Growth Mode Transition of Tetrahydrofuran Clathrate Hydrates in the

Clathrate hydrates are known to form a thin film along a guest/host boundary. We present here the first report of tetrahydrofuran (THF) clathrate hydr...
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Growth Mode Transition of Tetrahydrofuran Clathrate Hydrates in the Guest/Host Concentration Boundary Layer Yuichiro Sabase and Kazushige Nagashima* Department of Physics, Meiji UniVersity, 1-1-1 Higashimita, Tama-ku, Kawasaki 214-8571, Japan ReceiVed: June 4, 2009; ReVised Manuscript ReceiVed: October 6, 2009

Clathrate hydrates are known to form a thin film along a guest/host boundary. We present here the first report of tetrahydrofuran (THF) clathrate hydrate formation in a THF/water concentration boundary layer. We found that the THF-water system also forms a hydrate film separating the guest/host phases. The lateral growth rate of the film increases as supercooling increases. The thickness of the film at the growth tip decreases as supercooling and the lateral growth rate increase. These tendencies are consistent with reports of experiments for other hydrates and predictions of heat-transfer models. After film formation and slight melting, two types of growth modes are observed, depending on temperature T. At T ) 3.0 °C, the film slowly thickens. The thickening rate is much lower than the lateral growth rate, as reported for other hydrates. At T e 2.0 °C, however, the growth mode transitions spontaneously from film growth to continuous nucleation, and an agglomerate of small polycrystalline hydrates forms in each phase. Grain boundaries in the film and pore spaces in the agglomerate act as paths for permeation of each liquid. Timing when continuous nucleation starts is dominantly controlled by the time of initiation of liquid permeation through the film. Digital particle image velocimetry analysis of the agglomerate shows that it expands not by growth at the advancing front but rather by continuous nucleation in the interior. Expansion rates of the agglomerate tend to be higher for the cases of multipermeation paths in the film and the thinner film. We suppose that the growth mode transition to continuous nucleation is caused by the memory effect due to slight melting of the hydrate film. 1. Introduction Clathrate hydrates are ice-like crystals composed of a hydrogen-bonded network of water molecules that enclose guest molecules within cavities.1,2 Hydrate crystals are of interest for applications such as CO2 ocean sequestration,3-6 cool storage technology,7-9 and storage and transport of natural gas and hydrogen gas.10,11 Typically, hydrates form a thin film along the boundary between the water phase and the guest phase (liquid or gas). The formation of hydrate film has been studied for many kinds of hydrate formers (guest molecules), such as CO2, methane, hydrofluorocarbon (HFC), and so on. The lateral growth rate of the film along the boundary reportedly increases as supercooling increases.5,6,12,13 Ohmura et al. reported interferometric measurements of the thickness of HFC-134a hydrate film and showed that thicker film forms at lower supercooling.9 Mori and Mochizuki et al. reported heat-transfer analytic models of hydrate-film growth and its application to experimental data (lateral growth rate vs supercooling) to estimate the film thickness.14,15 The results show that film thickness decreases as supercooling increases. Further, the heat-transfer models predict that the lateral growth rate decreases as film thickness increases.6,14,15 After a film forms, it has been shown to grow in thickness much more slowly than it grows laterally.9,13 Thus, hydrate film does not form a large amount of hydrate unless the film is repeatedly broken to form new guest/host boundaries. Tabe et al.16 reported the formation of massive CO2 hydrates (hereinafter called a polycrystalline agglomerate) without breaking the film. They found that materials with surface free energies having large polar components, such as glass, promote perme* Corresponding author. E-mail: [email protected].

ation of water through the gap between the glass and the hydrate film. However, the process and mechanism by which the polycrystalline agglomerate forms are not well understood. Numerous growth experiments of tetrahydrofuran (THF) hydrates have been carried out in solutions where there are no guest/host boundaries.17-23 THF is miscible with water at all molar ratios. THF-17H2O solution forms a structure II hydrate24 at atmospheric pressure below 4.4 °C.25 THF hydrates are attractive for study because large single crystals are easily grown without the diffusion effect of guest molecules in the THF-17H2O solution. However, few studies have been performed under conditions where THF diffusion controls the growth process. If the THF-water system permits emulation of more complicated diffusion-controlled formation processes of various hydrates, it can be a useful model for hydrateformation applications and earth-science studies. When THF is poured on a water surface, THF and water gradually mix. During the transient state of mass diffusion, a guest/host concentration boundary layer exists. In this study, we present the first report of THF hydrate formation in the THF/ water concentration boundary layer. We describe the formation of the hydrate film, thickening, and growth mode transition from film growth to continuous nucleation with formation of polycrystalline agglomerates. In addition, we clarify the similarities and differences in hydrate-film formation and thickening between THF and other hydrate formers, as well as the controlling factors and mechanism for growth mode transition to continuous nucleation. 2. Experimental Section The samples used were dehydrated stabilizer-free THF reagent (99.5 wt % purity, Kanto Chemical Co. Inc., Japan) and

10.1021/jp905233n CCC: $40.75  2009 American Chemical Society Published on Web 10/26/2009

Growth Mode Transition of THF Clathrate Hydrates

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Figure 1. Schematic illustration of the temperature-controlled chamber and the growth cell in it.

ultrapure water. A food colorant (85 wt % dextrin and 15 wt % food red No.102, Kyoritsu foods Co. Inc., Japan) was used to visualize the mass-transport process. Figure 1 shows a temperature-controlled chamber, made from a block of stainless steel, and the growth cell (28 × 10 × 2.6 mm3) in it. A thin sample space was chosen to allow twodimensional (2D) analysis. The chamber was maintained at a constant temperature T by circulating coolant controlled within 0.1 °C. The growth process was observed through a doublewalled glass window. Experimental runs were carried out at atmospheric pressure over the temperature range 0.0 °C e T e 3.0 °C. The experimental procedure was as follows. First, 0.55 mL of water was injected into the growth cell and maintained at T. Then, 0.15 mL of THF was slowly injected from the top inlet onto the water surface over a period of 2-3 min; injection must be slow in order to prevent THF from mixing into the water by liquid flow. Both the THF and the microsyringe used had been cooled in a refrigerator at about 5 °C prior to injection. The two liquids completely filled the cell. The molar ratio of THF to water corresponds approximately to the ideal composition (THF-17H2O). Since THF is less dense than water, a concentration boundary layer forms horizontally; the boundary layer is uneven just after THF injection, and becomes even in 30 s. THF hydrates were artificially nucleated in the boundary layer by dipping a chilled wire (0.7 mm in diameter, cooled by liq. N2) through the air release port. Without this procedure, the two liquids mix by diffusion without nucleation, and the concentration boundary layer disappears. The chilled wire was withdrawn immediately after nucleation (i.e., dipping took about 1 s). Thus, the timing of artificial nucleation after contact of THF and water (the start of THF injection on the water surface) was fixed to about 3 ( 0.5 min in order to fix and minimize the mixing time of THF and water by diffusion. The inlets and air release port of the growth cell were sealed to prevent vaporization of THF. The growth process was then observed without any thermal and mechanical agitation. Another type of run was carried out to visualize the THF transport through the hydrate film and the polycrystalline agglomerate. In a modification of the procedure described above, about 1 mg of colorant was put into the THF phase from above, after the film had separated the two liquid phases. The colorant in the THF phase dissolves in the small amount of water that diffuses into the THF phase before separation of the two liquid phases by the film. The growth process was observed by a charge-coupled device camera and recorded by a time-lapse video recorder. The images obtained were analyzed by a personal computer. Overall phenomena of the small crystals in the expanding agglomerate

Figure 2. Sequential images of hydrate-film growth along the twophase concentration boundary layer at 1.0 °C. Times are measured from artificial nucleation. The origin of the x-axis and x ) 10 mm are located at the left and right sidewalls, respectively, of the growth cell. The arrow in part a shows the artificial nucleation point at about x ) 2 mm. The two-headed arrow in part b shows the concentration boundary layer visualized by light refraction.

are evident from the movies, shown at high speed, but not necessarily from the sequential images. To show these phenomena explicitly, velocity vectors of hydrate crystals in the expanding agglomerate were obtained by analysis of sequential images using a digital-image processing technique called particle image velocimetry (PIV),26 which is widely used for analyses of fluid motion. Displacements of tracer particles in the fluid are detected and used to calculate velocity vectors for fluid motion. In the present study, displacements of crystals were detected by analysis of sequential images from time t to t + 22 s using a digital PIV program (AV-FLUID-1, Image Sense Co. Ltd., Japan). 3. Results and Discussion 3.1. Formation of Hydrate Film. Figure 2 shows sequential images of hydrate-film growth at 1.0 °C. The upper and lower regions in each image correspond to THF and water, respectively. A concentration boundary layer exists horizontally between the two liquids. Elapsed times after artificial nucleation are shown in the figure. The origin of the x-axis and x ) 10 mm are located at the left and right sidewalls, respectively, of the growth cell. The position where the wire was dipped for nucleation is at about x ) 2 mm. Figure 2a shows the artificially nucleated hydrates in the concentration boundary layer at x ) 2 mm, indicated by an arrow. Figure 2b shows the lateral growth of the hydrate film along the concentration boundary layer. The growth tip of the film is wedge-shaped. The difference in the refractive index of THF and that of water causes the contrast in light refraction in the boundary layer (that is, the dark region), indicated by a twoheaded arrow. The contrast is quite sensitive to lighting and is evident only in this image. The hydrate grows horizontally, low in the concentration boundary layer, because THF hydrates preferentially grow at the ideal composition of THF-17H2O, which corresponds to a water-rich solution. Figure 2c shows further film growth; the growth tip is now round and thick. Figure 2d shows yet further growth; the growth tip is a thin wedge again. Figure 2e shows that the film completely separates the two liquid phases and slightly thickens at around x ) 10 mm. Thus, it is evident that the THF-water system forms a hydrate film along the guest/host concentration boundary layer.

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Figure 3. Time variation in growth-tip position for various T. Position is measured from the sidewall on the left side along the x-axis, as shown in Figure 2.

Figure 4. Mutual relationships among hydrate-film lateral growth rate V, film thickness at the growth tip, and supercooling ∆T: (a) V vs ∆T; (b) thickness vs ∆T; (c) V vs thickness.

Figure 3 shows the time variation in growth-tip position for various T. Position is measured from the sidewall on the left side along the x-axis, as shown in Figure 2. Experimental runs were carried out three times for each T (a total of 12 runs for T ) 3, 2, 1, and 0 °C), four of which are plotted in the figure. Growth rates fluctuate in the initial stage of growth. At 3 °C, fluctuations are particularly large and of long duration for all runs. The growth rate for a run at 1 °C decreases in the middle stage of growth and increases in the later stage, as shown in the figure. This correlates with the changes in growth-tip shape from thin wedge-shaped (Figure 2b) to thick rounded (Figure 2c) and back again to thin wedge-shaped (Figure 2d). This type of fluctuation is also observed for a run at 2.0 °C (not shown). Growth rates for other runs are almost constant except in the initial stage of growth. In order to characterize the lateral growth of hydrate film, we determined the mutual relationships among lateral growth rate V, film thickness at the growth tip, and supercooling ∆T ()Teq - T). Teq ()4.4 °C) is the equilibrium temperature of THF hydrate in solution at the ideal composition (THF-17H2O). Figure 4a shows a plot of V vs ∆T, Figure 4b shows a plot of thickness vs ∆T, and Figure 4c shows a plot of V vs thickness. Film thickness at the growth tip is measured 0.5 mm behind (left side of) the tip, because the tip shape is not rectangular

Sabase and Nagashima

Figure 5. Time variation in hydrate-film thickness at x ) 2, 7, and 10 mm at 1 °C, measured after the growth tip just reaches x ) 10 mm.

but rounded or wedged. For simplicity, V and thickness for each run were obtained by averaging the time-dependent values after the growth tip advances 2 mm away from the nucleation point until it reaches x ) 10 mm. Results for all 12 runs are plotted in the figures. Figure 4a shows that V increases as ∆T increases. This tendency is consistent with results reported for other hydrate formers.5,6,12,13 However, the orders of magnitude of V are much smaller for THF (1.8-61 µm s-1) than for CO2 (millimeters per second)5,6 and methane (tens to hundreds of micrometers per second)12,13 when compared over approximately the same range of ∆T. The values of V for three runs at each ∆T are scattered at large ∆T, i.e., for fast growth. This might be caused by the experimental procedure, in that, after THF injection onto the water surface, the sample was kept for only 30 s before artificial nucleation in order to minimize mixing of THF and water. Figure 4b shows that film thickness at the growth tip decreases as ∆T increases. This tendency is consistent with reported results of interferometric measurements of film thicknesses for HFC134a (80 µm at ∆T ) 1.5 °C and 10 µm at ∆T ) 6.9 °C)9 and heat-transfer model estimations of thickness.14,15 Hydrate-film thicknesses are orders of magnitude greater for THF (0.3-1.3 mm) than for HFC-134a,9 CO2 (1 µm, estimated using a heattransfer model),6 and methane (about 5 µm).13 The greater thickness for THF might be due to the complete miscibility of THF in water. THF concentration in the concentration boundary layer changes vertically from 100 to 0%, and thick film can grow minimally affected by diffusion of guest molecules in a region where the concentration is almost ideal (THF-17H2O). Figure 4c shows that V decreases as film thickness increases. Thistendencyisconsistentwithheat-transfermodelpredictions.6,14,15 Thicker film releases more latent heat at the growth tip, so V decreases. The lower V and thicker film for THF hydrate, in comparison with other hydrates, are also consistent with this tendency. Figure 5 shows the time variation in film thickness at x ) 2, 7, and 10 mm at 1 °C after the growth tip just reaches x ) 10 mm (Figure 2). The film is thinnest at x ) 2 mm and increases in thickness as x increases, because there is more time for diffusion of each liquid in the concentration boundary layer far from the artificial nucleation point (x ) 2 mm). In addition, the film melts slightly over time, due to the lack of THF or water in each liquid phase. Slight melting of the hydrate film has also been reported in water unsaturated by guest molecules (HFC-134a).7,9 After formation of the hydrate film and slight melting, we observe two types of growth modes: thickening of the film at T ) 3.0 °C and transition from film growth to continuous nucleation, forming polycrystalline agglomerates, at

Growth Mode Transition of THF Clathrate Hydrates

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Figure 8. Sequential images of growth mode transition to continuous nucleation at 1 °C. Times are measured from artificial nucleation. The arrow indicates the artificial nucleation point at x ) 2 mm.

Figure 6. Sequential images of hydrate-film growth in the thickness direction at 3.0 °C. Times are measured from artificial nucleation. Figure 6b1-b4 shows magnified images for the short time span in the region of the square in Figure 6b; times are the elapsed times from 202 min.

Figure 7. Hydrate-film thickness at x ) 2.7 mm as a function of time after artificial nucleation.

T e 2.0 °C. These results are described in sections 3.2 and 3.3, respectively. 3.2. Thickening of Hydrate Film at T ) 3.0 °C. Figure 6 shows sequential images of hydrate-film thickening at 3.0 °C. Times are measured from artificial nucleation. Figure 6b1-b4 shows magnified images in a short time span in the region of the square in Figure 6b; times are elapsed times from 202 min. Figure 6a shows the hydrate film formed and slightly melted. Figure 6b,c shows film growth in the thickness direction toward the water phase. The growth interface between the film and water phase has a faceted pattern. The hydrate grows preferentially in the thickness direction around the artificial nucleation position x ) 2.7 mm (Figure 6c), and is controlled by permeation of THF through the film (Figure 6b1-b4). The interface is faceted (Figure 6b1). THF permeates the film, appears just below the film (Figure 6b2), and spreads along the film (Figure 6b3). Then, crystallization proceeds and the interface becomes faceted again (Figure 6b4). This event occurs intermittently, as shown later in Figure 7. Figure 6d shows that the film grows in the thickness direction not only around x ) 2.7 mm but also around x ) 6.8 mm, and grows toward the THF phase above the film over the range x ) 0-5 mm. Figure 7 shows film thickness (growth distance) at x ) 2.7 mm as a function of time after artificial nucleation, obtained by analysis of the sequential images as in Figure 6. After the film starts to thicken toward the THF phase, thickness is measured from the upper interface of the initial film to obtain the growth distance toward the water phase. Thickness initially

decreases by slight melting and then increases and slightly decreases repeatedly. Film thickening occurs intermittently, as shown by arrows, repeating a series of processes of THF permeation through the film, crystallization, and slight melting. The average thickening rate at the preferentially growing tip at x ) 2.7 mm is 0.11 µm s-1; the results for two more runs at 3.0 °C are 0.14 and 0.04 µm s-1. These are 1 or 2 orders of magnitude smaller than the lateral growth rate at the same T (2.0, 1.8, and 3.1 µm s-1, respectively). The thickening rates reported for other hydrates are also much lower than the respective lateral growth rates. However, the thickening rate is higher for THF than for HFC-134a (tens of micrometers per 100 h)9 and for methane (micrometers per min).13 The relatively higher thickening rate for THF suggests faster permeation of THF through the film. 3.3. Growth Mode Transition to Continuous Nucleation. 3.3.1. Initiation of Continuous Nucleation. Figure 8 shows sequential images of growth mode transition to continuous nucleation at T ) 1.0 °C. Times are measured from artificial nucleation. Figure 8a shows the hydrate film formed and slightly melted. The arrow indicates the artificial nucleation position at around x ) 2 mm. Figure 8b shows a drastic change in growth mode. Continuous nucleation starts suddenly at around x ) 2 mm both below and above the film, resulting in formation of polycrystalline agglomerates, which expand into (Figure 8c-e) and finally fill both phases (Figure 8f). Agglomerate expansion rates are higher in the water phase than in the THF phase. Thus, the growth mode transitions spontaneously from film growth to continuous nucleation. Hereinafter, we focus on agglomerate formation in the water phase. Experimental runs were carried out three times for each T (0.0, 1.0, and 2.0 °C). Continuous nucleation always occurs after film formation, and sometimes occurs at the gap between the film and sidewall of the growth cell at x ) 0 mm (twice) and 10 mm (once). In these cases, additional runs were carried out to obtain three results for each T without the sidewall cases. Table 1 summarizes values of T, artificial nucleation position in the x-axis, and continuous nucleation position when it starts. Artificial nucleation is controlled at a single position in the range 1.9-2.8 mm, except for cases of two positions x ) 2.2 and 4.5 mm (run 1) and x ) 1.9 and 3.4 mm (run 6). These exceptional cases occurred when the chilled wire, upon withdrawal from the concentration boundary layer, caused some of the nucleated hydrates to migrate, resulting in two positions. In these cases, continuous nucleation started at two positions close to the artificial nucleation positions (x ) 2.1, 5.3 mm for run 1; x ) 1.9, 3.9 mm for run 6). Even though artificial nucleation was

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TABLE 1: Summary of T and Artificial and Continuous Nucleation Positions in the x Axis nucleation positions, mm run no. 1 2 3 4 5 6 7 8 9

T, °C 0.0 0.0 0.0 1.0 1.0 1.0 2.0 2.0 2.0

artificial

continuous

2.2, 4.5 2.4 2.8 2.3 2.0 1.9, 3.4 2.3 2.5 2.7

2.1, 5.3 1.7 2.2 2.4 2.2 1.9, 3.9 2.5 1.7 1.1, 3.2 Figure 11. Sequential images of hydrate film around x ) 2 mm, obtained under high magnification at T ) 1 °C, after film formation until initiation of continuous nucleation. Times are measured from artificial nucleation.

Figure 9. Magnified sequential images of THF permeation through the hydrate film and initiation of continuous nucleation for a special case of run 9. Times are measured from the start of THF permeation.

Figure 10. Correlation between artificial nucleation position in the x-axis and continuous nucleation position when it starts. Results for runs 1-9 are plotted with open circles, the sidewall cases (three runs) are plotted with filled circles, and the perfect correlation between artificial and continuous nucleation positions is shown by a solid line for comparison.

controlled at a single position x ) 2.7 mm for run 9, continuous nucleation started at two positions (x ) 1.1, 3.2 mm), as shown in Figure 9. THF permeates the film (Figure 9a,b) and then spreads to the right and left along the lower side of the film (Figure 9c), as indicated by two arrows. Thus, the permeation path splits into two directions, and continuous nucleation starts at two positions (Figure 9d). The effect of two nucleation sites (runs 1, 6, and 9) on the expansion rate of polycrystalline agglomerates (Figure 16) is discussed later in section 3.3.2. Figure 10 shows the correlation between artificial nucleation position and continuous nucleation position. The results for the nine runs (Table 1) are plotted with open circles, the sidewall cases (three runs) are plotted with filled circles, and the perfect correlation between artificial and continuous nucleation positions is shown by a solid line for comparison. The continuous nucleation positions are localized close to the artificial nucleation

positions, except for the sidewall cases at x ) 0 and 10 mm. Tabe et al.16 reported the formation of polycrystalline CO2 hydrates locally at the gap between the glass and the hydrate film. Although the hydrate film in the present study contacts the glass window over all regions of x, continuous nucleation is localized at around the artificial nucleation position, suggesting that crystal grain boundaries exist in the film only around the artificial nucleation position and can be the preferential paths for permeation of each liquid. Continuous nucleation is always initiated after a small protrusion of THF appears at the lower side of the film around the artificial nucleation position. However, image resolutions are low for runs 1-9 because the observation area covers the entire growth cell, so we obtained images at high magnification, focusing on these local processes, for a different run at T ) 1 °C. Nothing significant is observed at 16 min 36 s (Figure 11a). However, 4 s later, the contrast in the image changes in the film (arrow in Figure 11b), suggesting THF permeation through the film toward the water phase. In 40 s, THF reaches the water phase and forms a new boundary with a droplet-like shape (arrow in Figure 11c). The interface of the droplet has a faceted appearance, indicating that it is surrounded by another hydrate film (secondary hydrate-film formation). This situation remains unchanged for 281 s. Finally, continuous nucleation begins at the tip (Figure 11d). We suppose that the secondary hydrate film partially melts, and dense THF in the droplet is released into the water phase prior to continuous nucleation. Timings of all events until initiation of continuous nucleation were measured for all runs. Table 2 summarizes values of T, film-formation time, time of THF appearance (time from artificial nucleation until THF first appears below the film), THFpermeation time (time required for THF permeation through the film from the initiation of permeation), and induction time for nucleation measured from the time of THF appearance below the film. Film-formation time is included because it affects the mixing time of THF and water by diffusion before separation of the two liquids by the film. THF-permeation time was not obtained for all runs due to low image resolution. Induction times for nucleation vary from 18 to 890 s. Induction time increases as supercooling ∆T increases (Figure 12a), contrary to the tendency for induction times to be shorter at lower T. As mentioned previously, we suppose that continuous nucleation starts after partial melting of the secondary hydrate film with a droplet shape, and so can resolve the contradiction as follows. The time required for partial melting should be longer at lower T, since the film can be stabilized against melting. The

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TABLE 2: Summary of T, Film-Formation Time, Time of THF Appearance below the Film Measured from the Artificial Nucleation, THF-Permeation Time through the Film, and Induction Time for Nucleation from the Time of THF Appearance run no. 1 2 3 4 5 6 7 8 9

T, °C

film-formation time, s

time of THF appearance, min

THF-permeation time, s

induction time for nucleation, s

0.0 0.0 0.0 1.0 1.0 1.0 2.0 2.0 2.0

152 110 204 151 280 78 295 361 384

31 43 52 29 18 28 20 22 29

20

490 107 890 89 171 79 18 35 118

109 101

Figure 13. Sequential images of velocity vectors in the expanding agglomerate at 1 °C. Vectors are indicated by arrows twice as large as the actual displacements during the analyzed time period (22 s).

Figure 12. (a) Induction time for nucleation vs supercooling ∆T. (b) Induction time vs film-formation time, plotted from data in Table 2.

time for partial melting of the secondary hydrate film might cause delay of nucleation at lower T. Comparisons of three results at the same T suggest that induction time increases as film-formation time increases (Figure 12b). This correlation suggests that partial melting of the secondary hydrate film decelerates because the THF concentration in the water phase increases by diffusion through the concentration boundary layer during slow formation of the initial hydrate film. Comparisons of all times in Table 2 suggest that the start of continuous nucleation is dominantly controlled by the time of the initiation of THF permeation through the film (tens of minutes) and less dominantly controlled by the time required for THF permeation through the film (20-109 s), the time required for slight melting of the secondary hydrate film (unknown but less than the induction time of 18-890 s), and the actual induction time for nucleation measured after slight melting of the secondary hydrate film (unknown but less than 18-890 s). 3.3.2. Expansion of Polycrystalline Agglomerate. Movies of expansion of the polycrystalline agglomerate, shown at high speed, reveal the overall phenomena of the expansion process. The agglomerate initially expands from the position where THF permeates just below the film. When the agglomerate becomes large, the expanding region shifts away from the film toward the outer region of the agglomerate, and hydrate crystals at the advancing front of the expanding agglomerate melt. These phenomena are evident from the movies for all runs but not necessarily from the sequential images. To show these phe-

nomena explicitly, we performed digital PIV analyses of sequential images, modified experiments using colorant, and high-magnification observation of hydrate crystals at the advancing front. Figure 13 shows sequential images of velocity vectors in the expanding agglomerate, obtained by digital PIV analysis of the images in Figure 8c-e. Velocity vectors are indicated by arrows twice as large as the actual displacements during the analyzed time period (22 s). Figure 13a shows the initial stage of expansion. The displacement vectors indicate that each crystal migrates toward the outer region of the agglomerate, suggesting that continuous nucleation increases the number of crystals and pushes the crystals toward the outer region. When the agglomerate expands (Figure 13b,c), the displacement vectors disappear in the agglomerate close to the film at around x ) 2 mm. The displacement vectors reappear and velocity increases around the region 2-4 mm from the x ) 2 mm point, suggesting that the nucleation region shifts due to permeation of THF through the agglomerate. Velocities close to the advancing front in the agglomerate are almost constant, indicating that the crystals in this region migrated but no nucleation occurred. Figure 14 shows sequential images of colorant permeation through the hydrate film and through the agglomerate in the modified experiment at 1 °C. Colorant is added to the THF phase after the film forms (Figure 14a). The colorant permeates the film at about x ) 2 mm; no permeation is observed elsewhere (Figure 14b). The dense, red-color liquid protrudes in a pipe shape, indicated by the arrow (Figure 14c). Three permeation paths are evident in the film, indicated by the white arrows (Figure 14d). The pipe-shaped colorant randomly branches and propagates in the polycrystalline agglomerate (the agglomerate is not well illustrated in the image), suggesting that THF is transported through the pore space in the agglomerate. This result is consistent with the tendency for continuous nucleation

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Figure 14. Sequential images of colorant permeation through the hydrate film and agglomerate. Times are measured from artificial nucleation.

Figure 15. Sequential images of the advancing front of the agglomerate, obtained at high magnification. The circle in each image indicates the same hydrate crystal.

to occur not only at the artificial nucleation position just below the film but also in the agglomerate away from that position as discussed previously (Figure 13). Figure 15 shows sequential images of the advancing front of the agglomerate obtained at high magnification. Although the agglomerate expands with time, the hydrate crystals at the advancing front melt due to lack of THF in the water phase. The size of the hydrate, shown by a circle in each image, gradually decreases, and the crystals in the agglomerate are smaller than 0.1 mm. Thus, expansion of the agglomerate is caused not by growth of each crystal at the advancing front but rather by expansion from the interior with continuous nucleation. Figure 16 shows the time variation in the area of the agglomerate in the water phase, from which we can determine the expansion rate of the agglomerate. Times are measured from initiation of continuous nucleation. The area of the water phase at 0 min is about 170 mm2. Numbers next to the curves indicate the thickness (in mm) of the film at 0 min and at the position where THF permeates. Comparisons of three results at the same T show that expansion rates are highest for runs 1, 6, and 9, which involve two nucleation sites (that is, multipermeation paths in the film) as discussed previously (Table 1). Neglecting the special cases of two nucleation sites, expansion rates are highest for runs 4 and 5 at T ) 1.0 °C. In these cases, film thicknesses where THF permeates are the thinnest (0.9 and 1.0 mm, respectively). The expansion rate does not necessarily correlate with T.

Sabase and Nagashima

Figure 16. Time variation in the area of the agglomerate in the water phase. Times are measured from initiation of continuous nucleation. The area of the water phase at 0 min is about 170 mm2. The numbers next to the curves are the thickness (in mm) of the hydrate film at 0 min and at the position where THF permeates.

However, T might affect the expansion rate by means of filmformation time (that is, diffusion time of each liquid before film formation), hydrate melting rate at the advancing front, and so on. Thus, the expansion rate of the agglomerate is controlled by the effects of several factors, all of which relate to mass transport of each liquid. Our previous study showed that an optical system of Mach-Zehnder interferometer can quantitatively observe time-dependent concentration distributions of NaCl in the THF-water solution adjacent to the growing hydrates (this is not the case for film growth or nucleation).20,21 This technique should help in clarifying the effects of mass transport processes on the expansion rate of the agglomerate. Further study will be carried out. 3.3.3. Mechanism of Growth Mode Transition. Bishnoi et al.27,28 found that the induction time for hydrate nucleation decreases in water as a result of prior hydrate formation and dissociation (or prior ice growth and melting). This is called the memory effect. Xie et al.29 reported the continuous nucleation and formation of an agglomerate of polycrystalline hydrates of HCFC-141b without formation of a hydrate film, using meltwater containing a promoter (sodium dodecyl sulfate). Zeng et al.22 reported that the memory effect works for nucleation of THF hydrates. Although the present study and that of Tabe et al.16 use no treated water or promoter, continuous nucleation occurs spontaneously. The present study shows that, after hydrate film (and presumably secondary hydrate film) melts slightly, continuous nucleation occurs. Nucleation does not occur spontaneously, even though water and THF are kept at T for several hours, unless a chilled wire is dipped into the concentration boundary layer. Therefore, we suppose that the growth mode transition from film growth to continuous nucleation is triggered by the memory effect. However, questions still remain: why does the film not grow in the thickness direction at T e 2 °C when each liquid is transported through the film, and why does each nucleated crystal in the agglomerate not grow larger than 0.1 mm? The present results indicate that growth of the hydrate surface is more difficult than nucleation with the help of the memory effect in liquids at compositions deviating from the ideal. According to an interfacial kinetics model, growth of a perfect crystal

Growth Mode Transition of THF Clathrate Hydrates without dislocation is generally controlled by 2D nucleation on the crystal surface below the roughing temperature TR.30-33 Because an additional driving force for 2D nucleation (activation energy) is required, crystal growth is more difficult than for a rough surface above TR where many steps and kinks exist and incorporate molecules or atoms in the crystal lattice. At present, there are no measured data for the interfacial kinetics of hydratecrystal growth. Direct measurement of the relationship between the growth rate of a single crystal hydrate and interfacial supercooling is under way. 4. Conclusions We have shown that the THF-water system also forms a hydrate film in the THF/water concentration boundary layer separating guest/host phases. The lateral growth rate of the film, thickness of the film at the growth tip, and degree of supercooling are interrelated as follows: lateral growth rate increases as supercooling increases, thickness decreases as supercooling increases, and thickness decreases as lateral growth rate increases. These tendencies are consistent with reports of experimental results for other hydrates and predictions of heattransfer models. However, the orders of magnitude for lateral growth rate and thickness are smaller and larger, respectively, for THF hydrate than for other hydrates. After hydrate-film formation and slight melting, two types of growth modes are observed, depending on temperature T. At the higher temperature T ) 3.0 °C, the film slowly thickens, repeating a series of processes of THF permeation through the film, crystallization, and slight melting. Although the thickening rate is lower than the lateral growth rate of the film, as reported for other hydrates, the order of magnitude for the thickening rate is higher for THF hydrate than for the other hydrates. Thus, similarities and differences in hydrate-film formation and thickening between THF and others are clarified. At the lower temperature T e 2.0 °C, the growth mode transitions spontaneously from film growth to continuous nucleation, and polycrystalline agglomerates form in both liquid phases. The position of artificial nucleation for the initiation of film growth correlates with the position of continuous nucleation. This suggests that grain boundaries are created locally in the film as a result of artificial nucleation and act as paths for permeation of each liquid. After the liquid permeation through the film, a secondary hydrate film with a droplet-like shape forms. Induction time measurements for nucleation suggest partial melting of the secondary film prior to the continual nucleation. Timing measurements for all events until continuous nucleation show that the initiation of continuous nucleation is dominantly controlled by the time of the initiation of THF permeation through the film and less dominantly controlled by the time required for THF permeation through the film, the time required for the partial melting of the secondary hydrate film, and the actual induction time for nucleation after the partial melting of the secondary hydrate film. Digital PIV analysis of the agglomerate and magnified observation around the advancing front of the agglomerate show that the agglomerate expands not by growth at the advancing front but rather by continuous nucleation in the interior. Visualization of mass transport using colorant shows that pore spaces in the agglomerate also act as paths for permeation of each liquid. The expansion rate of the agglomerate tends to be higher for the cases of multipermeation paths in the film and thinner film.

J. Phys. Chem. B, Vol. 113, No. 46, 2009 15311 We suppose that the growth mode transition from film growth to continuous nucleation is caused by the memory effect resulting from slight melting of the hydrate film prior to nucleation. The present study suggests the importance of further investigation, including interferometric observation of the timedependent concentration distribution of THF in water and interfacial kinetics measurements of hydrate-crystal growth, to clarify the effects of mass transport processes on the expansion rate of the agglomerate and the mechanism of the growth mode transition. Finally, we note that the THF-water system has proven useful for fundamental growth experiments and observations, and might also be a useful model for hydrate-formation applications and earth-science studies. References and Notes (1) Sloan, E. D., Jr.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC: Boca Raton, FL, 2008. (2) Englezos, P. Ind. Eng. Chem. Res. 1993, 32, 1251–1274. (3) Brewer, P. G.; Friederich, G.; Peltzer, E. T.; Orr, F. M., Jr. Science 1999, 284, 943–945. (4) Aya, I. Direct ocean disposal of carbon dioxide. In Handa, N., Ohsumi, T., Eds.; TERRAPUB: Tokyo, 1995; pp 233-238. (5) Uchida, T.; Ebinuma, T.; Kawabata, J.; Narita, H. J. Cryst. Growth 1999, 204, 348–356. (6) Uchida, T.; Ikeda, I. Y.; Takeya, S.; Ebinuma, T.; Nagao, J.; Narita, H. J. Cryst. Growth 2002, 237-239, 383–387. (7) Sugaya, M.; Mori, Y. H. Chem. Eng. Sci. 1996, 51, 3505–3517. (8) Ohmura, R.; Shigetomi, T.; Mori, Y. H. J. Cryst. Growth 1999, 196, 164–173. (9) Ohmura, R.; Kashiwazaki, S.; Mori, Y. H. J. Cryst. Growth 2000, 218, 372–380. (10) Florusse, L. J.; Peters, C. J.; Schoonman, J.; Hester, K. C.; Koh, C. A.; Dec, S. F.; Marsh, K. N.; Sloan, E. D. Science 2004, 306, 469–471. (11) Lee, H.; Lee, J. W.; Kim, D. Y.; Park, J.; Seo, Y. T.; Zeng, H.; Moudrakovski, I. L.; Ratcliffe, C. I.; Ripmeester, J. A. Nature 2005, 434, 743–746. (12) Freer, E. M.; Selim, M. S.; Sloan, E. D., Jr. Fluid Phase Equilib. 2001, 185, 65–75. (13) Taylor, C. J.; Miller, K. T.; Koh, C. A.; Sloan, E. D., Jr. Chem. Eng. Sci. 2007, 62, 6524–6533. (14) Mori, Y. H. J. Cryst. Growth 2001, 223, 206–212. (15) Mochizuki, T.; Mori, Y. H. J. Cryst. Growth 2006, 290, 642–652. (16) Tabe, Y.; Hirai, S.; Okazaki, K. J. Cryst. Growth 2000, 220, 180– 184. (17) Makogon, T. Y.; Larsen, R.; Knight, C. A.; Sloan, E. D., Jr. J. Cryst. Growth 1997, 179, 258–262. (18) Larsen, R.; Knight, C. A.; Sloan, E. D., Jr. Fluid Phase Equilib. 1998, 150, 353–360. (19) Knight, C. A.; Rider, K. Philos. Mag. A 2002, 82, 1609–1632. (20) Nagashima, K.; Yamamoto, Y.; Takahashi, M.; Komai, T. Fluid Phase Equilib. 2003, 214, 11–24. (21) Nagashima, K.; Orihashi, S.; Yamamoto, Y.; Takahashi, M. J. Phys. Chem. B 2005, 109, 10147–10153. (22) Zeng, H.; Wilson, L. D.; Walker, V. K.; Ripmeester, J. A. J. Am. Chem. Soc. 2006, 128, 2844–2850. (23) Nagashima, K.; Suzuki, T.; Nagamoto, M.; Shimizu, T. J. Phys. Chem. B 2008, 112, 9876–9882. (24) Jeffrey, G. A. In Inclusion Compounds; Atwood, J. L., Davies, J. E. D., MacNicol, D. D., Eds.; Academic Press: New York, 1984; Vol. 1, p 135. (25) Gough, S. R.; Davidson, D. W. Can. J. Chem. 1971, 49, 2691– 2699. (26) Adrian, R. J. Exp. Fluids 2005, 39, 159–169. (27) Vysniauskas, A.; Bishnoi, P. R. Chem. Eng. Sci. 1983, 38, 1061– 1072. (28) Parent, J. S.; Bishnoi, P. R. Chem. Eng. Commun. 1996, 144, 51– 64. (29) Xie, Y.; Guo, K.; Liang, D.; Fan, S.; Gu, J. J. Cryst. Growth 2005, 276, 253–264. (30) Hillig, W. B. Acta Met. 1966, 14, 1868–1869. (31) Hayashi, M.; Shichiri, T. J. Cryst. Growth 1974, 21, 254–260. (32) Malkin, A. I.; Chernov, A. A.; Alexeev, I. V. J. Cryst. Growth 1989, 97, 765–769. (33) Jin, W. Q.; Lin, J.; Komatsu, H. J. Cryst. Growth 1990, 99, 128–133.

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