How Do Gas Hydrates Spread on a Substrate? - Crystal Growth

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How do gas hydrates grow on a substrate ? María Lourdes Martínez de Baños, Nelly Hobeika, Patrick Bouriat, Daniel Broseta, Eduardo Enciso, Franck Clement, and Ross Brown Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.6b00471 • Publication Date (Web): 01 Jul 2016 Downloaded from http://pubs.acs.org on July 14, 2016

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Crystal Growth & Design

How do gas hydrates spread on a substrate? Rev. 09:40

Friday 1st July, 2016

María Lourdes Martínez de Baños,†,§ Nelly Hobeika,†,‡,§ Patrick Bouriat,† Daniel Broseta,∗,† Eduardo Enciso,¶ Franck Clément,‡ and Ross Brown∗,‡ Laboratoire des fluides complexes et de leurs réservoirs (LFC-R), UMR CNRS 5150, Université de Pau et des Pays de l’Adour, 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, and Departamento de Química Física, Universidad Complutense de Madrid, Ciudad Universitaria, 28040 - Madrid, Spain E-mail: [email protected]; [email protected]

∗ To

whom correspondence should be addressed

† LFC-R ‡ IPREM ¶ Universidad § MLMdB

Complutense and NH contributed equally to this work

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Abstract Growth of gas hydrates as fast-growing polycrystalline crusts at interfaces between water and guest phases is well documented, but the mechanisms of hydrate growth on solid substrates are much less known. We report here on cyclopentane (CP) hydrate spreading on glass (fused silica) under CP. As seen for methane hydrate by Beltrán and Servio (Cryst. Growth Des. 10 (2010) 4339-4347), CP hydrate grows on glass as a ’halo’ radiating from the contact line of a ’primary’ drop. Complementary optical microscopies at micron resolution here allow identification of the mechanisms of halo growth and melting. We conclude that forms of water on the substrate control halo spreading, namely: a precursor film near the contact line and a breath figure (dew) condensed from the CP (halo spreading at ≤ 2 µms−1 at T ∼ 0 ◦ C or subcooling ∼ 7 ◦ C); and ’leap-frogging’ (at ∼ 10 µms−1 ) over ’secondary’ drops left behind by melting a previous halo. Halo thickening, about 5 nms−1 , is attributed to water condensation, either incorporation of water dissolved in CP (like ablimation) or settling of water ’fog’ from the CP. Halos spread slower on untreated, compared to hydrophilic glass, an effect attributed to the quantity of water present on the substrate; a similar trend is noted when the CP phase is not pre-equilibrated with water prior to the experiment. No hydrate halo was detected on hydrophobized (silane-treated) glass, where the breath figure is absent.

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1 Introduction Gas hydrates are ice-like crystalline structures made of hydrogen-bonded water molecules encaging molecules of a hydrate former (guest), such as light hydrocarbons, refrigerants, or rare gases, CO2 , etc. In the gas and oil industry, hydrates are considered a nuisance because they block hydrocarbon flow lines and their dissociation in marine sediments might render offshore platforms and pipelines unstable. Now, the huge energy resource of methane hydrates in marine sediments is viewed as an opportunity and many other applications of gas hydrates are emerging, such as gas separation, energy transport and storage and water desalination or purification. Research in this area mostly addresses inhibition or acceleration of the kinetics of gas hydrate crystallization by means of additives. For example, addition of mineral particles (e.g. oxides) to the water-gas system influences hydrate growth, 1 but the inhibiting or promoting mechanisms are still ill-understood. Hydrates of guest molecules sparingly soluble in water and vice-versa form preferentially at water-guest interfaces, as a polycrystalline crust that grows rapidly to full interface coverage. The crust then acts as a weakly permeable barrier to the water and guest molecules, impeding crust thickening. The morphologies and lateral growth rates of these crust layers are well characterized and understood, at least for the most common guest fluids, 2–8 even though some questions remain as to the respective effects of heat and mass transfers. 9,10 In this paper, we report and discuss observations of gas hydrate growing on glass as a ’halo’, a term coined by Beltrán and Servio. 11 These authors observed a methane hydrate crust growing rapidly on the surface of water drops on a glass substrate and then spreading radially into the methane-rich phase as a halo on the glass surface ’beyond the water boundary’. This halo propagated hydrate formation from one water drop to another, the ’bridge effect’. 11 Consistent with the resolution of their observations, Beltrán and Servio argued plausibly that the source of water feeding halo growth is that under the crust of the first drop, drawn out by capillarity between the halo and the ’naked glass’ 3



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substrate, i.e. the glass immersed in the guest fluid. Beltrán and colleagues 8 recently published further evidence of a methane hydrate halo growing from a water drop sitting on sapphire, another hydrophilic substrate. Hydrate halos might be relevant to geological processes where gas hydrates are present in sediments in an excess of gas, e.g. when these sediments overlay a zone of high gas saturation and low water or brine saturation (in a water-wet sand, this water forms capillary bridges between the grains). The halo growth investigated here is expected to be the dominant pore-scale process occurring in this so-called excess gas configuration. 12 The halo may act as cement between neighbouring sand grains and confer high mechanical rigidity to the hydrate-bearing sediment. 13,14 The halo often is seen in conventional experiments, at moderate resolution, e.g. by macro-photography, in which hydrate formation and growth at the water-guest interface are observed behind glass or sapphire windows. 15–19 Hydrate formation typically starts at the water-guest interface, which is rapidly covered with a hydrate crust, and then a halo is seen ascending the window, originating from the contact line between the window and the water-guest interface. Interestingly, halo growth is observed to be faster with repeated cycles of hydrate dissociation and reformation. 16 Additionally, contrasting the influences of substrate properties like wettability, thermal conductivity, etc. on the growth of the halo with their effects on the frost counterpart, 20 might provide clues why some mineral particles are better hydrate promoters than others. 1 So far, although understanding hydrate halo growth is of some importance, observational difficulties appear to have prevented detailed examination of the process. Cyclopentane hydrate is considered a proxy of natural gas hydrates because cyclopentane is sparingly soluble in water and like natural gas forms structure II hydrate. Here, complementary contrast modes in optical video-microscopy allow a detailed view of this model system, at high spatial (≤ 1 µm) and temporal (≤ 0.1 s) resolution. Like Beltrán and Servio, we examine a drop of water on a glass substrate immersed in the guest (hydrate-former).

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The observations contribute to understanding the mechanisms of halo growth and melting when the conditions for hydrate stability or dissociation are met, namely temperatures respectively below or above 7 ◦ C at atmospheric pressure, in the case of cyclopentane. Employing a microscope to observe hydrate formation imposes stringent conditions on the thickness of the sample, sample cell and cell holder, such as approaching the objective to within a few mm of the sample and maintaining a total thickness less than about 5 cm. The mild conditions of formation of cyclopentane hydrate ease design problems arising from these optical constraints. Hydrates are mainly made up of water molecules, in a proportion of 17/18 for cyclopentane hydrate, the other 1/18 being cyclopentane molecules. Yet hydrate halos grow in an environment where water is lacking: in between the substrate and the guest phase, in which very small amounts of water molecules are dissolved, in the range of 0.01 mol% for water in cyclopentane. Here, as in the study of Beltrán and Servio, the system is a water drop sitting on the substrate immersed in the guest. Considering the solubilities, it seems reasonable to assume that most, if not all, of the water feeding halo growth comes from the reservoir of water in the drop itself. These authors indeed suggested that water flows between the glass and the hydrate halo, but did not provide direct experimental evidence. Our aim is to re-examine the interaction of the hydrate halo with the substrate. We use a combination of optical microscopy contrast methods, including differential interference contrast (DIC), widefield fluorescence and confocal reflectance microscopies. Two kinds of fluorescent markers could be added to the water: a molecular probe used to highlight solid-liquid and liquid-liquid interfaces, and fluorescent latex nano-beads, used as flow tracers. These markers give access to details apparently not discussed previously. A further novelty of our system is that we deliberately pre-saturated the cyclopentane with water at room temperature. Lowering the temperature therefore causes demixing, simply because the solubility of water in cyclopentane drops with decreasing temperature. 21,22 We study here the interaction of the hydrate halo with the resulting ’breath figure’

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(dew on the glass) and ’fog’ (microdroplets of water in the cyclopentane bulk). The next section briefly reviews necessary background information on the physics of breath figures and their interaction with a new (crystal) phase forming on a substrate. The wetting behaviour of water and cyclopentane on glass is also important, but, as specific to a substrate, is discussed in the experimental section 3.2. Following experimental section 3, describing the setup, materials and methods, section 4 discusses the observations and the more straightforward conclusions. Section 5, preceding the general conclusion, presents the more tentative aspects of our interpretation of the observations.

2 Background information We briefly review two topics of surface physics relevant to our study. The first is pseudopartial or frustrated-complete wetting of a liquid, 23,24 here water, being strongly attracted to the substrate (glass), but unable to form a film of macroscopic thickness, i.e. complete wetting with zero contact angle, because long-range forces oppose it. This wetting behaviour is encountered in systems with antagonistic short- and long-range forces such as our glass–water–cyclopentane system. Indeed, strong attractive short-range forces exist between a hydrophilic glass substrate and water molecules, which adsorbs as a nm’s thin film on the substrate. Yet, a macroscopically thick water film cannot exist on glass because long-range van der Waals forces oppose it: the Hamaker constant of the water film sandwiched between glass and cyclopentane is positive. (We assume here that these forces are dominant, see the Supplementary Information, SI, section 3). As a consequence, a thin ’precursor’ film of water is expected to expand on the substrate from the edges of a water drop deposited on a dry substrate - that is, a substrate with no water on it. This precursor film is thicker than a few molecular layers, say 1-2 nm, at most for small molecules such as water, only when the contact angle with the substrate is very low. 23–25 Another consequence is that an excess of liquid water on the substrate does not form a

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stable thick film but rather two coexisting surface states: the thin water film described above, and domains of macroscopic thickness, which often turn out to be droplets. 26 Further illustrations of frustrated complete wetting include some of the lower n-alkanes on water near room temperature. 27 The second topic is ’breath figures’, the dropwise condensation of a non-completelywetting liquid on a substrate; and the interaction of such patterns with a new crystal phase forming on the substrate. The structure and evolution of breath figures formed from a vapour on a cold substrate, i.e. dew in the case of water, is a rich subject. 28–31 These droplets form only if the substrate is not completely wet by the liquid, i.e. the contact angle is non zero (a thick liquid layer would form on substrates completely wet by a liquid with vanishing contact angle). Substrate wettability strongly influences the amount of liquid condensed on the substrate and how these droplets grow and evolve. For a given duration of exposure, liquid is more abundant on the substrate for smaller contact angles, 30 because the energy barrier for heterogeneous nucleation is lower; 32 in addition, droplets that form at the early stages of condensation evolve faster into a film-like pattern. 30 In the case of water droplets, when one of these droplets on the substrate freezes into ice, the emerging ice crystal acts as a humidity sink: it grows while neighbouring droplets shrink and disappear, leading to an expanding droplet-free or depleted zone near the growing ice crystal. The bulk counterpart of this phenomenon is known in cloud physics as the Wegener-Bergeron-Findeisen (WBF) process; 33 it is driven by water molecules diffusing towards the ice crystal where vapour pressure is lower than that above the droplets of (super-cooled) liquid water. This phenomenon also occurs when one of the drops is salted (and hence the vapour pressure is lower above it). 34 In the experiments reported below, breath figures appear on the substrate on cooling cyclopentane pre-saturated with water at room temperature (∼ 20 ◦ C) and a droplet-free zone arises around the ice– or the hydrate– covered zone, for which one possible explanation is the WBF process.

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3 Experimental 3.1 Experimental setup

Figure 1: Experimental setup (schematic, not to scale): A photometric absorption cell is filled with cyclopentane at room temperature and a single drop of water is deposited on the lower face. The cell is inserted in a thermostated holder (not shown), on an inverted microscope. Angle θ is the contact angle. The experimental configuration is schematically depicted in figure 1. A photometric absorption cell (Hellma QS 110-2-40, path length 2mm, volume ∼ 700 µl) is filled with cyclopentane pre-equilibrated (unless otherwise specified) with water at room temperature (∼ 20 ◦ C). A small drop of water (∼ 1 µl), the ’primary’ drop, is deposited close to the centre of the lower face of the cell, using a low-flow-rate syringe pump (Aladdin-1002X) and a syringe needle with a bent tip. The cell is loosely stoppered, so that the pressure inside the cell is atmospheric pressure. The rectangular cell is inserted with its faces horizontal, in a cylindrical aluminium (AU4G) holder (not shown in fig. 1) with rectangular apertures for observations on an inverted microscope. The upper face of the cell-holder is in contact with an annular Peltier element (itself cooled by a water-cooled radiator not shown in fig. 1). The central holes of all elements of the setup allow passage of the full aperture beams of the microscope. The Peltier element is driven by a temperature controller (Accuthermo ATEC302) and a platinum resistance thermometer inserted in the cell holder (TME, ref. 29223B). 8


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All the above parts are enclosed in a dry nitrogen atmosphere to prevent condensation, in an ad hoc plastic holder with windows on the optical axis: a standard 45 mm diameter cover slip as lower, observation window (Knittel Gläser) and an IR filter above, to prevent local heating during DIC observations (cutoff 710nm, Edmund Optics). In preliminary observations, we employed an AE21 inverted microscope (Motic), equipped with a Ueye SE1240 camera (IDS). Most of the data reported here were recorded on a Ti Eclipse (Nikon) with a PROEM 512B EMCCD camera (Princeton Instruments) or an ORCA-4.0 sCMOS camera (Hamamatsu). Various contrast modes were employed, principally bright field (transmission), differential interference contrast (Nomarski phase contrast, DIC) and widefield fluorescence. Confocal reflectance at wavelength λ = 532 nm (a DPSS laser, Crystal Laser) was performed with a C1-Si ready laser scan head (Nikon). A simultaneous, but not confocal transmission channel is available (no pinhole). We used long working distance objectives ranging from x4 to x20, sometimes augmented with a x1.5 tube extender lens. The thickness of the cell and of the liquids themselves introduces strong axial smearing of the focus, so best results are obtained with objectives with a correction ring, such as the CFI SPFL ELWD x20 (Nikon). Sub-micron resolution is obtained for the highest magnification, e.g. with the x20 objective and the tube extender. Widefield fluorescence was performed with a high power LED (Thorlabs, λ = 505 nm) and appropriate filters (Semrock). The data were analysed with ImageJ 35 and gnuplot. 36 Micrographs shown here underwent only linear contrast enhancement to highlight specific features.

3.2 Substrates and contact angles The substrate, i.e. the inner wall of the photometric absorption cell, is made of fused silica (Heraeus, Suprasil 2 Grade B). In the early stages of this study, we used cells merely rinsed with ethanol and deionized water and dried after each experiment: the corresponding substrate is referred to below as untreated. As received from the manufacturer, these cells, 9



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initially were hydrophilic (contact angles θ ∼ 20 − 30◦ , but aged upon repeated use, with (poorly reproducible) contact angles as high as θ ∼ 90◦ . We therefore decided to render the glass highly hydrophilic by a ∼ 5 min exposure to a cold atmospheric plasma discharge prior to experiment. The plasma discharge was produced in a home-made setup (1 vol.% O2 in He) producing a plume of specific ionization wave-like discharge pulses, propagating in air at close to room temperature. 37 The plume, diameter ∼ 1 mm, was directed into the sample cell so it licked all the interior. The contact angle in the plasma-treated cells was in the ∼ 1◦ range after treatment, reverting to 60–90 ◦ over a period of days. For some experiments, the glass substrate was rendered strongly hydrophobic by treatment with a silane (Sigmacote, Aldrich), resulting in a contact angle ∼ 145 ◦ . We prepared primary drops in the millimetre range, much smaller than the capillary length (γ/g∆ρ)1/2 ∼ 4.5 mm, where γ ∼ 50 mN/m and ∆ρ ∼ 250 kgm−3 are the interfacial tension and density difference between water and cyclopentane, and g = 9.8 ms−2 is the acceleration due to gravity. Gravity therefore had a negligible effect on the drop shape, which was spherical or a spherical cap. A rough estimate of the contact angle, θ, was thus obtained from the drop radius on the glass r and the drop height deduced from focusing on the glass and at the top of the drop: cos(θ ) = (r2 − h2 )/(r2 + h2 ), where h is the true height, deduced from the apparent height, hA , corrected for refraction in water (refractive index nW ): h = nW hA . The top of the drop was most readily determined from cyclopentane emulsion after dissociating the hydrate, or by putting fluorescent tracer beads in the water. For small values of h or low contact angles, θ was obtained directly from confocal or wide-field reflectance micrographs of the interference fringes formed by rays reflected by the glass-water and water-cyclopentane interfaces. 38

3.3 Chemicals The water is ultra-pure (resistivity > 18 MΩcm, PureLab Classic from ELGA Labwater). Cyclopentane was bought from Sigma-Aldrich (reagent grade, purity > 98 %). In some 10


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experiments, a water-soluble fluorescent dye, DASPI (trans-4-[4-(dimethylamino)-styryl]1-methylpyridinium iodide, Aldrich), was added to the primary drop in small amounts (∼ 2 × 10−6 M). The fluorescence of this dye is enhanced when its geometry is constrained to the planar form, e.g. by viscous solvents or by adsorption at solid/liquid or liquid/liquid interfaces. 39 DASPI is a weak surfactant, so it also adsorbs onto the water-cyclopentane interface, where it slightly lowers the interfacial tension, e.g. by about 3 mN/m (with the above solution, relative to pure water-cyclopentane, ∼ 50 mN/m). In other experiments, rhodamine 6G– tagged PMMA nanobeads 40,41 were used as flow tracers for water in and around the primary drop. The beads, mean diameter of 27 nm, are stabilized in water by CTAB, a cationic surfactant. However, we diluted the stock suspension with deionised water to obtain a typical distance between particles ∼ 10 µm. The CTAB concentration is then in the ppm range.

3.4 Experimental protocol In this work, we focus on the substrate in the immediate vicinity of the primary drop, where the hydrate halo is observed. Crystallization and dissociation events on the surface of the primary drop at the water-cyclopentane interface, only briefly summarized below, will be reported elsewhere (see also refs. 42–44 ). An experiment starts with freezing the primary drop (usually at around -18 ◦ C), since hydrate does not form in a reasonable time at the initial cyclopentane-water interface (see SI 1.1). It forms readily from melting ice, slightly above 0 ◦ C. Subsequently, the temperature, T, is cycled around the dissociation temperature, Tdis ∼ 7 ◦ C, alternately dissociating and reforming hydrate. An experiment thus entails the following steps (the observations are thoroughly described in the next section). 1. Ice: Fast cooling from room temperature T ∼ 20 to T ∼ −18 ◦ C, to freeze the primary drop. A breath figure (’dew’) immediately forms on the substrate. The dew remains liquid (super-cooled) due to the very small size of the droplets, ∼ 1 µm. Water 11



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droplets also condense in the bulk of the cyclopentane (’fog’), some of which settle on the glass during all the rest of the experiment. 2. 1st hydrate halo: T is raised at ∼ 5 ◦ C/min to −5 ◦ C and then slower (∼ 1 ◦ C/min) and stabilised at the melting temperature, usually in the range 0–1 ◦ C. The ice melts and a thin polycrystalline hydrate crust covers the primary drop within minutes. 42 The underlying water in the drop is unconverted. A hydrate halo emerges from the contact line and spreads on the glass. As visualised by the motion of fog droplets, convection in the cyclopentane dies out as the temperature is stabilised. 3. Melting the 1st halo: T is raised above Tdis , usually to 8–9 ◦ C, and held constant until the halo and the crust are completely melted. An emulsion of cyclopentane in water forms in both the halo melt-water and over the primary drop, from the melting crust. 44 The emulsion droplets accumulate by buoyancy at the top of the drop, where they coalesce over a period of tens of minutes. The halo melt-water mostly sweeps back into the primary drop, leaving nonetheless a ring of ’secondary’ drops on the substrate. 4. The 2nd and further halos: The system is sub-cooled, most often to T ∼ 0–1 ◦ C, i.e. without prior freezing of the water. The hydrate crust nucleates at the cyclopentanewater interface of the primary drop, usually in the emulsion, but sometimes at the contact line. Cyclopentane hydrate formation is possible by virtue of the ’memory effect’, provided the temperature and duration of the previous hydrate melting (step 3) are not too large. 44 The crust starts covering the drop. A new halo emerges from the contact line. The temperature is again raised above Tdis to melt the new halo and crust, and so on.

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4 Results and discussion The results presented and discussed in this section are selected from a score of experiments conducted under various conditions. In the early stages of this study the glass cells and the cyclopentane were used as received, until we realized that the hydrophilicity of the glass (see 3.2) and the water content in the cyclopentane bottle evolved. These two parameters have in fact some impact on some of the properties investigated. Subsequent experiments were conducted with cyclopentane pre-equilibrated with water at room temperature (T ∼ 20 ◦ C) and glass cells having a well-defined surface state, either highly hydrophilic as a result of plasma treatment or strongly hydrophobic by silane treatment (see subsection 3.2). Unless otherwise specified, the data presented below are extracted from these experiments. The next three subsections describe and discuss the observations on hydrophilic glass, which includes the freshly plasma-treated glass (contact angle ∼ 1 ◦ ) and the untreated glass (contact angles up to ∼ 65 ◦ ). The same qualitative features are observed on the two sorts of substrates; however, some quantitative differences are noted, for reasons that will become clear below. The last subsection presents and discusses the observations on hydrophobized (silanetreated) glass (see 3.2).

4.1 The breath figure In most of the following set of observations, the water drop contains 2 × 10−6 M of the water-soluble fluorescent dye DASPI, used as a marker of water seeping out of the drop. The cell was freshly plasma-treated and filled with cyclopentane pre-equilbrated with water at room temperature (T ∼ 20 ◦ C). A drop of water placed on the lower face was observed to spread. In the example of fig. 2, the contact line radius was r ∼ 900 µm, the drop height h ∼ 7 µm and the contact angle θ ∼ 1 ◦ . Fig. 2 shows a strongly fluorescent

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Figure 2: The primary drop on highly hydrophilic glass, at room temperature. A nm’s thin, liquid water precursor film spreads outside the contact line, viewed as soon as possible after insertion in the sample cell. (a) DIC image, showing the contact line (diameter ∼ 1800 µm, scale bar 500 µm); (b) Fluorescence image, showing emission of DASPI adsorbed on the glass under the drop and an intense, diffuse corona spreading outside the contact line.

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corona extending ∼ 50 µm outside the contact line. It indicates the presence on the substrate of a thin precursor film of the aqueous DASPI solution, as expected for a system exhibiting frustrated-complete wetting.

Figure 3: Water from the cyclopentane-rich phase condenses as a breath figure on the highly hydrophilic glass during cooling down to form ice. (a),(b): Confocal reflectance and transmission pair at T ∼ −4 ◦ C, in the region of the contact line (lower edge of images), scale bar 20 µm; (c),(d): Widefield DIC (inverted contrast for clarity) and fluorescence images of the same region, showing the correspondence between microdoplets of condensation visible in (a)–(c) and dark spots, (d), punctuating the fluorescence of DASPI in the region of the precursor film;(e) Schematics of the primary water drop coexisting with the precursor water film on glass and the breath figure condensed from the cyclopentane phase. The bars are DASPI molecules. Upon cooling, the drop in the solubility of water in cyclopentane, from ∼ 0.03 mol% at 20◦ C to ∼ 0.01 mol% at 0◦ C, 21,22 leads to the appearance of a breath figure on the glass, fig 3(a)–(c), with droplets 2–3 µm in diameter. Fog droplets also appear, revealing strong convection in the cyclopentane bulk. See video 1 and the explanation in SI 4.1, for an

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example (with untreated glass). Interestingly, the microdroplets nearest to the primary drop coexist with the thin fluorescent film but exhibit weaker fluorescence. A close view of this region in the fluorescence imaging mode reveals a leopard skin pattern of dark spots corresponding to the microdroplets making up the breath figure, see fig. 3(c)–(d). Figure 3(e) shows the physical picture that emerges from these observations. Assuming the same contact angle for the dew droplets as for the primary drop, the former, diameter

∼ 2–3 µm, are by proportion 20–30 nm high, large compared to both DASPI and water molecules, but much less than the focal depth. Therefore, the intensity variations in the leopard skin are due either (i) to lateral differences in DASPI concentration in the bulk of the precursor film, or (ii) to differences in the environment influencing the quantum yield of DASPI. But molecular diffusion acting on a time scale of minutes would be expected to homogenize the DASPI concentration laterally, washing out the spots. The variations in fluorescence intensity thus reflect differences in the environment of DASPI molecules, which may deform freely (and therefore are less fluorescent) in the 20-30 nm-high dew microdroplets, whereas they are constrained (and therefore fluorescent) in the precursor film. From these observations, an upper limit of a few nanometres can be set on the precursor film thickness. Experiments with the fluorescent nano-beads (mean diameter 27 nm) provide further proof of the thinness of the precursor film. In all but one case, with both the highly hydrophilic and untreated glass substrates, the nano-beads remained trapped within the primary drop during all steps of the experiment, including when a hydrate halo was growing on glass. The exception was a massive water leak through a crack in the cyclopentane hydrate crust on the primary drop, observed both with highly hydrophilic glass (video 4 and SI 1.6) and with untreated glass (subsection 4.3). Such events could also be deduced from hydrate debris seen entrained in the water. However, they were rare and gave rise to localised, thick, halo, distinct from the generally observed regular halo front under discussion here.

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When T is lowered down to −15 to −20 ◦ C, the primary drop freezes within less than 0.1 s, trapping air bubbles and cyclopentane droplets as inclusions in the ice. Shortly after, a dew-free zone (depletion) grows on the glass around the contact line, see fig. 4 (and SI fig. 4). As shown in fig. 4 of the SI, the depletion zone slowly widens. This behaviour is consistent with diffusion of water down the concentration gradient in the cyclopentane, from the super-cooled water microdroplets to the surface of the ice, which acts as a humidity sink pumping water molecules out of the cyclopentane-rich phase, a process analogous to the WBF process, see section 2. A similar depletion zone appears around the hydrate halo, see fig. 6 and subsection 4.2. However, as discussed in section 5, another mechanism may prevail in that case. Other examples of breath figures with a depletion layer near ice are given in SI 1.2.

Figure 4: Three views of the contact line of a primary drop (dark band, extreme right), showing the breath figure and development of the depletion zone by a WBF-like process. The fraction of the substrate covered with microdroplets is here ∼ 20 %. (a)–(b): Consecutive video frames astride the formation of ice (T ∼ −15 ◦ C); (c) At the onset of ice melting, 411 s later, the depletion zone is apparent (arrow). Larger, out of focus disks, (a-b), are fog droplets in the cyclopentane bulk. DIC images, inverted contrast for clarity; scale bar 20 µm 17



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While characterization of the dependence of droplet radii and substrate coverage on elapsed time, temperature or substrate wettability is beyond our present scope, we noted a tendency to higher coverage on the highly hydrophilic glass (up to ∼ 20 % area at T ∼ 0 ◦ C or slightly below), see, e.g. fig. 4, in comparison to coverages ∼ 2 − 4 % on untreated glass (see fig. 7 and SI, fig. 4 and video 1), increasing very slowly with elapsed time (see video 1). This tendency agrees with what has been observed in previous work for water condensing from damp air on a substrate with varying wettability. 30 The difference with the present system is the time scale, commensurate with the diffusion coefficient of water molecules, which is 3-4 orders of magnitude higher in damp air (∼ 2 × 10−5 m2 s−1 ) 33 than in cyclopentane (as estimated from Wilke-Chang equation 45 ). The growth of the water droplets on the susbtrate is therefore much slower in our experiments (see, e.g. SI video 1), and the transition towards a film-like texture is thus expected considerably later than the

∼ 1 minute observed by Zhao and Beysens 30 for water condensing from damp air on a substrate with low angles (∼ 10 − 20◦ ). Another factor is expected to further slow down the droplet growth process in our experiments: the cyclopentane overlying the substrate is not renewed and the flux of water molecules on the substrate thus decreases with elapsed time, whereas damp air is circulating at a steady rate providing a constant flux of water molecules to the substrate in Zhao and Beysens’ experiments. 30 In the experiments where the cyclopentane was not pre-saturated with water prior to the experiment, sparser and poorly reproducible breath figures were observed to form on the glass substrate (data not shown). Indeed, less water was available for condensation on the substrate, and the humidity content in cyclopentane was neither known nor controlled.

4.2 Birth and growth of the halo In this subsection we report the observations and the more certain aspects of their interpretation. In view of the difficulties inherent in interpreting 2D images of an object that turns out to be thinner than even the depth of focus of the confocal microscope, building a 18


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tentative 3D model of halo growth is postponed to section 5, after all the data have been presented.

Figure 5: Initiation of the 2nd halo at the contact line (T ∼ 0 ◦ C). Rows 1–2: An ’island’ of hydrate crust nucleates (arrow, row 1) at the water-cyclopentane interface, in the emulsion left by the previous formation-melting cycle, cf. subsection 3.4. The island is attracted to the contact line (row 2), where the halo appears after a few seconds, visible here as a dark rim outside the contact line (last image, row 3, which shows the boxed region in row 2). DIC images; time shown in seconds; scale bars : rows 1–2: 50 µm; row 3: 10 µm.

4.2.1

Emergence of the halo

Prior to the halo, a hydrate crust has nucleated from ice meltwater near the contact line (1st cycle) or is present as floating ’islands’ at various places on the surface of the primary water drop (later cycles). Figure 5 illustrates 2nd halo formation from an island of crust initiated 19



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in the emulsion left by the 1st cycle. These pieces of hydrate at the surface ultimately merge and form a crust over the entire surface, trapping liquid water between the glass and the hydrate (picture an igloo). A few seconds after the crust touches the contact line, a hydrate halo emerges on the substrate, and expands over the interface between the glass and cyclopentane. During first hydrate formation (cf. subsection 3.4), this sequence of events is preceded by the melting of the ice, with some retraction of the contact line, presumably because of the decrease in drop volume upon ice melting. Smooth, polygonal hydrate crystals commonly appear in the ice melt-water at the contact line, see SI fig. 2.

4.2.2

Stabilized growth and halo texture

Once the halo has emerged at some points on the contact line, it tends to invade the gaps in between until it entirely surrounds the drop. Unlike the branched or ’seaweed’ patterns often observed with deposits left by evaporating, ’creeping’ salt solutions, the early halo protrusions do not evolve into an unstable front, 46–50 but into a compact structure with a stable advancing front, and a meaningful lateral velocity or spreading rate (see 4.2.4). The apparent texture of the body of the halo depends on the mode of observation and on the age of the region observed. Streaks parallel to the growth direction are observed in transmission and DIC images. The streaks become progressively more prominent and closer spaced with ageing, or equivalently, distance behind the halo front. A sharper change in the texture is apparent at a constant distance behind the halo, of the order of a few 10’s of microns (e.g. fig. 6). Assuming a uniform refractive index for the hydrate, the streaks indicate ridges or corrugations in the halo, bringing to mind the image of a drainage pattern spreading from the primary drop, like a river delta (Fig. 6). However, as will become clear later, the main source of water is that present on the substrate or in the bulk cyclopentane phase. Two origins of the ridges have been identified. First, consider the case of ’bare’ glass – in presence of the precursor film, but with no microdroplets apparent in the DIC image, 20


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Figure 6: Stages of development of a regular halo front at T ∼ 0 ◦ C, on the highly hydrophilic glass. (a) The halo front (white arrow) has just emerged from some points on the contact line of the primary drop (extreme left), which is surrounded by a depletion zone (black arrow); (b) About 2 min later, the halo front is continuous and has advanced ∼ 100 µm, while the depletion zone of the breath figure has receded and narrowed; (c) at t ∼ 9 min, the same halo has outpaced the depletion zone and is overrunning the breath figure. Scale bars: (a), (b) 20 µm; (c) 100 µm.

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such as immediately outside the contact line during the 2nd and later hydrate cycles. From detailed examination of the video images (e.g. SI video 2), we conclude that in this case, many, if not all of the ridges arise from the spontaneous appearance of microdroplets under the extreme edge of the halo, or the growth of previously undetected droplets. A possible mechanism is discussed in section 5. Secondly, where the halo progresses over the breath figure, the texture is well correlated with the distribution of condensation droplets on the glass (see SI, video 1). Larger droplets give rise to elongated bright streaks in the DIC images. These observations are already a first indication that lateral growth is fed by the water on the substrate, rather than by water flowing out of the primary drop. Such droplets are frequently pushed forward by the halo front before their complete incorporation (video 1 and SI 4.1). Observations with the pseudo-confocal transmission mode (v. sup. 3.1) show the same features. But confocal reflectance shows a surprisingly different aspect, due in part to interference between light rays reflected off the different interfaces present: glass-water, glass-hydrate, glass-cyclopentane, water (or hydrate)-cyclopentane. Figure 7 compares a pair of pseudo-confocal transmission and confocal reflection images, recorded simultaneously for the case of a halo advancing steadily at ∼ 0.5 µms−1 over the breath figure on untreated glass, under cyclopentane pre-saturated with water. The focus is on the glass. In reflection images, a band of width up to ∼ 50 µm behind the advancing front shows either features recognisable in the transmission image (fig. 7), or sinuous interference fringes (e.g. fig. 10(e)). The edge of the halo is systematically highlighted by a variation of brightness comprising three bands of different intensities that, keeping up with the front, sweep over the glass as the halo advances. Figure 7 shows an example with: the breath figure (marker 1); a first bright, narrow band at the extreme edge ( marker 2), here about 5 µm wide, often showing darker flecks corresponding to the most recently incorporated droplets of the breath figure; a band of gradually diminishing intensity (3 and fig.7 (c)), with width increasing with halo speed; a bright and dark streaked band (4). These features

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Figure 7: Simultaneous (a) transmission and (b) confocal reflectance views of a 1st hydrate halo (secondary droplets are absent) advancing on untreated glass (contact angle ∼ 65◦ ) at T ∼ 0 ◦ C, under cyclopentane water-saturated at room temperature. Numbered features are (1) the breath figure, (2) the halo front, (3) thinning behind the front, (4) fresh lacunar halo, (5) annealed halo, (6) the contact line, (7) water under the primary drop, behind the contact line. (c). Reflection intensity along the arrow in (b). Scale bar 20 µm. 23



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in general correlate well with the ridged appearance of the transmission image. Further behind the front (5), the streaks disappear with ageing, leading to a ’grainy’ aspect, in which the ridges are not or hardly visible. This reflection is nonetheless distinct from the that off the water-glass interface under the primary drop contact line (6), which is uniform grey (7). Surprisingly thus, the outer edge of the halo is much brighter than the precursor film ahead of it: the reflection signal rises abruptly at the halo outer edge and decays smoothly on the inner side (fig. 7(c)), into the dark band noticed above, marker 4 in fig. 7. That implies a thickness at the leading edge of the halo in the range of 10’s of nms, but not more than ∼ 100 nm (otherwise two or more fringes would be visible). The extreme edge of the halo is indeed expected to be an open (porous and permeable) polycrystalline sheet filled with (and surrounded by) liquid, both cyclopentane mostly above and water mostly below. This water is that encountered by the halo on the substrate and not immediately transformed into hydrate. A possible model of the halo edge is discussed in section 5.

4.2.3

Halo spreading in presence of secondary droplets

That some liquid water is present in or beneath the extreme edge of the halo and remains liquid over a few seconds is clearly observed at higher magnification when the advancing halo encounters a large (say, a few 10’s of µm) water droplet on the substrate (a secondary droplet, explained in the next paragraph). The water from the droplet is observed to quickly penetrate the halo’s edge by imbibition (water is more wetting towards the hydrate than cyclopentane, which is displaced by water), see fig. 8, video 2 and SI 4.2. A few seconds later, a part of this liquid water is rejected back into the secondary droplet as the rear of the halo advances and the secondary droplet itself covers with a polycrystalline hydrate crust. We call this highly reproducible sequence of events ’leap-frogging’ because the crust advances faster than the adjacent halo. Secondary drops, which result from the dissociation of earlier halos, are larger and 24


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much more variable in size than the dew condensed or the fog settled from the cyclopentane. They play the rôle of the non-hydrate nucleated drops in the study of Beltrán and Servio. 11 Figure 8(b) shows the interaction of the advancing hydrate halo with a large (∼ 100 µm) secondary droplet. When the halo touches the droplet, most of the water in the droplet is rapidly (within ∼ 1 s) imbibed into the halo, as seen from the retraction of the contact line and from the movement of cyclopentane droplets at the drop surface, acting as tracers (SI 4.2 and video 2). This systematic observation suggests that the halo front is porous and imbibes water as it is encountered, because water wets the hydrate more than cyclopentane. At the same time, a hydrate crust propagates over the droplet from the contact point. This is the end of the ’bridge effect’ and contamination reported by Beltrán and Servio. Interestingly, although the droplet contact line at first retreats in this process, it accompanies the new crust, which closes to closely match the original shape of the droplet. All the above leap-frog steps are observed when the halo reaches drops on the substrate. Video 2 in the SI shows the whole sequence in detail. SI fig. 7 shows a transmission-confocal reflectance pair of images of the hydrate crust over this secondary drop. It is likely that as for the crust covered primary drop, liquid water is still present within. The smooth texture of the hydrate allows estimation of the drop height from interference fringes. The maximum possible height, 4 µm, and the diameter are consistent with a contact angle ∼ 1 ◦ .

4.2.4

Rate of halo spreading

The rate of halo spreading over the glass depends on the amount of water present on the substrate: ’bare’ glass (just the precursor film), glass with a breath figure or with secondary droplets. Figure 9(a) shows the region of the contact line of a 1st hydrate halo (therefore no secondary droplets present), at T ∼ 0 ◦ C. On ’bare’ glass, close to the contact line, i.e. in the breath figure depletion zone, the halo widens at ∼ 0.5 µms−1 , see fig. 9(c), which shows 25



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Figure 8: Hydrate ’leap-frogging’ over secondary or other water drops accelerates propagation over the substrate (T ∼ 0 ◦ C). (a) DIC overview of the halo in the 3rd cycle ; (b) Enlargements of the boxed area (contrast inverted for clarity). Dark spots in (b) are cyclopentane emulsion from the previous cycle. T = 0◦ C. Scale bars: 50 µm. the front progression along three tracks A–C in the images. As the depletion zone narrows, tracks A and B in fig. 9(a), the halo accelerates moderately. Finally the halo overruns the breath figure, track C in fig. 9(b), accelerating to ∼ 1.2 µms−1 . Although, in the depletion zone, liquid water exists on the substrate only as a nanometres thick layer, the precursor film, cf. fig. 2, the observation that the halo velocity is stable or even increases with elapsed time or distance to the primary drop, is an additional indication that this drop is not the main source of feed water. When a secondary droplet is encountered the halo advances much faster, for example

∼ 3.6 µms−1 in fig. 8, compared to ∼ 1.4 µms−1 over the adjacent glass, and speeds up to ∼ 10 µms−1 were observed. These speeds are in the same range as the spreading of the crust over the primary drop. Halo propagation resumes at its former velocity on closure of the crust on the secondary droplet. A similar process to leap-frog may explain why the halo accelerates on reaching the

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Figure 9: Halo growth accelerates away from the contact line on highly hydrophilic glass (T ∼ 0 ◦ C). (a) The halo close to the contact line; (b) further out ; (c) The halo front relative to the contact line along tracks A (circles), B (squares) and C (triangles), with local speeds by linear regression. Data silences are fluorescence observation, seeking DASPI carried out of the primary drop (not detected). The halo at B, ∼ 50 µm wide in the first video frame, is shifted horizontally 62.5 s to highlight the increase of speed with distance from the contact line. Track C, from a different part of the same primary drop, is shifted down 300 µm to fit in the graph. Scale bar for (a)–(b): 50 µm. 27



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breath-figure. Indeed, if we assume that its velocity over microdroplets is the same as that of the crust over larger drops, i.e. ∼ 10 µms−1 , and furthermore ∼ 0.5 µms−1 above a bare substrate (more precisely, a substrate with only the precursor water film), then for 20 % dew coverage (freshly plasma-treated glass), the velocity expected over the breath figure is 0.2 × 10 + 0.8 × 0.5 = 2.4 µms−1 , consistent with the observed ∼ 2 µms−1 ; for 3 % dew coverage (untreated glass), the expected velocity is 0.03 × 10 + 0.97 × 0.5 ∼ 0.8 µms−1 , of the order of the observed ∼ 0.5 µms−1 (see 4.2.2). In summary, the spreading of the cyclopentane hydrate halo on glass is very dependent on the quantity and nature of the water present on the substrate. At T ∼ 0 ◦ C the halo front velocity is a minimum, ∼ 0.3–0.5 µms−1 , on the nanometres thin precursor water film. It is larger when microdroplets of condensed water are present on the substrate, up to ∼ 2.5 µms−1 , depending on the amount of water (dew coverage) on the substrate; and still larger in the presence of secondary droplets, up to ∼ 10 µms−1 typical of velocities observed at water/cyclopentane interfaces. 42,44 A caveat is in order here, concerning the halo velocity over a nanometres thin water film. We assumed a constant value (∼ 0.5 µms−1 ), which might be an overestimation far from the contact line on bare untreated glass. Thus, with this substrate and cyclopentane not presaturated with water prior to the experiment, we observed in one experiment a very sparse breath figure on the substrate and complete arrest of the halo (at our resolution), at a distance of a few 100’s of microns from the primary drop (data not shown).

4.2.5

Melting of the halo

The halo was melted by raising the temperature at ∼ 1 ◦ Cmin−1 to ∼ 9 ◦ C and holding at the final temperature until all hydrate had dissociated. In agreement with our estimation that the main heat fluxes in our setup pass by conduction through the glass, the halo melts before the majority of the crust over the primary drop. In these conditions, transmission and DIC images show that the ridged pattern in the halo disappears in two stages. The 28


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Figure 10: Stages of melting of the 1st halo on untreated glass (T ∼ 9 ◦ C). Transmission, (a)–(e) and simultaneously recorded confocal reflectance images, (e)–(h). (a),(e): moment of greatest halo extent (t = 0 s); (b),(f): halo nearly detached from the glass (t = 134 s); (c),(g): early stage of retreat of the unstable melt-water film (t = 143 s); (d),(h): secondary drops left on the glass(t = 160 s). Recorded at ∼ 0.75 s/frame; scale bar 20 µm.

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coarser, brighter features disappear first, leaving a similar but finer and fainter pattern, see fig 10(b). Simultaneous confocal reflectance images, when available, show well contrasted, smooth interference fringes due to an unstable film of melt-water. Depending on how fast the film retracts to the primary drop, cyclopentane emulsion is sometimes observed to replace the finely structured hydrate, pieces of which may sometimes be seen rotating as solid objects, showing they are not in contact with the substrate. (fig. 10(c),(d)). The instability of the water film is consistent with the pseudo-partial wetting character of water on glass in presence of cyclopentane. Using cyclopentane emulsion or other debris as tracers, we observe that a brief (again seconds) outward flow of melt water from the contact line is sometimes simultaneous with inflow from the periphery of the melting halo. After a few seconds, the flow is always inwards, everywhere. In the overall melting process, which lasts a few tens of seconds as illustrated in fig.10 and in SI fig. 8, part of the water resulting from halo melting is retracted towards the primary drop, and the other part is left on the substrate in the form of ’secondary’ droplets with typical sizes ∼ 10–100 µm. The droplets all lie in an annular region around the primary drop, fig 10(h). As the water film thickens, the retreating contact line becomes smooth and finally comes to rest close to or outside the position at the start of the cycle. Hence the primary drop tends to spread and flatten with successive cycles. Most often, immediately after melting, no water drops of any size could be detected in the inner annular region swept by the smooth contact line, though they may appear later by dew or fog settling. The glass appears ’bare’, except for the (invisible) nm’s thick film associated with frustrated complete wetting (see section 2). The dynamics of dewetting are discussed further in the SI, section 4.3.

4.2.6

Evidence for halo thickening

The thickness of the very edge of the growing halo must be at most of the order of the thickness of the uniform film of water with the same volume as the combined water pre30


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cursor film and dew droplets present on the substrate, or about 20–30 nm if microdroplets condensed from cyclopentane cover the substrate. Strictly speaking, this thickness has to be corrected by a factor of ∼ 1.3, the density ratio between liquid water and the density of water in cyclopentane hydrate. Differencing images suggests that the halo thickens with time, but the best evidence of thickening is provided by observation of melting, as discussed now. As noted above, the halo melts in two stages. SI figure 9 illustrates that cyclopentane emulsion forms in the melt-water in between the coarser features that disappear in the first stage of melting. In agreement with the earlier disappearance of these features, this observation suggests that the coarser brighter features are thinner areas of the halo. The most compelling evidence for thickening occurs when highly contrasted fringes appear due to interference between the specular reflections off the melt-water–glass and the water-cyclopentane interface, e.g. figs. 7(f) or SI fig. 8 and SI videos 1 & 3. The thickness of the halo at any point may thus be estimated post mortem by counting the fringes from the edge, in the fleeting quiescent period (seconds) before the film retracts to the primary drop. The equivalent film thickness typically exceeds 1 µm. Considering the rate of halo advance, the rate of thickening is in the range 5–10 nms−1 at T ∼ 0 ◦ C. A second estimate of the thickness follows from the quantity of water left as secondary drops on the substrate, assuming the same contact angle as for the primary drop. The value is consonant, but lower, of the order of a few tens to hundreds of nanometres, due to the retracted water. Possible sources of water feeding the thickening are ’ablimation’, strictly a vapour to solid transition, the reverse of sublimation, that we apply here to the ’vapour’ of dissolved water molecules in cyclopentane; and settling of water fog microdroplets from the bulk of the cyclopentane phase (see for example SI, video 1). Under our conditions, ablimation must dominate settling of fog droplets, which was too rare to account for the observed ageing of the texture of the halo. For example, assuming a fog droplet diameter of 2 µm,

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the rate of deposition needed to sustain thickening at 5 nms−1 would be of the order of 1 drop per second per 30 µm square, one to two orders of magnitude more than the observed fog settling. Thickening of hydrates of immiscible guests has been ascribed to slow diffusion of water and guest molecules in opposite directions through the already formed, more or less porous and permeable hydrate crust. 51 Whereas annealing and infilling of the porosity must cause this mechanism to taper off with time, growth by ablimation (and fog settling) may be significant long-term mechanisms for hydrate thickening from the outside, here 5 nms−1 ∼ 1 mm/day for cyclopentane hydrate at 0 ◦ C.

4.3 Halo growth by water breakout from the primary drop The above results establish water on the substrate outside the primary drop as a major source of growth of the halo. As a probe of interaction of the halo with water originating inside the primary drop, we also performed experiments with a drop containing fluorescent tracer particles. They did not show any general radial flux towards the contact line that could explain the growth of a regular halo around the drop. On the contrary, particles appeared to diffuse randomly in the primary drop, remaining blocked behind the contact line, see SI fig. 6. On a few occasions, with untreated glass, they were observed up to

∼ 10’s of µm outside the contact line. But even in the example in SI fig. 6, recorded two hours after halo initiation, the few beads that had escaped all lay within 50 µm of the contact line, whereas the halo had completely covered the sample cell. On rarer occasions, the beads revealed massive outflows at specific points, at or close to the contact line, mostly only one per primary drop, and sometimes observed to be associated with a crack in the crust. The ’halo’ was then irregular, with noticeable longer, thicker and spear-shaped tongues protruding from the breakout. Adhesion to the glass was variable, as deduced from combined DIC and fluorescence images. Mostly they showed beads channelled by structures in the halo, see figure 11, implying tunnels between the halo 32


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Figure 11: An example of water breaking out by incomplete closure of the hydrate crust over the primary drop, forming a rapidly advancing (∼ 2 µms−1 ) halo tongue, in a case of the 2nd hydrate cycle with water-saturated cyclopentane and untreated glass. Left hand images: combined DIC (showing the crust and the halo) and fluorescence ; right hand, with the DIC lamp extinguished: fluorescence shows the beads and substrate heterogeneities (striations) revealed by DASPI. (a),(b): t = 0; (c),(d): t ∼ 65 s; (e),(f): t ∼ 95 s. T ∼ 1 ◦ C, scale bar 100 µm.

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and the glass- to extend the analogy above, picture the entrance tunnel of an eskimo igloo. In this example, with untreated glass and water-saturated cyclopentane, the breakout causes the halo to advance much faster (∼ 2 µms−1 ) than on ’bare’ glass (< 0.5 µms−1 ). Weak adhesion to the glass was also shown by pieces of the halo waggling. In another case, the edges of the tongue ceased spreading although the water flow continued. The edges were pinned to the glass, but shed steps behind them, possibly suggesting arching of the halo to accommodate the influx of water from the primary drop (see SI 4.4 and video 4). Dark streaks in the fluorescence of DASPI outside the primary drop highlight inhomogeneities in the glass that clearly directed the growth of the tongues. Since the striations are not visible in DIC alone, we attribute them to inhomogeneities of surface state rather than of profile. Nanobeads, which at the start of the experiment did not spontaneously migrate from the primary water drop to cyclopentane, accumulate in these dark streaks. The streaks may therefore correspond to a thicker water layer (at least the bead diameter), which would be consistent with the lower fluorescence of DASPI, cf. subsection 4.1. Figures 10 & 11 in the SI show another example of breakout, where the halo velocity decreases with time, as expected in the case that the source of water is the primary drop. In these somewhat exceptional examples, the situation envisioned by Beltrán and Servio 11 was clearly observed: water flows from the primary drop to feed the advancing halo. Such leakage is likely to be favoured on substrates less wetting to water, because compared to the much flatter drops on highly hydrophilic glass, the larger curvature of the water-cyclopentane interface corresponding to higher contact angles would lead to greater stress on the hydrate crust.

4.4 Hydrophobic substrate Neither the breath figure nor the halo were detected on glass hydrophobised by silanisation, even under cyclopentane saturated with water at room temperature. On cooling the watersaturated cyclopentane, we only observed micron sized fog droplets settling on the glass 34


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Figure 12: No halo was detected on silanised glass: Comparison of (a): the breath figure on hydrophilic glass and (b): settling fog droplets on hydrophobic glass; (c) the liquid primary drop sitting on hydrophobic glass is a nearly complete sphere (arrow shows contact line); (d) the hydrate covered drop, shortly before melting. The focus is on the glass throughout; (a)–(c): inverted DIC, (d): reflectance; scale bars: (b): 10 µm, (c): 20 µm, (d) 50 µm.

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from the bulk guest phase. They were easily distinguished from the breath figure on hydrophilic glass, cf. fig. 12(a)–(b), by the rings and dark central spot in DIC images. The primary drop rested on a very small contact area, with high contact angle, e.g. θ ∼ 165 ◦ in fig. 12(c). As above, the hydrate was formed from melting ice or from the emulsion in later cycles. In general, the drop then rested on a narrow, roughly annular contact region surrounding a central dimple in the hydrate crust, suggesting avoided contact with the substrate. Hence only the glass and the contact area appear in focus in fig. 12(d). No halo was detected on silanised glass, even after waiting several minutes.

5 Tentative 3d model of the halo and its interactions with water on the substrate We enlarge here on the brief discussion of the reflectance images appearing in section 4.2.2. Before interpreting the vertical structure of the halo and its interaction with water on the substrate, we recall briefly how contrast arises by interference in the confocal reflectance images. See SI section 2 for numerical details. Although only relative rather than absolute thicknesses can be deduced from interference fringes at a single wavelength, 38 the known thickness of the precursor film in this work provides a reference point ( ≤ 10 nm, see 4.1). The thin water film on the substrate is in fact similar to a Newton black film: light waves are reflected with similar amplitudes but in phase opposition off the two faces of the film. The reflectance, R, is therefore small at vanishing film thickness, and periodic (period about 200 nm) as the film thickens, e.g. R ∼ 3.5 × 10−4 for a 5 nm water film between the glass and the cyclopentane and maximum at R ∼ 5.7 × 10−3 for a 100 nm film, actually greater (as observed) than the reflectance of the the thick water layer (no interference) under the primary drop, R ∼ 2.2 × 10−3 . The reflection off the precursor film in frustrated complete wetting should therefore be weak, as should the reflection off the halo it could produce, which have similar thickness 36


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and refractive index (see SI 2). Yet surprisingly, the edge of the halo is much brighter than the precursor film ahead of it. As pointed out above, that implies a combined thickness of water and hydrate at the leading edge of ∼ 100 nm. The dark band behind the front (marker 3, fig. 13) is therefore either a thinning towards ∼ 10 nm or a thickening to ∼ 150– 200 nm. Only the latter is consistent with the rate of thickening and the age of the halo 15 µm or ∼ 30 s behind the leading edge (thickening at ∼ 5 − 10 nms−1 , from melting data, halo speed ∼ 0.5 µms−1 , for the halo in fig. 7 ). The halo is at its youngest and thinnest at the edge, where under steady state growth, the thickness cannot much exceed that of the water precursor film. We deduce the presence of a ∼ 100 nm wedge of water under the extreme edge of the halo and advancing concomitantly with it. The fresh, extremely tenuous edge of the halo is lacunar and porous to cyclopentane and to water, cf. the irregular flecked aspect (markers 2 & 4, fig. 13). This flecking diminishes with the age of the halo or distance behind the edge, consistent with the observations of Davies et al. on methane hydrate growing at the interface between water and methane behind a sapphire window. 51 SI video 1 illustrates the annealing of the rear of the cyclopentane halo. The thickness of the water under the edge, noticed above, tapers away from the edge as the infilling of the halo consumes it. Figure 13 shows a schematic representation. We surmise that the halo and the wave advance together over the glass, in a self-sustaining process, in which water from the precursor film and the microdroplets ahead of the front is imbibed between the hydrate and the glass. This process was observed for all secondary droplets encountered by the halo, cf. section 4.2.3 and video 2 in the SI. Indeed, such a water wedge may arise because the initial hydrate halo most likely emerges out of contact with the glass, at the interface between the water precursor film and the cyclopentane. The wedge may subsequently reach a steady travelling state, balancing water loss into the halo as discussed above and capillary imbibition from the precursor film. Imbibition is favoured by the relative hydrophilicity of both glass and hydrate. Presence

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Figure 13: Schematic radial section of the halo front (vertical scale much exaggerated), growing between the glass and the guest phase, showing sources of feed water and processes contributing to halo lateral growth and to thickening (WBF, Wegener-BergeronFindeisen process). Dashed lines indicate approximate correlations with the reflectance micrograph in fig. 7(b). The instability of the travelling water wedge under the front drives tangential fluctuations of its thickness, that in turn give rise to the ridging of the halo.

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of a water wedge under the halo edge would explain the following points. • First, by drawing in water from ahead on the substrate, the halo would tend to thin the precursor film and deflate any microdroplets present, providing an alternative mechanism to the WBF process to explain the depletion zone. Deflation through the precursor film would furthermore be insensitive to currents in the cyclopentane, explaining why the radial growth symmetry of the depletion zone is maintained even in observed cases of strong oblique convection down to the substrate (visualised by fog drops). • Second is the observation of microdroplets forming under the extreme edge of the halo, on glass that was apparently ’bare’ just seconds before the arrival of the front (cf. section 4.2 and SI video 2). Like the microdroplets in the breath figure, they may be interpreted as the spontaneous response under frustrated complete wetting to a local film thickening. • Third, these microdroplets manifest tangential fluctuations of thickness of the water under the edge, driven by the inherent instability of a thick water film. Once formed, a microdroplet under the halo edge is seen to be carried forward with the halo front, contributing feed water to thickening of the halo along a radial direction. Microdoplets of the breath figure or settled from the water fog in the cyclopentane contribute further to the ridging by the same process when they are overrun by the halo. These processes explain the radially ridged texture of the halo. • Finally, we note the dip in the fluorescence intensity of DASPI under the halo front (SI fig. 3). We may understand the dip as due to the lower constraints on the molecule in the thicker water layer under the halo front. Qualitatively, even, the outer edge of the dip is sharper than the inner edge (SI , fig. 2(e)), as would be expected for a wedge of water. It is also observed that the DASPI signal increases ahead of the front, consistent with the thinning of the precursor film by deflation posited above. 39



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6 Conclusions and outlook Cyclopentane hydrate is considered a model system for a practically important but experimentally more difficult system, natural gas hydrate. Thus, the two systems are structure II (SII) hydrates, and the guest and host (water) molecules have a very low mutual solubility. Cyclopentane hydrate also shows significant phenomenological similarities with methane hydrate, studied by Beltrán and Servio, 11 despite the latter being an SI structure. Therefore, we first highlight the similarities and differences between our observations and those of Beltrán and Servio. We then summarize our results and point to further questions and possible future work. On (hydrophilic) glass, both systems form tenuous halos that emerge from the contact line of a water drop sitting on the substrate. Prior to the emergence of this halo, hydrate nucleation occurs at the interface between the primary water drop and the guest phase or at the contact line of the water drop, giving rise to a crust of polycrystalline hydrate covering the drop. As a rule, the halo emerges from the contact line only on completion of the crust in the vicinity, or even complete closure over the drop. Similarly, DuQuesnay et al. 8 report halos of methane hydrate growing on sapphire, from the cold side of the primary drop in their experiments, as soon as that side was covered with crust (called ’film’ in their paper). These halos then spread over the substrate, with a leading edge that advances in a rather regular and stable manner. In both systems, the spreading of the halo over the substrate is responsible for the propagation of hydrate from one drop to another drop– the ’bridge’ effect noted by Beltrán and Servio. The main differences lie in the speed of hydrate propagation. Beltrán and Servio observed methane hydrate halos advancing at speeds of the order of 10 µms−1 , somewhat higher than the speeds up to ∼ 2 µms−1 found here for cyclopentane hydrate on highly hydrophilic glass (lower values, albeit in the same range, are found on moderately hydrophilic glass). The hydrate crust, observed growing at water-guest interfaces, advances 40


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laterally at speeds ∼ 10 µms−1 for cyclopentane, much lower than the 100’s of µms−1 reported for methane. Note however that the subcooling in the methane hydrate experiment (∼ 9–10 K) was larger than here with cyclopentane hydrate (∼ 7 K), and that the solubilities of the water and guest in the other phase are higher (by about one order of magnitude) for the water-methane system than for the water-cyclopentane system. These parameters (subcooling and mutual solubilities) are known to favour hydrate nucleation and crust growth 10 – for example to the point that ice formation is not required for forming methane hydrate in the conditions of the cited work. Consistent with the resolution of their study, Beltrán and Servio suggested most plausibly that the main water feed controlling the spread of the methane hydrate halo was water drawn out of the water drops by capillarity between the halo and the substrate. An interesting and surprising result, deduced from correlating all the microscopy contrast modes used here, is that the halo appears to spread over the glass in a self-sustaining association with a water wedge derived from the water on the substrate. Contrary to expectation, evidence is shown that this hydrate halo grows laterally and thickens on the glass substrate by water sources external to the primary water drop. As illustrated in figure 13, these sources include the (super-cooled) liquid contained in the precursor film near the water drop and in the microdroplets of water condensed out of the cyclopentane presaturated with water at a higher temperature. These microdroplets are either dew ’breath figures’ or fog droplets that settle on the substrate, and others that remain suspended in the bulk of the cyclopentane phase for a while. Another source is provided by the larger ’secondary’ droplets left on the substrate by a previous sequence of halo formation and melting. Depletion of microdroplets of the breath figure around the primary drop and the growing halo may arise through thinning of the precursor film by capillary imbibition under the halo (we think the dominant mechanism). A Wegener-Bergeron-Findeisen type process may also ferry water from the super-cooled droplets on the substrate to the hydrate. Ablimation of dissolved water in the cyclopentane may be the major long term contribution

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to thickening of the halo, locally helped by fog droplets settling out of the guest phase. The relative contributions of all these processes should be further investigated. The present results show the impact on hydrate halo growth of factors such as substrate wettability and the degree of water saturation of the cyclopentane phase. The hydrate halo was not detected on hydrophobic (silane-treated) glass, and the hydrate halo grows quicker when the substrate is more water-wettable (hydrophilic) and when the cyclopentane phase is oversaturated with water at the temperature of interest, a condition achieved here by pre-saturating the cyclopentane with water at room temperature (20 ◦ C). Several further factors are worth future study. Here, fused silica is an amorphous, isotropic substrate, and the halo is indeed observed to spread isotropically around the primary water drop. Crystalline substrates, such as (synthectic) quartz or cleaved mica, might introduce anisotropy, influencing the growth of the halo. The degree of subcooling is a another factor expected to play an important role. In closing, we should like to point out that the hydrate halo has similarities (and differences) with two other crystallisation processes. The first is frosting, specifically frost halos growing around a freezing water drop on a substrate. Frosting occurs either via ablimation, the direct vapour to solid phase transition (the reverse of sublimation), or via condensation, the direct transformation of super-cooled liquid microdroplets into ice, in a manner that depends on substrate wettability, vapour humidity and temperature. In our system, dissolved water molecules directly transforming into hydrate is similar to ablimation frosting. Water droplets in the ’fog’ being incorporated into the halo corresponds to condensation frosting. Frost halos forming on a substrate near a freezing water drop are the result of a complex process which involves evaporation of water from the freezing water drop (due to the released heat), the condensation on the cold substrate of subcoooled water microdroplets and then frost propagation from the frozen water drop through these microdroplets, in a manner that depends on water vapour concentration, substrate thermal conductivities and wettability. 20

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The second analogy is the creeping of evaporating salt solutions. Similar to the hydrate halo, evaporating salt solutions give rise to salt crystallites on the substrate (usually glass), well beyond the extent of the initial aqueous drop. The observed growth patterns are diverse and depend in a complex manner on the type of salt, the rate of evaporation, the various surface energies involved, etc. But contrary to the hydrate halo here, growth is ensured by transport of fresh aqueous solution from the ’reservoir’ to the tip of the creeping crystallites, either aside and on top of the crystallites (top supplied creeping), or in the narrow space between the crystallites and the substrate (bottom supplied). This topic lapsed after the early works by Washburn 46 and Hazlehurst et al., 47 but is now experiencing a revival. 48–50 In conclusion, gas hydrate growth brings into play a rich mixture of physical processes, so progress is to be expected from the consideration of the similarities and differences between hydrate and frost halos and creeping salt solutions.

Acknowledgement MLMdB acknowledges a PhD. grant from CNRS and Communauté de communes de Lacq-Orthez. Funding by the ’Hydre’ project (Agence Nationale pour la Recherche, ANR 15-CE-06), the ’Mefhysto’ project (Conseil régional d’Aquitaine), and by the Pôle 4N nanosciences en Aquitaine and Communauté d’agglomération de Pau-Pyréneés is acknowledged here. We thank Pr. W. González-Viñas, Universidad de Navarra, Spain, and Dr. B. Bera, University of Amsterdam, The Netherlands, for helpful discussions.

Supporting Information Available Further examples of the processes discusses in the text; discussion of the interference fringes; estimation of the Hamaker constant; videos of halo growth and melting; further examples of breath figures. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Crystal Growth & Design - cg-2016-00471m.R2: For Table of Contents Use Only Title: How do gas hydrates spread over a substrate ? Authors: María Lourdes Martínez de Baños, Nelly Hobeika, Patrick Bouriat, Daniel Broseta, Eduardo Enciso, Franck Clément, Ross Brown

Synopsis: Phase contrast and fluorescence microscopies, applied at ∼ 1 µm resolution to cyclopentane hydrate spreading from a primary drop on glass, suggest a new view of how a gas hydrate propagates over a substrate: water on the substrate controls spreading and texture, rather than that from the primary drop. A nm’s thin ’breath figure’ on the glass appears particularly important.

[58 words; the graphic has been uploaded as ’cg-2016-00471m.R3_TOC_PAGE.jpg’]

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How Do Gas Hydrates Spread on a Substrate? - Crystal Growth

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