Roles of wettability and supercooling in cyclopentane hydrate

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Roles of wettability and supercooling in cyclopentane hydrate spreading over a substrate Abdelhafid Touil, Daniel Broseta, Nelly Hobeika, and Ross Brown Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02121 • Publication Date (Web): 14 Sep 2017 Downloaded from http://pubs.acs.org on September 15, 2017

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Roles of wettability and supercooling in cyclopentane hydrate spreading over a substrate Abdelhafid Touil,∗,† Daniel Broseta,∗,† Nelly Hobeika,† and Ross Brown‡ †Laboratoire des fluides complexes et de leurs réservoirs (LFCR), UMR CNRS 5150, Université de Pau et des Pays de l’Adour, Av. de l’Université, B.P. 1155, 64013 Pau Cedex, France ‡ Institut des sciences analytiques et de physico-chimie pour l’environnement et les matériaux (IPREM), UMR CNRS 5254, Université de Pau et des Pays de l’Adour, Hélioparc, 2, Av. P. Angot, 64053 Pau Cedex, France E-mail: [email protected]; [email protected] Phone: +33 (0)5 59 40 76 85

Abstract We use transmission optical microscopy to observe cyclopentane hydrate growth in sub-mm, open glass capillaries, mimicking cylindrical pores. The capillary is initially loaded with water and the guest fluid (cyclopentane) and thus possesses three menisci, that between water and cyclopentane (CP) in the middle, and two menisci with the vapors at the ends. At temperatures T below the equilibrium temperature Teq ≈ 7 ◦ C, the hydrate nucleates on the water-CP meniscus, rapidly coating it with an immobile, polycrystalline crust. Continued movement of the other two menisci provides insights into hydrate growth mechanisms, via the consumption and displacement of the fluids. On water-wet glass, the subsequent growth consists of a hydrate ’halo’ creeping with an underlying water layer on the glass on the CP side of the meniscus. Symmetri-

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cally, on CP-wet glass (silane-treated), a halo and a CP layer grow on the water side of the interface. No halo is observed on intermediate wet glass. The halo consists of an array of large monocrystals, over a thick water layer at low supercooling (∆T = Teq − T below 5 K), and a finer, polycrsystalline texture over a thinner water layer at higher ∆T. Furthermore, the velocity varyies as ∆T α , with α ≈ 2.7, making the early stages of growth very similar to gas hydrate crusts growing over water-guest interfaces. Beyond a length in the millimetre range, the halo and its water layer abruptly decelerate and thin down to sub-micron thickness. The halo passes through the meniscus with the vapor without slowing down or change of texture. A model of the mass balance of the fluids helps rationalize all these observations.

Introduction Gas hydrates are non-stoichiometric crystalline solids made up of cages of water (host) molecules trapping ’guest’ molecules at low enough temperature or high enough pressure. Important guests include CO2 , N2 , CH4 and other low-molecular-weight hydrocarbons. Long considered a nuisance because they may plug natural gas pipelines, they are now viewed as promising materials for applications as diverse as gas storage and separation, secondary refrigeration and waste or salted water treatment. The stability of hydratebearing sediments is controlled by that of the natural gas hydrates present, as is gas recovery from those sediments. In many of these situations or applications, substrates are present and play an important yet poorly understood role, which motivates the present microscopy study of the spreading of the model system, cyclopentane (CP) hydrate, in the simplest of pores - round glass capillaries. Gas hydrates usually nucleate at a water-guest interface, and then rapidly spread over the interface as a thin polycrystalline film, the crust, whose morphology and growth have been thoroughly investigated over the past two decades 1–10 . The transport of water and guest molecules is extremely slow across this crust, which thus thickens very slowly 1 . Gas 2


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hydrates may also expand from this crust into the bulk of the aqueous or the guest-rich phase 11–14 . In what follows, it will be useful to keep in mind the salient features of this process. For given guest molecule and pressure, the driving force is supercooling (commonly called subcooling in the literature on gas hydrates), ∆T = Teq − T, where Teq is the hydrate dissociation temperature at this pressure and T the system temperature. Supercooling is the equivalent of the salt supersaturation of strongly salted aqueous solutions, which drives salt crystallization 15 . With increasing supercooling, the crystallites are smaller, resulting in a smoother crust, and the rate of lateral growth over the water-guest interface increases strongly 2,5,8,9 . The rate also increases when the guest is more soluble in water, e.g. CO2 hydrate crusts advance faster over water than CH4 hydrate crusts at similar ∆T, 10 pointing to the role played by guest solubility in water 4,6 . Solid substrates promote gas hydrate formation 16–21 . For example, hydrophobic substrates promote nucleation at the mineral-water-guest contact line and subsequent growth of gas hydrate, possibly because of local gas enrichement and ordering of the water molecules very near the substrate 21 . But hydrophilic particles, such as glass beads or other oxide particles, are also known to accelerate conversion into hydrate, as inferred from macroscopic measurements, such as gas consumption or heat release 16,17 , rather than by direct observations. The roles of the wettability, surface area and size distribution of solid particles, or of pore size distribution in the case of mesoporous particles, are still poorly understood. Some progress was made in experiments conducted on model substrates, starting with flat substrates. It is a common observation that gas hydrate creeps on glass or sapphire windows, above the contact line of the water-guest interface 22–24 . Beltrán and Servio 25 coined the term "halo" for gas hydrate growing on solid substrates. These authors observed methane hydrate halos creeping out of the contact line of water drops sitting on flat glass under methane, just after completion of a hydrate crust over the drop surface, and then

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radiating widely, thus propagating hydrate formation to the neighboring drop – the "bridge effect". Viewed growing over a flat substrate, such hydrate halos are hard to detect by transmission microscopy, and Beltrán and Servio plausibly assumed that the water needed for halo growth (feed water) was drawn from the drop to the halo front by capillarity in a thin gap between the glass and the halo, in a manner similar to the so-called ’bottom-supplied creeping’ process by which some salt crystallites grow on glass walls from a reservoir of saturated aqueous solution such as a sessile drop 26–29 . Phase contrast and fluorescence microscopy already provided a more detailed view of cyclopentane hydrate halo growth on flat glass 30 . Feed water was shown to be already present on the substrate in the form of a precursor film or droplets, and to come from the overlying guest phase by ’fog’ settling and antisublimation. Substrate wettability was also shown to strongly impact the existence and growth rate of these halos: rapid lateral growth was observed under the guest fluid over water-wet (hydrophilic) substrates, vs. no growth over hydrophobic silane-treated glass 30 , in agreement with previous observations by Jung and Santamarina 31 and by Esmail et al 32 . Nguyen et al 21 recently observed CO2 hydrate growing from the contact line along a hydrophobic glass-water interface. In practical situations solid substrates are curved, with radii of curvature or pore sizes ranging from tens of microns in highly-permeable sediments, to nanometers in some mesoporous particles used as hydrate promoters 33 . A few observational studies in water-wet (glass or silicon) micromodels with pore or channel dimensions in the 10100 µm-range showed complex growth processes, including nucleation at water-guest interfaces followed by growth over the water films wetting the substrate 34–36 . These processes control the filling of the pore space by gas hydrates, and ultimately the flow and mechanical (macroscopic) properties of the hydrate-bearing porous medium 37 . They also influence mineral–hydrate adhesion 38 . Here, we report optical transmission microscopy of cyclopentane (CP) hydrate halos 4


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creeping out of the water–cyclopentane meniscus in open round glass capillaries, with the purpose of understanding how substrate wettability and supercooling influence the spreading of a hydrate on a solid substrate. CP is very sparingly soluble in water and similarly to natural gas, it forms a structure II hydrate, stable at temperatures below Teq ≈ 7 ◦ C and at atmospheric pressure, which considerably eases its handling. For these reasons it has been widely used in many fundamental studies and considered a proxy of natural gas hydrates 39,40 . There are indeed many similarities between both hydrates, but also differences, notably when the nature of the guest phase, liquid or vapor, is involved 41 . We therefore draw the reader’s attention to the due caution called for before carrying over all conclusions of studies of CP hydrate to the more common gas hydrate systems. The experimental configuration has many advantages from both fundamental and practical standpoints. From a fundamental standpoint, round glass capillaries mimic model (cylindrical) pores, and therefore insights into how hydrates grow and fill the porous space in highly-permeable sediments are to be expected. From a practical standpoint, glass capillaries are available at low cost in a large range of shapes (round, square, rectangle, etc.) and sizes, from microns to millimetres. Their wettability can be easily adjusted, e.g. in this study by means of silane chemistry. They are relatively good conductors of heat, so that their interior rapidly adjusts to a change in external temperature, and they are available with good optical quality. In round capillaries, refraction effects provide a "help from a hindrance" for detecting ultra-thin (submicron) films such as the halo, provided the capillary section is appropriately chosen 42 . The Materials and Methods section presents the round glass capillaries and how their wettability was altered by silane treatment and characterized by contact angle measurement, as well as the experimental configuration and procedure. The Results section presents the morphologies and growth rates of cyclopentane hydrate halos advancing either over water-wet or over cyclopentane-wet, i.e. hydrophobic capillaries, as a function of temperature. The proposed mechanisms of halo growth are then discussed and compared

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to the much better characterized mechanisms of gas hydrates growing over water-guest interfaces. Some remaining questions and prospects are adressed in the "Conclusions and outlook" section.

Materials and Methods Materials 10 cm-long cylindrical capillaries in fused silica (hereafter loosely called "glass") were used as received from VitrotubesTM . The inner and outer diameters, ID = 2R = 200 µm and OD

= 330 µm, ensure that even ultra-thin (submicron) hydrate of water layers lying against the inner wall of these capillaries are readily revealed by simple transmission microscopy (see below, section "Glass wettability and thin layers on the glass"). We used deionised water (resistivity > 18 MΩ cm, PureLab Classic from ELGA Labwater) and cyclopentane (98%+ purity, Aldrich). In some experiments, the capillaries were rendered hydrophobic (oil-wet) by a silane treatment adapted from Dickson et al. 43 . A solution of 10−2 M dichloro-dimethyl-silane in dry cyclohexane (both Aldrich) was introduced by capillary rise and left for one hour under inert N2 atmosphere. Unreacted silane was removed by rinsing repeatedly in pure dry cyclohexane. Finally the capillaries were washed in absolute ethanol and dried at 110 ◦ C for 30 min.

Experimental configuration Capillaries were loaded with pure water and cyclopentane by plunging one end through the interface of these two liquids in a beaker; cyclopentane climbs by capillarity first, followed by water. The two liquids each occupy a few millimeters separated by the watercyclopentane meniscus. A vapor-water and a cyclopentane-vapor meniscus are thus also

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present (see Figure 1). Unless otherwise specified, the capillary is left open on both sides. The lengths of the liquid columns can be adjusted by controlling the residence times of the capillary end in each phase or by evaporation after loading. It might be thought that when being displaced by the water in the loading process, some cyclopentane could remain on the capillary wall, e.g. as a thin residual film between the water and the glass. In this case, high apparent contact angles, θ, of the water-cyclopentane meniscus with the wall (figure 1), would have been noted, as well as a strong hysteresis, or difference between the values of θ when the meniscus is moving in one direction or the other. We did not observe these features (see next section). In addition, the contact angles of the water-vapor meniscus with the wall were observed to be similar in a capillary loaded with water alone, that was then dried and loaded through cyclopentane, as above.

(a)

θ

vapor water

h

2R

cyclopentane liquid (CP)

glass capillary

water

vapor

CP

water

b

(b)

CP

(c)

Figure 1: Schematic view of a capillary loaded with water and cyclopentane (a), with a zoomed-in view of the meniscus at 0 ◦ C in the case of an untreated glass capillary (b), contact angle, θ = 13 ◦ , and a silane-treated glass capillary (c), θ = 106 ◦ . Capillaries loaded with water and cyclopentane were placed in a heating-cooling stage (Linkam CAP500, with LINKSYS temperature control software). An important feature of this stage is a rack and pinion that slides the capillary up to 2.5 cm along its axis in a

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narrow groove cut in a silver slab that ensures good thermal homogeneity. The capillary is viewed through a small hole at the centre of the slab and centred on the optical axis. Temperature is controlled to within ±0.2 ◦ C in the interval of interest, from about −40 ◦ C to 20 ◦ C. The microscope, an Olympus B50, is used here in transmission mode. Camera images (Ueye UI 3360), the time and the temperature (from LINKSYS) are stored in video format by means of a home-made software application developed in C++ with the QT suite.

Glass wettability and thin layers on the glass Most of the observations reported here were carried out in the vicinity of the meniscus between water and cyclopentane (figure 1), which was checked at the start and the end of each cycle of hydrate formation. Its shape is a spherical cap, unaffected by gravity, because it is much smaller than the capillary length, (σwg /g∆ρ)1/2 ≈ 4.5 mm, where σwg ≈ 51 mN/m 44 and ∆ρ ≈ 0.25 g/cm3 are the interfacial tension and density difference between liquid water and cyclopentane, and g is the acceleration due to gravity. In each experiment, glass wettability was assessed from the contact angle of the meniscus with the glass wall, θ, measured in the water phase (Figure 1a), inferred from h, the height of the meniscus cap (negative for angles larger than 90 ◦ ), and R=ID/2, the internal radius of the capillary:

tan θ =

R2 − h2 2Rh

(1)

In the untreated glass capillaries used in this study, θ is observed to be small, denoting strong preferential wetting by water, figure 1(c). These angles are reported for each experiment in Table 1. In the silane-treated glass capillaries, θ is slightly above 90 ◦ , and increases slightly with decreasing temperature, from θ ≈ 100 ◦ at T = 0–10 ◦ C, figure 1(c), to 124 ◦ at −10 ◦ C and 150 ◦ (cyclopentane-wet) at −20 ◦ C, figure 2. Note that refraction enlarges the apparent capillary bore and that the contact angle cannot be deduced by

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merely drawing a tangent on an image of the meniscus at the contact line. See ref. 42 for the correction of this aberration.

w CP

T = 10 °C 0 °C θ = 103 ° 104 °

-10 °C 124 °

-19 °C 147 °

Figure 2: Photographs of a meniscus between water (left) and cyclopentane (right) in a silane-treated capillary at various temperatures from 10 to −19 ◦ C, showing the increase in contact angle with decreasing temperature.

Importantly, refraction produces bright reflections (cusps) on the inner wall of the capillary when the conditions are met for total internal reflection of the impinging light rays. These conditions were provided by Hobeika and coworkers 42 : the refractive index n of the material lying against the inner wall must not exceed a certain limit that depends only on the refractive index of the glass wall, n g , and on the ratio of the inner to outer diameters, ID/OD. This limit refractive index can be calculated from the laws of refraction and is found to be 1.36 with our values of n g ≈ 1.46 and ID/OD=200/330=0.606. Therefore, in contact with water or cyclopentane hydrate (n ≈ 1.33–1.36), the inner wall appears as a bright cusp, whereas it is barely visible when covered with cyclopentane (n ≈ 1.41) due to the very weak internal reflection. The bright cusps for n < 1.36 remain bright provided the thickness of the material lying against the wall exceeds the penetration depth of the 9


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illuminating light, ≈ 140 nm for the glass-water-hydrate system of interest. When the layer thickness decreases below this penetration depth, so does the intensity of the bright cusp, which however remains visible for thicknesses commensurate with this depth 42 . Thus, a

≈ 100 nm film of water or hydrate intruding between the cyclopentane and the glass is conspicuous due to its associated cusps.

Experimental procedure The capillary loaded with water and cyclopentane is submitted to cycles of temperature variation around the equilibrium temperature Teq =7 ◦ C, while video-recording hydrate formation and growth at T < Teq and dissociation at T > Teq . Remember here that direct hydrate formation from liquid water and CP would require extremely long waiting times, especially with the small volumes involved. In practice, it is necessary to pass through ice for forming hydrate for the first time. Accordingly, the temperature sequence in all experiments is as shown in figure 3, which also shows snaphots of the water-CP meniscus in the case of a water-wet capillary: i) The sample is cooled from TR ≈ 20 ◦ C, inset figure 3(a), until the sudden formation of ice (initiation to completion in less than 1 s) occurring at TI ≈ −20 to −40 ◦ C; the ice has a grainy, polka-dotted texture due to air or CP inclusions; rapid ice growth from the inner wall to the center of the capillary induces some displacement and deformation of the water-CP meniscus, in the form of a protuberance pointing towards the CP, inset (b). ii) When T is raised to slightly above 0 ◦ C, the ice is seen to melt and a distinct solid of CP hydrate rapidly forms as a crust at the interface between CP and melt water, keeping roughly the same shape as that of the ice-CP interface just before ice melting. Subsequent hydrate growth is controlled by substrate wettability and supercooling, inset (c). iii) The CP hydrate is next melted by raising the temperature to above Teq = 7 ◦ C, 10


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(a)

TR

(d)

CP-E

CP

w

Teq (c) T

∆T = Teq - T

FH

0 °C Temperature

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(f)

(e)

SH

v (b) TI

Ice

0

i

ii

iv

iii

Time

Figure 3: Typical temperature profile in a CP hydrate formation and dissociation experiment. Shading is to better distinguish the different steps. Images (e) and (f) show the hydrate halo creeping on the capillary inner wall, under cyclopentane, with the arrows indicating the growth direction. W: water. CP-E: cyclopentane emulsion in water. FH: first hydrate halo. SH: second hydrate halo.

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which gives rise to an emulsion of CP droplets in water; these droplets rise buoyantly to the top of the capillary, inset (d). iv) Shortly after hydrate dissociation, a second formation is triggered at the water-CP meniscus (and from the emulsion) by lowering T to below Teq , to a given supercooling ∆T = Teq − T. By virtue of the memory effect 45 , there is no need to go through the ice formation and melting steps. Once the meniscus is covered with a hydrate crust, the spreading of the halo onto the substrate is controlled by supercooling and by substrate wettability, see insets (e) and (f) for water-wet glass. Carrying out this second hydrate formation and growth allows these processes to be investigated in the absence of ice, in supercooled water down to −10 ◦ C, or a supercooling of 17 K. The absence of ice was attested by the fact that on warming the samples, there was no change in the texture of the solid phase until reaching the dissociation temperature of CP hydrate (≈ 7 ◦ C). The sequence of hydrate melting (iii) and formation and growth at a different supercooling, ∆T, (iv), can be repeated. The growth processes that follow the completion of the hydrate crust on the watercyclopentane meniscus are presented and discussed in the next section. In addition to observing the neighborhood of what initially is a meniscus between liquid water and CP, the positions of the two other menisci with the vapors may be followed. Unlike the watercyclopentane meniscus, they are mobile and their motion, much slower than that of the halo, provides information on the consumption of water and CP and on the mechanisms of hydrate halo growth.

Results All experiments except those in the last subsection were carried out in untreated, hence water-wet, glass capillaries.

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Halo morphologies and initial velocities In water-wet capillaries, the hydrate halo is observed to systematically advance along the capillary wall on the guest (cyclopentane) side of the meniscus (see Figures 3 through 7). Its morphology and lateral velocity Vh depend very strongly on the supercooling ∆T, as illustrated in Figure 4, which gathers snapshots of hydrate halos grown to the same distance from the contact line, ≈ 0.45 mm, at ∆T from 2.8 to 13 K. We focus first on morphologies, then on lateral velocities. Halo morphologies. For the mildest supercoolings, e.g. for ∆T = 2.8 K in Figure 4, the halo consists of an assemblage of large, plate-like or polygonal crystals. Contrary to the intimate contact between the halo and the glass in our observations of propagation on a flat substrate, the poor tiling of the wall by the large crystals leaves a wide gap between the hydrate halo and the glass. Spreading of the halo on the cyclopentane side is fed by a layer of water flowing through this gap, as is attested by observation of occasional migration of small hydrate crystals or cyclopentane emulsion droplets, see movie M1 in the Supporting Information (SI). The water layer is thicker at lower supercooling. The contact line of the water layer in the gap with the glass wall lies constantly slightly ahead of the edge of the halo (boxes in the top panel of figure 4) and the contact angle, θ, is similar to that in the absence of the hydrate halo, see previous section. On increasing supercooling (decreasing T), the hydrate halo advances as an assemblage of small crystallites that nucleate at numerous locations at the halo front (secondary nucleation events) 46 , hence growing each to smaller size and giving rise to a smoother halo, similar to what is observed for hydrate polycrystalline crusts formed along waterguest interfaces 2,8–10,47 . The hydrate halo grows closer to the glass wall, and the liquid water layer sandwiched between the halo and this wall is too thin to be visible under our microscope (see Figure 4). However, due to the proper choice of capillary dimensions, the hydrate halo and the water layer cause a bright cusp on the inner wall (see above, section

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Exp 1: ∆T = 2.8 K, ∆t = 1873s

Exp 3: ∆T = 5 K, ∆t = 250s

Exp 15: ∆T = 7 K, ∆t = 86s

Exp 18: ∆T = 9 K, ∆t = 40s

Exp 19: ∆T = 11 K, ∆t = 11s

Exp 20: ∆T = 13 K, ∆t = 23s

Figure 4: Snapshots of hydrate halos grown in cyclopentane to similar distances from the water-cyclopentane meniscus (≈ 0.45 mm) along the glass capillary wall at various temperatures or supercoolings. ∆t is the time elapsed since the halos have started advancing from the meniscus. The boxes in the two upper images highlight how the water layer between the hydrate halo and the wall leads slightly on the halo.

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"Glass wettability and thin layers on the glass"), so that their presence and lateral advance along the glass can be precisely monitored. Qualitative evidence for halo thickening with time could be obtained by subtracting images of the same growing halo captured at different times. Hydrate halos have been shown from previous high-resolution microscopy investigations in our laboratory to thicken very slowly, at a rate in the order of a few nanometers per second for cyclopentane hydrate at T ≈ 0–1 ◦ C 30 . Halo lateral velocities Vh . In all experiments, these velocities are observed to be constant from the moment the halo emerges from the meniscus up to a distance of ≈ 1 to 5 mm. Beyond this distance, an abrupt decrease in velocity is observed to occur at the lowest temperatures investigated (T = −6, −4, −2 ◦ C and, occasionnally, 0 and 1 ◦ C): this feature is further presented in the next section. At temperatures above 0 ◦ C we did not observe any significant differences between the velocities of the first and second hydrate halos: in other words, the presence of tiny water droplets on the capillary wall left by the melting of a previous hydrate halo had no or little effect on velocities. Table 1: Summary of initial halo velocities and contact angles measured in glass capillaries for various supercooling conditions.

Exp 1 2 3 4 5 6 7 8 9 10

∆T K 2.8 4.0 5.0 5.7 5.7 6.0 6.0 6.0 6.1 6.3

Vh µms−1 0.3 0.7 1.9 2.8 3.5 3.6 3.7 4.0 4.3 5.2

θ ◦

Exp 11 12 13 14 15 16 17 18 19 20

11 21 19 11 13 18 16 21 15 15

15


∆T K 6.6 6.6 7.0 7.0 7.0 8.0 9.0 9.0 11 13

Vh µms−1 5.2 5.4 4.1 5.4 5.4 7.9 8.7 11.6 14.6 21.0

θ ◦

19 8 14 16 20 24 32 13 18 13

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The ’initial’ velocities are reported as a function of supercooling ∆T in Table 1 and graphically in Figure 5. Halo velocities Vh increase with ∆T much faster than linearly. A power-law fit of the data, Vh = A∆T α , yields α ≈ 2.7 and A ≈ 0.024 µms−1 K−α , with ∆T in K. 100.0

10.0

Vh (µm/sec)

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Vh = 0.024 ∆T 2.7

1.0

0.1 1

10

100

∆T (°C)

Figure 5: Initial halo velocities Vh as a function of supercooling for the experiments reported in Table 1. This power law, as well as the morphological evolution of the halo with supercooling, are very similar to what has been observed for polycrystalline gas hydrate crusts growing laterally along water-guest interfaces (for a review, see ref. 5 ). In particular, the lateral velocities of these crusts V have been observed to increase with ∆T as a power law with an exponent log V/ log ∆T in the range of 2.5, whether the guest fluid is methane, CO2 , ethylene, propane or a mixture of these compounds 2,3,10 . This behavior has been accounted for 2 by means of a heat transfer model 48 , which predicts the product of the crust lateral velocity and the crust thickness to be proportional to ∆T 3/2 , and the assumption 2 that the initial crust thickness is inversely proportional to ∆T, consistent with the observations by Li et al. 47 We argue below (next section) that there are strong similarities between the growth processes of a hydrate crust over a water-guest interface and that of a hydrate halo 16


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over a water-wet substrate, on condition that enough water is supplied to the halo front by the water layer traveling along with the halo, sandwiched between it and the substrate. Cyclopentane hydrate halos have previously been observed by high-resolution microscopy, and their velocities measured at T = 0– 1 ◦ C, in a different configuration: a water drop sitting on flat glass under cyclopentane, with the hydrate halo creeping out of the contact line on glass 30 . The radial velocities were considerably smaller (two to five times) than the velocities measured here (Vh ≈ 3.6–5.4 µms−1 , see table 1), and primarily depended on the sources of water contributing to halo growth, either the water present on the substrate as precursor films and breath figures or droplets left by the melting of a previous halo, or present in the cyclopentane as a ’fog’ and as dissolved molecules 30 . In this earlier study, no or little evidence was found of water being drawn out of the drop by capillarity between the halo and the substrate. One possible reason for such a difference is the geometry of the substrate, which here is curved and leaves more room for water to flow between the halo and the substrate. Another reason is that the bulk water in our open capillaries remains on one side in contact with the atmosphere and therefore at constant pressure, unlike when water escapes through the contact line from a water drop sitting on flat glass and entirely enclosed by a hydrate crust. In a few experiments (#3 to 7 in Table 1), the movements of the water-vapor and cyclopentane-vapor menisci were monitored along with that of the halo. They highlight the volumes of water and cyclopentane incorporated into the hydrate halo and its underlying water layer, both advancing with a velocity Vh along the capillary wall. Figure 6 shows snapshots obtained in one of those experiments. When the hydrate halo and the water layer are advancing in liquid cyclopentane, these two menisci are observed to move in the same direction as that of halo growth, albeit at much lower rates Vwv and VCPv , cf. Table 2. The movement of the water-vapor meniscus corresponds to water being incorporated in the hydrate halo and in its accompanying water layer. Recalling that this structure II hydrate contains one CP molecule per 17 molecules of water, it will be realised that the

17


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hydrate halo

water

(a)

CP

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vapor

t = 0

t = 165 s

(b) vapor

t = 55 min

water

(c) t = 64 min

(d) Figure 6: Snapshots from experiment 4 showing the hydrate halo growing along the capillary wall, together with the water-vapor and cyclopentane-vapor menisci. At early times (a,b), the halo in cyclopentane and the CP-vapor meniscus both advance in the same direction. At late times, (c-d) (images recentred), when the halo has overrun the CP-vapor meniscus and is continuing its advance along glass in vapor, the CP-vapor meniscus moves in the opposite direction.

18


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Table 2: Halo, CP-vapor and water-vapor meniscus velocities in the direction of halo growth, measured before (Vh , VCPv and Vwv ) and after the CP-vapor meniscus is overrun 0 0 0 by the hydrate halo (Vh , VCPv and Vwv ).

Exp 3 4 5 6 7

Exp 4 5 6 7

Halo in cyclopentane ∆T Vh VCPv Vwv K µms−1 µms−1 µms−1 5.0 1.86 0.33 0.42 5.7 2.82 0.37 * 5.7 3.47 0.33 * 6.0 3.59 0.12 * 6.0 3.69 0.48 * Halo in vapor 0 0 0 ∆T Vh VCPv Vwv K µms−1 µms−1 µms−1 5.7 2.71 -0.20 0.26 5.7 4.31 -0.35 0.48 6.0 3.21 -0.13 * 6.0 3.53 -0.45 * * not determined

amount of CP incorporated into the hydrate is very small. The at first sight paradoxical movement of the CP-vapor meniscus in the same direction as the water-vapor meniscus is due to displacement of CP by the advancing hydrate and its underlying water layer. Monitoring the advance of the two menisci necessitated prolonged observation, raising the question of how evaporation might influence the velocities of menisci. CP is much more volatile than water due to the 20-fold difference in vapor pressures. Indeed, in separate experiments without the hydrate, we evaluated the drift in the CP-vapor meniscus to be

≈ 0.04 µms−1 at T = 1–2 ◦ C. The drift in the water-vapor meniscus was much smaller. Taking account of this effect, the data of experiment 3 (see Table 2) show that the vaporwater and the cyclopentane-vapor menisci advance at approximately the same rate, 0.42 vs. 0.37(= 0.33 + 0.04) µms−1 . The first figure, 0.42 µms−1 , would have been somewhat lower, had the effect of the small amount of water left on the substrate in the form of a film or small droplets been taken into account. However, we were not able to quantify this effect. As a first conclusion, the two velocities Vwv and VCPv can be considered as 19


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approximately equal when corrected for the water left on the substrate for the former and for CP evaporation effects for the latter. A simple mass balance model of halo growth in a round capillary is developed in the SI, in which concentric cylinders of hydrate and water advance along the glass wall at a rate Vh . The layers are thin compared to the capillary radius, eh /R , ew /R 1 and their thicknesses are simply related to Vh , Vwv and VCPv . This model predicts VCPv to be very slightly less than Vwv due to the small quantity of CP incorporated in the hydrate, in agreement with experimental observations. Determination of the thicknesses of the hydrate and water sleeves would require resolving very small differences between VCPv and Vwv , less than experimentally feasible in typical situations. However, order of magnitude bounds can be inferred (see the SI), which are consistent with the data reported in Table 2. The hydrate halo advances faster than the CP-vapor meniscus, so that it finally overruns it, as recorded in snapshots (c-d) in figure 6, and in movie M2 of the SI. At this moment, 0

the CP-vapor meniscus changes direction, i.e. VCPv < 0 in table 2, while the hydrate halo keeps advancing under the vapor with approximately the same texture and velocity. The consumption of CP takes place in fact on the other side of the CP-vapor meniscus, and it is reasonable to assume that CP also forms a layer over the hydrate halo conveying CP molecules to the halo front. The above model can be extended to describe these features (see the SI).

Strong slowing down of the halo front In the experiments conducted at high supercooling (at ∆T = 13, 11 and 9 K), we observed an abrupt transition in halo advance, from the constant velocity regime above to strong deceleration. Occasionally, we also observed some slowing down of the halo past some propagation distance in experiments conducted at supercoolings between 6 and 9 K. Figure 7 shows how sharp may be the transition between these regimes. Measuring time, t, and position, l (t), from the break point, the rates of growth are very similar at all 20


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three temperatures and furthermore are compatible with a square root law: l (t) ∝ t1/2 , figure 8. The best fit of our data is l (t) = Bt1/2 , with B = 17 µms−1/2 .

(a)

2500 Halo tip position (µm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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2000 1500 1000 T = -6 °C T = -4 °C T = -2 °C

500 0 0

200

halo front

400

CP

600 time (sec)

halo front

(b)

(c)

Figure 7: (a ) Halo front position or distance from the water-CP interface as a function of time in experiments 18, 19 and 20; (b ) View of a ’young’ halo (T = −4 ◦ C) with a rough texture visible in transmission; (c) past the break point, this halo decelerates and thins to sub-micron thickness only revealed by the cusps along the inner wall. Past the break point the overall thickness of the halo and its accompanying water layer also decreases, to the extent that they are only detectable from the bright cusps on the inner wall, figure 7(b-c), and figure 9 in our previous work 42 . These cusps arise because cyclopentane is replaced on the wall by the hydrate halo and its water layer, whose lower refractive indices (1.33–1.36 vs. 1.41) ensure total internal reflection (and hence a bright cusp) on the inner wall, see the section above. The decrease in intensity at the advancing edge signals tapering to a thickness below the penetration depth of the light rays, which we have estimated to be ≈ 140 nm 42 . 21


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10000 1000 Distance (µm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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T = -6 °C T = -4 °C T = -2 °C

100 10 1 1

10 100 1000 time from break point (sec)

10000

Figure 8: Log-log plot of the halo front position vs. time, both plotted from the break point. The straight line is a t1/2 law. In next section, we analyze these results in more detail, and discuss the possible causes and mechanisms of the sudden decrease in the velocities and overall thickness of the halo and its accompanying water layer.

Substrate wettability effects As reported in table 1, contact angles θ were observed to vary only slightly from one capillary to another, all in the interval 8–24 ◦ , except for experiment 17 (32 ◦ ). It is interesting to note that experiments 17 (θ ≈ 32◦ ) and 18 (θ ≈ 13◦ ), conducted at the same temperature (T = −2 ◦ C), exhibited a significant difference in halo velocities, respectively 8.7 and 11.6 µms−1 , with a higher velocity on the most water-wet substrate. This prompted us to carry out experiments with silane-treated glass capillaries (see Materials and Methods). These substrates are intermediate-wet at ambient temperature, with contact angles slightly above 90◦ ; and increasingly cyclopentane-wet at lower temperatures (θ ≈ 124 ◦ at T = −10 ◦ C, see figure 2). Figure 9 illustrates one of these experiments. Submitting the silane-treated capillary to the same protocole as above, we noted the formation of ice at temperatures somewhat above those in the untreated glass, e.g. TI = −20 ◦ C in figure 9 vs. ≈ -30 to -40 ◦ C in untreated capillaries. This trend in ice nucleation temperatures with substrate wettability 22


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is consistent with observations by other workers 49 . It may be due to some ordering of the water molecules in the liquid phase near hydrophobic surfaces 21 . On warming to slightly above 0 ◦ C, we observed ice melting and the build-up of a polycrystalline hydrate crust at the interface between the melt water and cyclopentane. This crust did not evolve, even after 10’s of minutes (images not shown). In particular no halo was seen. Warming further to slightly above 7 ◦ C triggered dissociation of the hydrate and formation of an emulsion near the meniscus, figure 9(c). The emulsion converted into hydrate as T was lowered below Teq . Upon decreasing T stepwise, we finally observed at T = 0 ◦ C a hydrate halo creeping on the inner wall on the water side of the meniscus, figure 9(b-c).

water

CP

CP

vapor

(d)

(a) after 15 min

hydrate halo

(e)

(b) after 15 min

after 44 min

(f)

(c) ∆T = 7 K

∆T = 17 K

Figure 9: Snapshots from an experiment conducted in a silane-treated capillary. (a) The capillary is initially very slightly cyclopentane-wet, contact angle 100 ◦ at the initial supercooling, ∆T = 7 K (T ≈ 0 ◦ C); (b) Following the first thermal cycle, cf. figure 3 (crust on the meniscus but no halo, data not shown), a halo is formed during the second cycle (see section "Substrate wettability effects"; (d-f) The CP-vapor meniscus shows rapid consumption of CP by the halo and the associated liquid CP film. Time intervals indicated are between successive images.

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Direct evidence for cyclopentane consumption and incorporation into the growing hydrate halo is shown in the snapshots figure 9(d-f), from an experiment conducted at low temperature (T = −10 ◦ C, ∆T = 17 K): the CP-vapor meniscus is seen retreating and ultimately disappearing when reaching the hydrate crust separating the bulk water and CP phases. Comparing figures 9(b) and 9(e), we see from the disappearence of the bright cusp on the water side that the halo is accompanied by a thick film of CP (> 140 nm, the optical penetration depth). This is evidence that CP wets the hydrate to some extent, otherwise it would not imbibe the narrow space between the silane-treated glass and the halo, as we further discuss in the next section. Substrate wettability thus plays a key role in CP hydrate spreading, controlling the direction of halo growth. Halo grows on the water side of the water-CP meniscus if the substrate is wetted by the guest fluid (here, cyclopentane), and on the guest side if the substrate is water-wet. If the substrate is intermediate-wet, there is no halo. We also measured halo velocities, which were found in the range of 0.4 to 1.5 µms−1 for ∆T = 12 to 17 K, with no sign of halo deceleration over distances of a few mms. These values are considerably smaller than the initial halo velocities measured in the opposite direction, on hydrophilic, untreated capillaries (at ∆T = 11 and 13 K, see previous section). The slower spreading compared to untreated glass capillaries, probably is due to the difference in wettability: the silane-treated capillaries used here are only weakly CP-wet, 180 − θ ≈ 60–70 ◦ at the temperatures of interest, compared to the strongly water-wet untreated glass, θ ≈ 8 – 24◦ .

Discussion of halo growth mechanisms Substrate wettability controls the direction of growth of the CP hydrate halo from the water-guest interface. It grows on the side of the fluid that is less wetting to the substrate, helped by a layer of the more wetting fluid sandwiched between the halo and the substrate,

24


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which conveys the wetting fluid to the halo front. In this section, we attempt to give more substance to this physical picture and to shed light on the mechanisms of hydrate halo growth on a substrate. We first draw out the implications of the strong resemblence of spreading of the halo with the growth of a gas hydrate crust at an interface between bulk water and the guest fluid, observed both for water-wet glass (see above, section "Halo morphologies and initial velocities") and CP-wet glass (see previous section). Finally we will discuss the strong deceleration after the halo has travelled a certain distance over the substrate.

General considerations The two substrates involved here differ both in roughness and wettability. The glass wall is smooth and its wettability with respect to the water and guest fluid has been characterized, by means of contact angle measurements (see above). The wettability of the hydrate halo has not been characterized, since contact angle measurements would require planar and smooth hydrate surfaces 50 . Gas hydrates are often assumed to be prefentially wet by water in presence of the guest fluid. Our observations suggest that for CP hydrate, this wetting preference is not strong but moderate. Prior to halo growth, the hydrate crystals are observed to form on the water-CP meniscus, where they then remain and keep growing; and sometimes in the emulsion at the rear of the meniscus, where they grow towards the water-CP meniscus until they touch it, and then continue to grow from this point of contact (data not shown). CP hydrate crystals, once formed on the water-CP meniscus, are observed to continue their growth over this interface, facing water on one side and cyclopentane on the other: a strong wetting preference (for water) would rather lead to crystal expulsion in the water phase, as is observed at water-oil interfaces with other types of crystal-forming systems, e.g. fat crystals 51–53 . Finally, we must remember the ability of liquid cyclopentane to imbibe the narrow space between silane-treated glass and the hydrate halo (see previous section), which would not be possible if the hydrate were 25


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strongly water-wet. Readers are referred further to the large body of work recently reviewed by Zanini and Isa 54 and by Binks 55 , addressing how the wettability, shape and deformability of particles determine their presence at oil-water interfaces, and how deeply they are located in one of these two phases, e.g. they are immersed deeper in the more-wetting phase, and ultimately how the corresponding oil-water emulsions (Pickering emulsions) behave. A further complexity arises here because hydrate particles grow over the interface, fed by molecules coming from both sides.

Linear regime of halo growth Schematic pictures of the advancing hydrate halo are proposed in figure 10, which shows the two geometries, hemispherical and lenticular, quite generally considered in the literature for particles at water-oil or water-air interfaces, as well as for gas hydrate crusts growing over the interface between bulk water and bulk guest fluid 2,48,56,57 . The lenticular geometry, stricly speaking that of a deformable or "soft" halo, has been considered and analyzed by some authors 57 in relation to water-oil emulsions stabilized (or not) by gas hydrates. The features that we discuss next do not depend much on the particular geometries, unlike other features such as emulsion stability 44 . The angles α, β and γ at the hydrate-water-guest contact line (see figure 10) obey respectively the Young equation

σhg − σhw = σwg cos(γ)

(2)

sin( β) sin(α) sin(γ) = = σwg σhw σhg

(3)

and Neumann’s contruction

where the equilibrium interfacial tension between the aqueous phase and guest fluid, σwg , is known (≈ 51 mN/m with CP as guest fluid), but not that between hydrate and guest 26


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glass capillary 𝜃

ew water layer Th, Ch eh

𝜎hw

𝛾 𝜎wg 𝛼

𝛽

hydrate halo

T, C guest

(a)

𝜎hg glass capillary ew eh

water layer

Th, Ch 𝜎hw 𝛽

hydrate halo

𝛾

𝜃 𝜎wg

T, C

𝛼 guest

𝜎hg

(b)

Figure 10: Enlarged view of the halo front with two possible geometries: hemispherical (a) and lenticular, typical of a soft solid with angles determined by Neumann’s construction (b). The substrate is strongly water-wet (low contact angle θ). fluid, σhg , and that between hydrate and the aqueous phase, σhw (see the recent reviews by Aman et al. 58 and by Maeda 59 ). In the absence of surfactant adsorbing on the hydrate, σhg > σhw and, therefore, in the hemispherical configuration, cos(γ) > 0 or 0 < γ< 90◦ . As discussed above, we expect γ to be quite large: the hydrate is not strongly wet by water. For simplicity, we consider here a water-wet substrate, but the arguments below may easily be transposed to a situation where the substrate is CP-wet, using a diagram like figure 10 with the water and guest phases exchanged. Figure 10 highlights how the water-wet character of the glass substrate is responsible for the existence, ahead of the halo front, of a water-guest interface concave towards the guest phase, provided the contact angle θ is small enough. This interface is formed by the leading edge of the water layer, extending ahead of the halo front, with an interfacial area increasing with the water-wet character of the substrate, i.e. smaller θ. Its radius of curvature is similar to that of the water-CP meniscus in the absence of the hydrate halo, i.e. 27


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R/cos(θ ), cf. the boxes in figure 5, and thus much greater than the thicknesses of the halo and water layers. Figure 10 is not to scale in this respect. The extended water-guest interface ahead of the halo front resembles that between a bulk aqueous phase and a guest fluid, where a polycristalline gas hydrate crust is advancing, a situation widely investigated over the past two decades, most attention being paid to crust morphology and velocity. The crust front is often modelled as hemispherical, figure 10(a), a larger part of the crust being immersed in water when the water-wet character of the hydrate increases. Provided water arrives fast enough here through the water film between the glass and the hydrate, the two situations are similar, and the insights gained from the above investigations are directly applicable to halo fronts advancing over water-wet substrates. Physical modeling 2 has dealt with either the heat transfer at the crust front 2,60 , where the heat generated by hydrate formation is evacuated by conduction, or with the diffusive mass transfer of guest molecules to the crust front 1,4,6 , driven by the gradient in guest-concentration in the water phase. Here, we remember that guest solubility in the liquid water equilibrated with the guest fluid far from the growing front, is higher that the solubility in the water equilibrated with the hydrate, at the front. The heat and mass transfer processes are inter-related, as recently analyzed rigorously by Mochizuki and Mori 61 , who derived the temperatures and guest concentrations in water and temperatures around the front and for the lateral growth rate of the crust. They found, at least for methane hydrate crusts under typical conditions, that the temperature at the crust front, Th , is nearly unperturbed, i.e. Th ≈ T. The rate of lateral growth of the crust is controlled by the diffusive supply of the guest substance to the crust front, an effect due to the fact that thermal diffusivity is more than two orders of magnitude larger than the mass diffusion constant of guest molecules in water 13 . This analysis can be transposed to hydrate halo growth on a water-wet substrate, considering that the thermal diffusivities of water and quartz or silica are not so different. The concentration of guest molecules in the water near this interface is C = C ( T ), the

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equilibrium concentration of a (metastable) guest-saturated water phase at temperature T, see figure 10. This concentration is higher than in the aqueous phase at the halo front, Ch = C ( Th ), corresponding to a liquid water-hydrate equilibrium at the temperature Th ≈ T.

1

As a preliminary conclusion, a hydrate propagating as a halo over water-wet substrates under the guest fluid should obey similar laws and therefore, as is indeed observed experimentally, have similar morphology and lateral growth rate to those of hydrate crusts propagating over water-guest interfaces, provided the water layer between the substrate and the halo conveys enough liquid water to the halo front. The strikingly similar exponents of the power-law dependence of the rate of spreading on the supercooling (see above, section "Strong slowing down of the halo front") is an illustration of this analogy.

Halo propagation beyond the break point A full treatment of the complicated, coupled, convective fluid mass and heat flows in our system would require sophisticated numerical methods, like those deployed by Mochizuki and Mori in their analysis of the rate of growth of gas hydrate crusts at water-guest interfaces 61 . Such a numerical analysis is beyond the aim and scope of this paper, but a crude, qualitative argument provides insight into the second regime of halo propagation. The above section "Strong slowing down of the halo front" reports experiments in which the CP hydrate halo, after having propagated with a constant lateral velocity, strongly decelerates past some distance or time. This deceleration is simultaneous with the thinning of the water layer, see figure 8, resulting in strong viscous resistance to water transport, quantified by a pressure drop given by the plane-Poiseuille expression: ∆Pvisc = 12

µw lv e2w

1 From

(4)

the scarce data available 62 , cyclopentane solubility in water very slightly increases with decreasing T, and it is likely that cyclopentane solubility in liquid water equilibrated with cyclopentane hydrate decreases with decreasing T, as is the case with the most common sparingly soluble hydrate-formers.

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where ew is the thickness of the water layer (supposed to be constant), v is the average water velocity, l the length of the hydrate halo and µw the viscosity of water. The pressure drop balances the Laplace pressure jump across the water-CP interface at the edge of the water layer, ∆PL ≈ σwg cos(θ )/R. The velocity v is somewhat larger than Vh = dl/dt, because part of the liquid water arriving at the front readily transforms into hydrate and is incorporated into the halo. The mass flux of water flowing between the halo and the glass wall, 2πRew ρw v, remains in part liquid, with thickness ew and density ρw , or mass flux 2πRew ρw Vh , and in part is incorporated into the hydrate halo front, with thickness eh and density ρw,h , or mass flux 2πReh ρw,h Vh , leading to:

v = (1 +

eh ρw,h )V ew ρw h

(5)

where the density of water in the hydrate is ρw,h =0.785 g/cm3 , assuming that all large cavities in the structure II hydrate are occupied by cyclopentane molecules. Equating ∆PL to ∆Pvisc , the following differential equation is obtained

12

e ρ µw (1 + h w,h )ldl/dt = σwg cos(θ )/R 2 ew ρ w ew

(6)

which is integrated as a Lucas-Washburn law s l ( t ) = ew

σwg cos(θ ) t1/2 6Rµw [1 + (eh ρw,h )/(ew ρw )]

(7)

In the last equation all quantities under the square root sign are known except the ratio eh /ew , which however has a very limited influence on the value of the prefactor of t1/2 . For values eh /ew varying between 2 and 0, this prefactor lies in the range of 170ew to 270ew , to be compared with the value obtained by fitting the experimental points in figure 8 with a square-root law, i.e. 17 µms−1/2 . The resulting value of ew , in the range of 0.1 µm, is consistent with the observation by optical microscopy reported above (section "Strong

30


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slowing down of the halo front"), that the thickness of the hydrate halo and its underlying water is commensurate with the light ray penetration depth ray, 140 nm. Here, the halo length l has been counted from the break point, which amounts to neglecting the viscous pressure drop generated by water flow in the (thicker) layer till the break point. The agreement between experimental observations and the predictions of this very simple model is rather surprising considering the assumptions made. The viscous Poiseuille regime does not set in immediately, but is preceded by a regime of linear (constant-velocity) advance, a feature also observed at early times for Poiseuille imbibition flows in capillaries. Another assumption is the constant value of the contact angle θ while the halo and its water layer are advancing along the glass substrate. A further assumption, embodied in the plane Poiseuille permeability value, e2w /12, is that of a water layer with uniform thickness ew or, equivalently, a smooth halo surface. In some experiments where we sealed the capillary on the water side rather than leaving it open, we observed the hydrate halo to slow down faster than in open capillaries, and later the hydrate crust between water and cyclopentane to break down. The liquid cyclopentane then entered the water phase and formed channels through the water zone, quickly wrapped with a hydrate crust (data not shown). Cavitation in the water zone, with bubbles of vapor, was occasionnally observed, signalling again a strong pressure drop in the water as compared to the guest phase. The latter cavitation phenomenon looks like that recently observed with strongly salted water sealed in thin capillaries by salt crusts formed by evaporation 63 . At this point it is indeed worth mentioning again the analogous process of salt creeping from the edges of an evaporating drop of salted water on a hydrophilic substrate 27,29 . The situation when brine flows between the substrate and the crystallites is referred to as bottom supplied creeping. The evaporation of the water, itself related to the water vapor pressure or humidity above the salt front, is the driving force for this phenomenon 26 , just as the transfer of guest molecules in liquid water is that for the growth of gas hydrate 31


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halos on water-wet substrates. In concluding this section we may speculate that the break point between the two regimes of growth corresponds to viscous drag in the water sleave superseding molecular diffusion at the crystal interface, as the rate-determining process.

Conclusions and outlook Understanding gas hydrate growth over solid substrates is important for a variety of natural or industrial processes, involving for instance sedimentary materials or the particles considered for gas storage or separation or for water treatment, whether mesoporous or not. This behavior has been little investigated by direct microscopy observations, unlike gas hydrate growth over water-guest interfaces, which has been a dominant topic in gas hydrate research over the past two decades. The experiments presented here provide a coherent physical picture of cyclopentane hydrate growth behavior over solid (glass) substrates under various supercooling and substrate wettability conditions. Water-wet (bare glass), guest-wet (silane-treated glass at low temperature), and intermediate-wet (silane-treated glass above 0 ◦ C) substrates have been considered, and the range of supercooling conditions extended from 2.8 to 17 K. The experiments consisted in triggering hydrate formation on the meniscus between the host (water) and guest (cyclopentane) fluids in open glass capillaries with controlled wettability and then, once this meniscus was covered with a hydrate crust, in observing susbsequent hydrate growth under the optical transmission microscope. This growth, which occurs as a halo emerging from the edges of this hydrate crust and creeping on the glass substrate, depends both on substrate wettability and supercooling. Substrate wettability controls the direction of growth of the CP hydrate halo on the substrate: towards the guest side of the water-guest meniscus, i.e. under the guest phase, when the substrate is water-wet, and vice-versa, when the substrate is guest-wet. There

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is no hydrate halo growing on intermediate-wet glass. The mechanisms for hydrate halo growth are similar whether the substrate is water-wet or guest-wet: in both cases there is a liquid layer of the fluid that wets the glass substrate flowing between the substrate and the hydrate halo and conveying the water or guest molecules to the halo front. Supercooling has also an important role, which has been investigated in detail in the case of water-wet substrates. Initially, the effects of supercooling on halo morphology and velocity are similar to those observed for gas hydrate crusts growing laterally at water-guest interfaces. At low supercooling (high temperature), the halo morphology is rough and composed of large monocrystals that leave considerable space for liquid water to flow between the halo and glass. At high supercooling (low temperature) the halo is smooth and grows very close to the glass wall: the water layer between the halo and glass is thin. The halo lateral velocity, which is steady in the early stages of halo growth, strongly increases with supercooling, in a manner similar to what is observed for gas hydrate crusts growing at water-guest interfaces. This similarity can be explained as follows. In the early stages of halo growth, there is no limitation for the transport, through the wetting fluid layer, of fluid molecules from the bulk water at the rear of the water-guest meniscus to the halo front. Because its leading edge has a low contact angle with the substrate, this layer advances ahead of the halo front (see Figure 10) and has therefore a large area of contact with the other phase: the configuration is very similar to that of a gas hydrate crust advancing along an interface between bulk water and bulk guest, where the transfer processes occurring near and at the crust front are the limiting factors for growth. This similarity has been clearly demonstrated to hold in water-wet capillaries, and the experimental demonstration remains to be carried out in guest-wet capillaries. Here, different to gas hydrate crusts growing at water-guest interfaces, there is a limiting factor to halo growth, flow of water between the glass and the hydrate sleeve. Past some distance, the halo decelerates and its underlying water layer thins down to

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sub-micron thickness; it is so thin (and long) that a strong resistance to the flow of water is exerted. This phenomenon has been observed only for the strongest supercoolings (or lowest temperatures). While a clear understanding of why and for what conditions this sudden change occurs has still to be reached, the measured halo velocities and thicknesses can be reconciled within a very simple approach adapted from the Lucas-Washburn model. An extension of these investigations to more common gas hydrates is underway. In fact, the experimental setup and procedure lends itself relatively easily to adaptation to a water– gas system under pressure, as we have shown in recent work on contact angles inferred from micrographs of the water-CO2 meniscus in a microcapillary 42 . Here, the situation was particularly challenging, in that tenuous hydrate halos with thicknesses as low as a few tens of nanometers were present and advancing on the glass. Their visualization turns out to be possible in cylindrical capillaries with a standard transmission microscope. Better insight into hydrate crystal morphologies and inhibiting or promoting mechanisms of surfactants or other additives (such as asphaltenes) will require minimization of refraction effects, and therefore use of square or rectangular capillaries, in combination with higherresolution microscopy. Future work will also focus on the effects of the substrate curvature on halo growth.

Acknowledgements This study was supported by Agence Nationale de la Recherche, project HYDRE (ANR 15CE06). We thank Profs. Patrick BOURIAT and Manuel ILDEFONSO for their support and insightful comments.

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Supporting Information Available • Movie1.avi: From experiment 3 in Table 1. Shows how hydrate halo growth is fed by water from behind the initial water-cyclopentane interface. Droplets of cyclopentane emulsion and small hydrate crystals slip into the water film between the hydrate halo and the glass and act as flow tracers. • Movie2.avi: From experiment 6 in Table 1. Shows successively the dissociation of the hydrate halo at ≈ 7 ◦ C, the formation of a new hydrate crust on the watercyclopentane meniscus on lowering the temperature to T ≈ 1 ◦ C, and the propagation of a hydrate halo under the cyclopentane liquid phase. The halo finally overruns the cyclopentane-vapor meniscus and advances under the vapor with no change of speed or texture (see Table 2). • ModelSI.pdf: Model of cyclopentane hydrate halo growth in a round capillary. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Graphical TOC Entry vapor water

CP

vapor water-wet substrate water layer

hydrate halo cyclopentane (CP)

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Roles of wettability and supercooling in cyclopentane hydrate

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