Langmuir 1994,10, 3701-3704
3701
Flow in “Unsaturated”Porous Media Due to Water-Insoluble Surfactants: Role of Momentum Transfer from a Spreading Monolayer Milind V. Karkare and Tomlinson Fort* Department of Chemical Engineering, Vanderbilt University, Nashville, Tennessee 37235 Received October 21, 1993. In Final Form: July 11, 1994@ When certain water-insoluble surfactants are added to a part of a wet but water “unsaturated” porous medium, significant water movement from the surfactant-containing to the surfactant-free region occurs. This water movement has been ascribed to momentum transfer from a spreading surfactant monolayer to the underlying water molecules (Gibbs-Marangoni flow). The work reported here explores the applicability of this concept to water movement caused by 1-hexadecanolspreading in wet sand. Surfactant movement and water movement are measured separately and are shown to be independent. Acontribution from the momentum transfer mechanism to water movement in this system is thus invalidated. Some consequences of the widely different rates of surfactant and water movement are considered. Very slow rates of surfactant spreading require system premixing but are also responsible for long-term stability of uneven water distributions in the system.
Introduction
by a molecular process in which each molecule of surfactant was associated with a definite amount of water. When particulate material is packed together, a strucCrisp6 made a careful study of two-dimensional transture with a network of interconnected pores is formed. If port and defined and investigated a quantity he called these pores are partially filled with water, the system is the flow constant, Ks. He found Schulman and Teorell’s “unsaturated”. The water covers the surface of each proposed molecular process untenable and suggested that particle and collects in spaces between particles. If certain a n experimental artifact could have caused the behavior water-insoluble surfactants (e.g., 1-hexadecanol) are apthey found. plied to part of such a system, a significant water In a n interesting series of papers, O’Brien, Feher, and movement occurs from the “surfactant-containing” into Leja7-9 investigated surfactant spreading and related the “surfactant-free” region of the system. This flow water movement. They followed the progress of the phenomenon was first reported by scientists in Argentina’ and has been systematically studied in our l a b o r a t ~ r y . ~ ? ~monolayers both by interferometry and by monitoring temperature transients. Water movement under the The Argentine group4 suggested that the main driving monolayers was measured by photographing very small force for water movement was the existence of a surface plexiglass particles suspended a t various depths. The tension gradient between the two regions. depth of moving water was found to be greater than Surface tension gradients can cause water movement reported by Schulman and Teorell. The energy available in two ways. One way is by establishing capillary pressure from the spreading pressure was calculated and compared differences between the surfactant-containing and the with that required to move the water. Spreading speeds surfactant-free regions. The second way is by Gibbsof different materials were measured. Fast-spreading Marangoni flow, which we define as the dragging of water surfactants moved more water than slow-spreading surmolecules by momentum transfer from a spreading factants. The spreading speed was strongly dependent surfactant monolayer. The role of capillary pressure on the spreading pressure for a given homologous series differences is explored in a recent publication from our of compounds. laboratory3 and is shown to be capable of explaining both Benedetto et al.1° investigated a n application of Gibbsour results and the results of the Argentine group. This Marangoni flow. They showed that “eye drops)’ which paper focuses on Gibbs-Marangoni flow. contain solutions of polymers that have surfactant propAreview of relevant literature on surfactant spreading erties produce thicker tear films than normal by virtue of is presented in our earlier paper.2 The first quantitative their ability to drag water with them when they spread study of the dragging of water by a spreading monolayer over the ocular surface with each blink of the eyelid. was made by Schulman and T e ~ r e l l .They ~ devised a n All the investigations of Gibbs-Marangoni flow menelegant experimental system for measuring water transtioned so far were carried out on bulk water surfaces where port and calculated a n apparent boundary layer thickness the spreading of surfactant monolayers was relatively of 0.03 mm. This thickness varied with the viscosity of unrestricted. In “unsaturated” porous media the situation the underlying solution but not with the velocity of the is different. Channels for spreading are narrow and surfactant monolayer. They concluded that flow occurred tortuous, and the water in them is of varying depth. Consequently, the rates of spreading should be much * To whom correspondence should be addressed at the Departreduced. However, Tschapek and co-workers in Argenment of Chemical Engineering, Box 1604,Station B, Vanderbilt University, Nashville, TN 37235. Abstract published in Advance A C S Abstracts, September 1, 1994. (1)Tschapek,M.; Wasowski, C.; Torres Sanchez,R. M. Colloids Surf. 1981,3,295. (2)Karkare, M.V.; La, H. T.; Fort, T. Langmuir 1993,9, 1684. (3)Karkare, M.V.; Fort, T. Langmuir 1993,9, 2398. Wasowski, C.; Falasca, S. Colloids Sur$1984,11, (4)Tschapek,M.; 69. ( 5 ) Schulman,J. H.; Teorell, T. Trans.Faraday SOC.1938,34,1337. @
(6)Crisp, D.J. Trans. Faraday SOC.1946,42,619. (7)O’Brien, R.N.;Feher, A. I.; Leja, J. J.Colloid Interface Sci. 1975, 51, 366. ( 8 )O’Brien, R.N.; Feher, A. I.; Leja, J. J.Colloid Interface Sci. 1976, 56,469. (9)O’Brien, R.N.;Feher, A. I.; Leja, J. J.Colloid Interface Sci. 1976, 56,474. (10)Benedetto, D. 0.; Shah, D. 0.; Kaufman, H. E. Invest. Ophthalmol. 1975,14,887.
0743-7463/94/2410-3701$04.50/00 1994 American Chemical Society
Karkare and Fort
3702 Langmuir, Vol. 10, No. 10, 1994 tina1,4believed Gibbs-Marangoni flow to be responsible for some of the water movement they observed. If this were true, water and surfactant movement should be correlated. In the search reported here water movement and surfactant movement in wet but “unsaturated” sand are measured independently to determine whether a correlation actually exists.
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Experimental Section Materials. l-Tetradecanol (97%) and l-hexadecanol (99%) were obtained from Aldrich Chemical Co., Milwaukee, WI,and were used as received. l-He~adecanol-l-~*C (Lot No. 092H9204) was supplied by Sigma Chemical Co., St. Louis, MO. Deionized water was distilled from alkaline m n 0 4 solution before use for water movement experiments. Chloroform (ACS certified, Spectranalyzed) obtained from Fisher Scientific Co., Springfield, NJ, was used to prepare stock solutions ofradiolabeled and unlabeled l-hexadecanol. ScintiLene (a xylene-based cocktail for nonaqueous samples), used for liquid scintillation counting, was obtained from Fisher. Sand was Washed Sea Sand (Lot No. 915262B), purchased from Fisher. The specific gravity of the sand was determined to be 2.6 g/cm3. The apparent density of sand in packed columns was 1.42-1.48 g/cm3. The shape and size of the sand particles were determined with an electron microscope. The sand particles showed a wide variation in shape and size. The average diameter defined as the average of length and width of the particles was -0.2 mm. The surface area ofthe sand particles was determined to be -130 cmVg as determined by measuring the dimensions of many sand grains with the microscope. Water Movement Measurements. The experimental setup and the technique of following the water movement have been described.2 A quantity of water was blended with sand using a spatula. The wet sand mixture was then divided into two equal parts. One part was used to fill a 5-cm length of a glass tube held in vertical orientation. A measured quantity of l-hexadecanol dissolved in a small amount of chloroform was sprinkled over the other part of the wet sand and blended with the spatula. The chloroform evaporated. Then, the surfactant-water-sand mixture was packed to a 5-cm depth directly on top of the wet sand which was already in the glass tube. This entire process was done quickly to minimize evaporation of water. No mechanical separation or screen separated the surfactantcontaining and surfactant-free sand. The ends of the tube were then closed with Teflon plugs, and the tube was placed horizontally. After a specified time (from 2 min up to 10 days), the water content of different sections of the sand column in the tube was determined gravimetrically and was reported as weight percent based on the weight of dry sand. Surfactant Movement Measurements. A stock solution of l-hexadecanol-l-14C(specificactivity lO.BpC/mg)was prepared in a 10-mL volumetric flask by dissolving a 10-mg sample in chloroform. Radioactivity of the sample was determined using a Beckman Scintillation Counter, Model LS3801 (Beckman Instruments, Inc., Imine, CA),and was reported in units ofcounts per minute (cpm). The measured specific activity of the stock solution was -2.5 x lo7cpdmg. Specific activity was reduced by adding sufficient unlabeled l-hexadecanol in chloroform t o -1 mL of stock solution to achieve a ratio oflabeled to unlabeled molecules of -350. The new solution had an activity of -3 x lo6 cpdmL. The final concentration of the l-hexadecanol in chloroform was 42.1 mg/mL. This diluted stock solution was used to add surfactant to the sand column in controlledamounts. A calibration curve relating radioactivity (in cpm units) t o the amount of surfactant was prepared by measuring the radioactivity of samples containing 8 g of sand, 1mL of water, a known amount of l-hexadecanol from the diluted stock solution, and 12 mL of ScintiLene cocktail in disposable 20-mL borosilicate glass scintillation vials. The calibration curve was linear (correlation coefficient = 0.997) in the range 0.001 mg to 1 mg of l-hexadecanol. Background counts obtained with 8 g of sand and 1mL of water in the vial with 12 mL of cocktail but no radioactive material were -36 cpm with a standard deviation of -8 cpm. When the amount of surfactant in a given sample was 0.001 mg, the radioactivity of the sample was -50 cpm with a standard deviation of -8 cpm. Since any measured activity below 50 cpm
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Figure 1. Water content profiles after 2 min, 30 min, and 1 day. Initial surfactant concentration was 0.1 mg/g of dry sand in the left half (0-5-cm section) of the column. was statistically insignificantrelative to background count, 0.001 mg was taken as the minimum detection limit for these samples of radioactive l-hexadecanol. The middle 10-cmsection of a 20-cm-long glass tube was packed with wet sand of uniform 12 w t % water content. A quantity (0.2-0.3 mL) of dilute radiolabeled stock solution was premixed with the sand in the left half of the sand column in the tube. The amount of surfactant added was approximately 10 times that required to form a monolayer. After a specified time (1,3, or 7 days), samples weighing -8 g were obtained from different places along the column length. These samples were collected in disposable 20-mL borosilicate glass scintillation vials. A 12-mL quantity of ScintiLene cocktail was added to each vial, and the vials were shaken to extract the l-hexadecanol from the sand. The sand settledtothe bottom of the vials but was never separated from the ScintiLene solution. The radioactivity ofthese samples was measured. The amount of l-hexadecanol in the samples was determined from the calibration curve. Surfactant concentrations were reported in units of milligrams of surfactant per gram of dry sand for all samples with radioactivity above the minimum detection limit. A “radioactivity balance” was always obtained by counting representative samples from both sides of the column to ensure that all radiolabeled l-hexadecanol was accounted for. A room temperature of 23 “C was maintained during all experiments.
Results and Discussion Rate of Water Movement. In the first set of experiments, the initial water content of the wet sand was a uniform 12%by weight based on dry sand weight. The sand on the left side of the column also contained 0.1 mg of l-hexadecanol per gram of dry sand. Analyses after 2 min, 30 min, and 1 day indicated significant water movement. Figure 1 shows that more than half this movement occurred in the first 2 min. Most of the water movement was complete in 30 min. After this time, the water content profile in the left half (0-5 cm section) of the column remained constant, but the profile in the right half (5-10 cm section) ofthe column showed some change. The 5-6-cm section lost some of the water that it had gained in the first 30 min to the 6-10-cm section. However, specificwater movement, defined as the amount of water gained by the right half of the column per gram of sand in the column, was almost constant (0.022 glg sand after 30 min and 0.023 glg sand after 1day). Water content profiles from experiments that lasted 3 and 7 days showed no significant change from the profile after 1day. The results from many water movement experiments with l-hexadecanol surfactant are summarized in Figure 2, in which the specific water movement is plotted as a function of the duration of the experiment. Similar experiments lasting 2 months were carried out with
Flow in “Unsaturated Porous Media
Langmuir, Vol. 10, No. 10, 1994 3703
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Figure 2. Specificwater movement after vaned equilibration times. Initial surfactant concentration was 0.1 mg/g of dry sand in the left half (0-5-cm section) of the column. 1-tetradecanol as the surfactant and showed that a water profile like that shown in Figure 1was stable for a t least this time period. The back-flow of water from the right half to the left half of the column was insignificant.2 Rate of Surfactant Movement. Tschapek and Wasowskill attempted to determine the rate of surfactant movement in wet but “unsaturated” porous media. They showed qualitatively that the rate of surfactant spreading in such systems was some thousand times slower than on a bulk water surface and that surfactant movement was much slower than water movement. The technique they used consisted of placing wet sand samples taken from the initially surfactant-free part of their system in flat dishes and then adding sufficient water to cover the sand completely. Surface tension was then measured. Tensions below that of pure water were taken to indicate the presence of surfactant in the sand. This technique is a t best a qualitative indicator of the presence of surfactant. The area ofthe water surface in the dish was much smaller than the air-water interfacial area in the sand sample. Therefore, the area occupied by surfactant molecules on the water surface in the dish was different from the area occupied by the same molecules on water in the sand pack. Also, “transfer”of surfactant molecules to the bulk water surface may not have been complete. A quantitative technique for following surfactant movements is the use of radioactive tracers and liquid scintillation counting. Radiolabeled l-he~adecanol-l-’~C was used in this work because it is commercially available and is an effective mover ofwater. With the stock solutions used in the experiments, the minimum detectable surfactant amount in sand was -0.001 mg. Mass of a 1-hexadecanol monolayer on wet sand was expected to be -0.2 mgfg sand. Thus, the technique used to follow surfactant movement was both very sensitive and quantitative. In the second set of experiments, the initial water content of the sand was again 12%. To the wet sand in the left halves (0-5-cm sections)ofthe columns was added 0.1-0.2 mg of radiolabeled 1-hexadecanol surfactant, in chloroform solution, per gram of dry sand. This concentration of surfactant yielded the water movement results described in the previous section. Results of surfactant analysis after 1,3, and 7 days are shown in Figure 3. After 1day, some surfactantmolecules had moved to the 5-6-cm section of the column. The amount of surfactantbeyond 6 cm was below the minimum ~
(11)Tschapek, M.; Wasowski, C. Colloids Surf. 1982, 5, 65.
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Figure 3. Profiles of 1-hexadecanolconcentration after 1 , 3 , and 7 days. Initial surfactant concentrationwas 0.1-0.2 mg/g of sand in the left half (0-5-cm section) of the column. Data mg/g of sand are not points for surfactant concentrations < shown because they are below the minimum detection limit, though measurements were made at the positions indicated. detection limit. After 3 days, the amount of surfactant in the 5-6-cm section increased somewhat, and avery small amount of surfactant was detected in the 6-7-cm section. After 7 days, measurable amounts of surfactant were detected in the 7-8-cm column section. In all cases, the quantity of surfactant detected decreased as distance from the part of the column which initially contained surfactant increased. To interpret these results properly, it was necessary to establish how much l-hexadecanol-l-14C surfactant was required to form a close-packed monolayer in the “unsaturated” wet sand. The surfactant area of the dry sand was -130 cmz/g. The surfactant actually spread at the air-water interface within the sand pack. This interface had a n area 2 months) stability of uneven distributions of water in a sand pack. It also indicates the need for premixing of surfactant with the sand that is to be dewatered. Acknowledgment. We thank William Van Wurm for obtaining some of the water movement data presented in this work. Financial support was provided by the National Science Foundation, Grant No. CTS-9213478. (14)Mansfield, W. W. Aust. J. Chem. 1959, 12, 382.
