Langmuir 1996, 12, 2041-2044
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Determination of the Air-Water Interfacial Area in Wet “Unsaturated” Porous Media Milind V. Karkare† and Tomlinson Fort* Department of Chemical Engineering, Vanderbilt University, Nashville, Tennessee 37235 Received October 2, 1995. In Final Form: January 2, 1996X A method is proposed for determining the area of the air-water interface in wet but unsaturated porous media. The method depends on determining the critical concentration of surfactant necessary to achieve water movement within the system. Effective surfactants are insoluble in water, are spread as monolayers at the air-water interface, and form solid monolayers which have little or no effect on the surface tension of water until surface concentration of surfactant molecules reaches a known critical value. At this critical concentration, capillary pressure gradients are established within the system, and water moves. Studies of the effects of different water concentrations on air-water interfacial areas show the correct trends and trend toward the correct limits. Advantages and limitations of the technique are discussed. The airwater interfacial area in wet unsaturated porous media has not previously been experimentally accessible.
Introduction When wet particulate material is packed together, the spaces between particles from a network of interconnected pores. If the amount of water is insufficient to fill the pores, the water which is present coats the surface of the (hydrophilic) particles and collects in the spaces between them. The remaining pore space is filled with air. The area of the air-water interface in such systems is an important quantity for effective modeling of drying/airstripping processes, trickle bed reactors, fluidized bed reactors, and other situations where gas-liquid transport is important. This air-water interfacial area has not been experimentally accessible. The present paper describes a method of determining it. The method depends on knowing the space occupied by surfactant molecules when they spread as a monolayer at the air-water interface. We have reviewed the literature on surfactant spreading on water.1 All reports in the review describe spreading experiments on bulk water where the surface is flat and of significant size. When water is present in an “unsaturated” porous medium, the water film is curved, very thin, and of nonuniform thickness. Surfactant behavior on thin water films in such systems has received very little attention. However, we have shown that if certain water insoluble surfactants are applied to part of such a system, a significant water movement from the “surfactant containing” into the “surfactant free” region of the system occurs.1,2 We have established criteria for surfactant effectiveness as water moving agents1 and have proposed a capillary pressure model which quantitatively explains the flow.3 We have also shown4 that, in contrast to earlier suggestions,2,5,6 momentum transfer from the spreading monolayer does not contribute to the flow process. * To whom correspondence should be addressed at the Department of Chemical Engineering, Box 1604 Station B, Vanderbilt University, Nashville, TN 37235.
[email protected]. Phone: (615) 322-2441. FAX: (615) 343-7951. † Present address: W. R. Grace & Co., Construction Products Division, 62 Whittemore Ave., Cambridge, MA 02140. X Abstract published in Advance ACS Abstracts, March 15, 1996. (1) Karkare, M. V.; La, H. T.; Fort, T. Langmuir 1993, 9, 1684. (2) Tschapek, M.; Wasowski, C.; Sanchez, R. M. T. Colloids Surf. 1981, 3, 295. (3) Karkare, M. V.; Fort, T. Langmuir 1993, 9, 2398. (4) Karkare, M. V.; Fort, T. Langmuir 1994, 10, 3701. (5) Tschapek, M.; Wasowski, C. Colloids Surf. 1982, 5, 65. (6) Tschapek, M.; Wasowski, C.; Falasca, S. Colloids Surf. 1984, 11, 69.
0743-7463/96/2412-2041$12.00/0
As an extension of this work, we investigated the effect of surfactant concentration on water movement. We found that a reproducible “critical” quantity of surfactant is necessary to move water. In this paper we show how this critical quantity can be used to calculate the area of the air-water interface in wet but “unsaturated” porous media. The systems actually studied were wet sand and wet glass beads. The surfactant was 1-tetradecanol. Experimental Section The sand was Fisher Washed Sea Sand (Lot No. 915262B) purchased from Fisher Scientific Co., Springfield, NJ. The specific gravity of the sand was determined to be 2.6 g/cm3, while the apparent density of the sand in packed columns was 1.421.48 g/cm3. Glass beads of 0.09 mm nominal diameter were purchased from Jaygo, Inc., Mahwah, NJ. The specific gravity of the beads was 2.84 g/cm3, while the apparent density of the beads in packed columns was 1.70-1.75 g/cm3. The shape and size of the sand particles and glass beads were determined with a scanning electron microscope. Many measurements were made. Dimensions of the particles were determined from photomicrographs by measuring grain sizes with a ruler. The sand particles showed a wide variation in shape and size. The average diameter, defined as the average of the length and width of the particles, was 0.2 mm. The glass beads were spherical in shape with a narrow particle size distribution. The measured average diameter of the 0.09 mm beads was 0.13 mm. 1-Tetradecanol (97%) was obtained from Aldrich Chemical Co., Milwaukee, WI, and was used as received. Deionized water was distilled from alkaline KMnO4 solution before use in water movement experiments. Chloroform (ACS certified, spectranalyzed) obtained from Fisher Scientific Co. was used to prepare stock solutions of 1-tetradecanol. The experimental setup and technique for following the water movement have been described.1 The middle 10 cm section of a 20 cm long glass tube was used to pack wet sand or glass beads with known water content. The left half of the column also contained surfactant in small amounts. The column was placed horizontally. After 24 h, the water content of different sections along the column was determined gravimetrically and was reported as wt % based on the weight of dry sand or beads. All experiments were performed at room temperature of 23 °C.
Results and Discussion Typical results when an excess of 1-tetradecanol is applied to one side of a column of “unsaturated” wet sand are shown in Figure 1. The assembly contained approximately 90 g of sand. The specific geometric surface area of the sand was about 130 cm2/g. The initial concentration of water was a uniform 9.0% throughout © 1996 American Chemical Society
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Figure 1. Movement of water in wet sand caused by a spreading monolayer of 1-tetradecanol. Position indicates distance from the left end of the column. Sand in the 0-5 cm section contained 0.3% 1-tetradecanol, and sand in the 5-10 cm section was surfactant free, at the beginning of the experiment which lasted 24 h.
Karkare and Fort
Figure 2. Effect of varying amounts of surfactant on water movement. The indicated amount of 1-tetradecanol was added to the left side of the column at the beginning of the experiment.
the column. The initial concentration of 1-tetradecanol on the left side was 0.3%. Both numbers were based on the weight of the dry sand. The system was unsaturated, since complete pore filling would have required about 3 times as much water as was present. The figure shows that after 24 h the water content on the left side had decreased from 9% to 5.0-5.5% and that the water content on the right side had increased from 9.0% to 12-13%. The new distribution of water was stable for as long as we measured it (2 months). Our capillary pressure model3 explains these results. The water within the partially filled pores is held in place by capillary forces, and equilibrium is achieved when the capillary pressure, ∆P, is uniform everywhere. If the curved water-air interfaces can be modeled as segments of spheres so that their radii of curvature (r) are equal, and γ is the surface tension of water, then
∆P ) 2γ/r Because the sand surface is wet by water, the water-air interface is concave, so r and ∆P are both negative. If a surfactant like 1-tetradecanol is applied to one side of the assembly, it spreads over the air-water interface on that side and γ is lowered. As a result, ∆P on the side covered by surfactant is made less negative and the capillary pressure equilibrium is brought out of balance. The water moves to a new position where capillary pressures are balanced again. We wanted to learn how variation of alcohol concentration affected this water movement and so began a systematic study. A number of experiments were performed with initial water content a uniform 12 wt %. The amount of 1-tetradecanol added to the left side of the assembly was varied by 3 orders of magnitude, from 0.0025% to 0.6% of dry sand weight. Results of these experiments are given in Figure 2, which shows that there is a sharp demarcation between effective and noneffective quantities of this surfactant. When the amount of 1-tetradecanol added was below about 0.001 wt %, essentially no water movement was effected. When the amount of 1-tetradecanol added was above about 0.001 wt %, water movement occurred. Water movement
Figure 3. Monolayer behavior of 1-tetradecanol. The areas per molecule of surfactant at which an effect on the surface tension of water (surface pressure) is first observed and at which the equilibrium spreading pressure is achieved are noted.
increased as the amount of 1-tetradecanol increased from 0.001 wt % to 0.003 wt %. Quantities of 1-tetradecanol greater than 0.003 wt % moved no additional water. These results prompted us to review the monolayer behavior of 1-tetradecanol.1,7 This surfactant has an extremely low solubility in water. Its equilibrium spreading pressure is 45.4 mN/m at 23 °C. Data obtained with a film balance and presented in Figure 3 show that 1-tetradecanol forms a solid monolayer which effects essentially no reduction in surface tension until the area per 1-tetradecanol molecule is reduced to about 0.22 nm2. The solid monolayer is not very compressible. The area per surfactant molecule at the equilibrium spreading pressure is about 0.19 nm2. This information, with our capillary pressure model, can explain both the critical concentration of 1-tetradecanol necessary for water movement and also the shape of the curve shown in Figure 2. As the amount of (7) Gaines, G. L., Jr. Insoluble Monolayers at Liquid-Gas Interfaces; Interscience Publishers: New York, 1966.
Air-Water Interfacial Area
1-tetradecanol applied to our wet unsaturated system increases, the air-water interfacial area available to each surfactant molecule decreases. Capillary pressures are unaffected at first. However, when the area is reduced to 0.22 nm2 per surfactant molecule, the surface tension in the left side of the assembly falls. A capillary pressure gradient between the left and right sides is established, and water moves to reestablish equilibrium. As more 1-tetradecanol is applied, the surface tension of the water on the left side continues to fall. Since 1-tetradecanol forms a solid monolayer, large changes in surface tension, and therefore differential capillary pressure, are effected by relatively small additions of surfactant. The maximum effect on surface tension and differential capillary pressure occurs when sufficient surfactant is present to achieve the equilibrium spreading pressure. Increases in the amount of surfactant above the amount necessary to achieve the equilibrium spreading pressure should have no further effect on these quantities. This explanation led directly to a possible new method for determining the area of the air-water interface in wet but unsaturated porous media. The area is, simply, the product of the number of molecules of surfactant required to just initiate water movement (Ccrit) times the area occupied by each molecule when water movement just begins, which for 1 tetradecanol is 0.22 nm2. To obtain the most accurate value for Ccrit, the water movement data around this concentration are replotted with a linear surfactant concentration scale (plot not shown here). A tangent is then drawn to the rising water movement curve. The point of intersection of this tangent with the baseline is taken as Ccrit. For the example shown in Figure 2, Ccrit was determined to be 0.001 28 wt % or 0.000 012 8 g/g of sand. Using Avogadro’s number and the molecular weight of 1-tetradecanol (214.4 g/mol), the specific surface area of the air-water interface was calculated to be 79 cm2/g of dry sand or 71 cm2/g of wet sand mixture which contains 12% water. We wanted to confirm the validity of this new method. Direct confirmation was not possible because no other experimental method to measure the air-water interfacial area in wet unsaturated porous media was known. Calculation of the area by mathematical modeling is very complex and had not been attempted. We did know that the air-water interfacial area had to decrease as percent water saturation increased since more water would progressively fill up the pore spaces. We decided to repeat the experiments with different amounts of water to see if we could observe this trend. Ccrit values were determined at different initial water contents. With practice, we found that six to eight experiments at a given water content could define the rising part of the water movement vs the amount of surfactant present curve and so allow us to calculate Ccrit. These critical amounts of surfactant were transformed to air-water interfacial areas, as described above. Results of these experiments are shown in Figure 4 in which air-water interfacial area is plotted as a function of initial wt % water. The graph shows that as water saturation increased the area calculated for the air-water interface did decrease. It is also most significant that the line connecting the data points extrapolates to the (independently determined) 130 cm2/g area of the dry sand at 0 wt % water and to 0 cm2/g at 30 wt % water which is the quantity of water just sufficient to saturate the system. A second, but similar, set of experiments was conducted using glass beads instead of sand. The beads were spherical with a narrow particle size distribution. Average bead diameter was 0.13 mm. The air-water interfacial
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Figure 4. Effect of varying amounts of water in wet sand on the critical amount of 1-tetradecanol necessary to effect water movement.
Figure 5. Effect of varying amounts of water in wet glass beads on the critical amount of 1-tetradecanol necessary to effect water movement.
area vs initial wt % water curve found for the beads is shown in Figure 5. Again, as water saturation increased, the area calculated for the air-water interface decreased. And again, the line connecting the data points extrapolates to the proper limits. These are the (independently determined) 167 cm2/g area of the dry beads at 0 wt % water and to 0 cm2/g at 22.5 wt % water, which is the quantity of water just sufficient to saturate this system. Results of both sets of experiments qualitatively confirm the validity of the method, which we now propose as a new technique for measuring air-water interfacial areas in wet but unsaturated porous media. We do note that the areas obtained in this way are areas for a 1-tetradecanol covered water surface. 1-Tetradecanol was chosen as the surfactant because it has a very high equilibrium spreading pressure and forms a solid monolayer which has little or not effect on the surface tension of water until the surfactant molecules are almost close-packed in the monolayer. Other surfactants could also be used as long as they followed the criteria for effectiveness established by our earlier work.1 We also note that there are hysteresis effects in these systems. The location of the water, and presumably the area of the air-water interface, depends on whether the water has most recently sorbed into or desorbed from the pore spaces.3 All of the areas reported here are desorption
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completion of water movement depends on the unsaturated hydraulic conductivity of the packed material. This time can be determined for any system by conducting experiments like those described. The second practical consideration involves the amount of material needed for tests. We have usually used a 2.75 cm diameter × 10 cm long column but, in a number of experiments, have investigated water movement in columns with lengths varying from 5 to 50 cm. Water movement data from these experiments show that column length does not affect the results obtained. We believe that a much smaller column, with smaller sample size, can be used to determine the air-water surface area in wet unsaturated porous media. Shortening the column should facilitate rapid completion of water movement. Summary and Critique
Figure 6. Effect of time on water movement in wet sand. Initial water concentration was a uniform 12 wt %. Initial concentration of 1-tetradecanol surfactant was 0.1 wt % on the left side of the column.
areas since water moves out of the surfactant-containing region of the system where surface areas are measured. Desorption areas are of prime importance for understanding drying/dewatering processes. However, it would be most interesting to also obtain sorption areas and so obtain information about the hysteresis effect. Two practical considerations involved in this method were investigated. In all the experiments described so far, the assembly was analyzed for water content 24 h after addition of the surfactant. This time period may be long if many measurements are to be made. So, we investigated the time required for water movement to be complete. Figure 6 shows water movement as a function of time for different sand columns, all of which initially contained a uniform 12 wt % water, and 0.1% tetradecanol in their left halves. In these systems most water movement is complete in less than 1 h. The time required for
A technique is described for determining the air-water interfacial area in wet but unsaturated porous media. The technique depends on determining the “critical” quantity of surfactant necessary to move water in such systems. The technique appears to give accurate information about the area of air-water interface. It is applicable to small specific areas, on the order of 100 cm2/g or less. It works at room temperature with very simple and inexpensive equipment. It is limited to water wet solids. Like vapor adsorption methods, the technique measures surfaces in interconnected spaces. However, in contrast to vapor adsorption methods which may require a multilayer (e.g., BET) model for surface area determination, our new method is definitely limited to a monolayer. The area per surfactant molecule at which water movement begins is accurately known. The water surface on which spreading occurs is both fluid and energetically homogeneous, which should lead to consistent and easily comparable surface areas in a wide variety of systems. Acknowledgment. Financial support for this work was provided by the National Science Foundation, Grant Number CTS-9213478. LA950821V
