the CSD are essentially the same within the 95% confidence interval, on the basis of a one-factor ANOVA test. The average maximum and minimum surface tensions obtained in the first five cycles using the CB and the pedestal were also compared; the results are shown in Table 4. The first compression minimum surface tension measurement was ignored in the analysis because the lung surfactant film may behave differently from the subsequent cycles. The comparison also showed that surface tension measurements using the two methodologies are in good agreement. Figure 14 is a plot of surface tension vs. relative surface area to indicate that the results obtained in the CB experiment are also reproducible by using the CSD methodology. From Fig. 14, it appears that a slightly higher compression ratio is required to reduce surface tension to 5 mJ/m2 in the CSD than in the CB system. This slight difference may be due to the fact that the BLES samples used in the two experiments were from different batches and the quality of the adsorbed film may have been slightly different, a frequent occurrence at low BLES concentrations (18).
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Fig. 13. Comparison of dynamic experiments performed by use of the captive bubble and the constrained sessile drop arrangement of BLES (0.5 mg/ml) at 37°C, period of 3 s, and compression ratio of 18%.
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The ability of the sharp edge to prevent film leakage was tested further by studying the stability of a spread DPPC film. The result is shown in Fig. 15. The amount of DPPC (0.02 mg/ml) spread on the surface of the drop was 0.03 µg, and the resulting film was compressed at a rate of 3.15 molecules·
–2·min–1 to 34% of its original surface area and held in the compressed state for 10 min. During the 10-min period, the volume of the sessile drop was seen to decrease because of evaporation. The volume of the drop is decreasing steadily, with no sudden decrease that could be attributed to film leakage. It is important to point out that if film leakage occurred, surface tension would increase toward its equilibrium value. Lost DPPC molecules from the surface of the drop due to film leakage would not be replenished from the bulk because they were deposited onto the surface of the sessile drop. It is also interesting to note that the slow evaporation and the concomitant decrease in surface area caused a further decrease in surface tension to a value of 0.75 mJ/m2 at the end of 10 min.
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Fig. 15. Film leakage test of the sharp edge of the pedestal by studying the stability of spread dipalmitoyl phosphatidylcholine (DPPC) film. The amount of DPPC (0.02 mg/ml) spread onto the surface of the sessile drop was 0.03 µg.
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In conclusion, the CSD arrangement eliminates both the problems of film leakage as well as concentration restrictions due to opaqueness of surfactant suspension at higher concentrations. With the automated control of ADSA, the experimental arrangement can be operated at the periodicity of human breathing, requiring only small amounts of surfactant. Results obtained from the CSD arrangement agree very well with those obtained from the CB at relatively low concentrations, i.e., the only ones accessible in the original CB configuration.
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GRANTS
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This work was supported by a grant from the Canadian Institute of Health Research (grant MOP38037 and Ontario Graduate Scholarship for Science and Technology (L.M.Y. Yu).
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ACKNOWLEDGMENTS
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We thank BLES Biochemicals for the generous donation of the BLES samples.
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FOOTNOTES
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Address for reprint requests and other correspondence: A. W. Neumann, Dept. of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Rd., Toronto, ON, Canada M5S 3G8 (E-mail: neumann{at}mie.utoronto.ca).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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