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# The floatability of aerosols and wave damping on Titan's seas

Daniel Cordier, Nathalie Carrasco

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Daniel Cordier, Nathalie Carrasco. The floatability of aerosols and wave damping on Titan's seas. Nature Geoscience, 2019, 12, pp.315-320. 10.1038/s41561-019-0344-4. insu-02112962

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# The floatability of aerosols and wave damping on Titan's seas

Daniel Cordier<fnref n="1" />* and Nathalie Carrasco²,³

Titan, the enigmatic large moon of Saturn, is unique because it is the only satellite of the solar system that is surrounded by a dense atmosphere. Thick layers of photochemical organic aerosols shroud the surface and sediment to the ground. In polar regions, large lakes and seas of liquid hydrocarbons were discovered by the Cassini-Huygens mission. Aerosols that sediment above the lakes run into a liquid surface in which new interactions can take place. In this paper, we address the question of the first contact between the aerosols and the lakes: do the aerosol particles float or rapidly sink into the lakes? We investigated the possible effects of a floating film or slick formed by this organic material and other products of the atmosphere. We also compared the wave damping effect on Earth's oceans to the Titan counterparts. According to this work, Titan appears to be a much more favourable place for such a damping. By inhibiting the formation of the first ripples, this phenomenon could impede the existence of waves at wavelengths larger than a few centimetres. This effect could explain the remarkable smoothness of the sea surface often noticed in Cassini observations.

Titan, the main satellite of Saturn, is the only satellite of the solar system that possesses a dense atmosphere. However, perhaps the most striking feature of Titan is the presence of a thick layer of haze, the source of inspiration for many works focused on photochemical products and aerosol properties<fnref n="1" />. Also, the presence of oceans of liquid hydrocarbons was conceived in the early 1980s, and the Cassini orbiter has revealed a collection of seas and lakes in the polar regions of Titan². These structures involve diameters up to more than several hundred kilometres. Airfall deposits of photochemically produced organics may coat the surface of the seas. Potential interactions between haze particles and liquid surfaces are therefore likely. To understand the fate of the aerosols at the surface of Titan's lakes, a first parameter to be investigated is their floatability. This issue of flotability is neither anecdotal nor formal. During the pre-Cassini era, in the different context of radar volume scattering, the near-surface properties of Titan's ocean have already been considered³. In the scenario envisaged, particles or macromolecules were suspended in the liquid and maintained by some vertical currents. In the case in which some material could accumulate at the sea surface over time and build up a layer of some thickness, the presence of a such surface film can affect the gas, heat and momentum exchange between the sea of the atmosphere. On Earth, it is well-known (and has been for centuries)⁴ that an oil film damps the sea surface waves. At the surface of terrestrial oceans, biogenic surface microlayers appear due to the secretion of fish and plankton⁵, and they are detectable by satellite radar through their wave-damping effect⁶. Therefore, it appears particularly relevant to discuss the existence of a possible film, made of atmospheric products, that covers some areas of Titan's sea surface. During flybys over other major seas and lakes⁷⁻⁹, Cassini RADAR measurements suggest millimetre-level flatness surfaces. Infrared ground imagery also revealed very smooth surfaces for two of them¹⁰,¹¹. Even if infrared off-specular glints were observed¹², which probably correspond to rougher zones, the Cassini observations draw a picture of impressively smooth marine surfaces. If the physical and/or chemical properties of some

molecules or particles may lead to the appearance of a layer, or microlayer, at the surface of liquid formations, then the properties of the seas could be drastically affected. The question addresses major properties of this unique case of 'exo-oceanography'.

## Material that can sediment to the surface of Titan

To avoid any ambiguity, we reserve the term 'aerosols' to solid particles that make up the thick hazy layer of Titan. This photochemical haze extends roughly from the surface up to about 1,000 km altitude¹³ and it is made of aggregates of monomers. Aggregates show a fractal structure (Supplementary Fig. 1) and contain up to several thousands of monomers¹⁴, each of which can be approximated by a sphere¹⁵. The monomer radius (r (m)) determinations agree at a value of around 50 nm (ref. ¹⁶). Each Titan haze model, based on a microphysical description, depends on the rate of particle production among several parameters¹⁷. The aerosol mass production, derived empirically, has values¹⁷ that spread around ~10⁻¹³ kg m⁻² s⁻<fnref n="1" />. With the haze layers in a steady state, the 'mass production rate' is also the average 'mass deposit rate' of the aerosols, that is, the sedimentation rate over the surface of Titan. The adopted value corresponds, at ground level, to 1 nm per year, if we assume a density of around 10³ kg m⁻³. These organic particles should not be surrounded by liquid in Titan's dry regions, but in the most humid ones, aerosols can play the role of nucleation cores for liquid methane droplet formation¹⁸. Even if observational evidence for rainfall on Titan is rare¹⁹, the polar regions are recognized to be the wettest from climate simulations²⁰. In these regions, the precipitation of liquid methane is governed by the presence of small particles (micrometre or submicrometre), known as cloud condensation nuclei, and aerosols are very good candidates for this role. In summary, a certain amount of aerosols should reach the seas as dry particles, whereas the remaining could reach the sea embedded in liquid droplets.

Titan's aerosols are the end products of a complex chemistry in which a plethora of small molecules is generated. Some of them are detected by space-borne instruments²¹ or by Earth telescopes²².

<footnote n="1">¹Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, Université de Reims Champagne-Ardenne, Reims, France. ²LATMOS, UMR CNRS 8190, Université Versailles St Quentin, Guyancourt, France. ³Institut Universitaire de France, Paris, France. *e-mail: daniel.cordier@univ-reims.fr</footnote>
On the theoretical side, models account for the production of these species²³. Due to the local thermodynamic conditions, some of these compounds condensate to form either liquid droplets or ice crystals. For instance, the VIMS (visible and infrared mapping spectrometer) instrument aboard Cassini allowed the detection of micrometre-sized particles of frozen hydrogen cyanide (HCN ice) over Titan's southern pole²⁴. The mass flux, to the surface, of these compounds is not negligible. Models indicate a mass flux for HCN of the same order of magnitude as that of aerosols²⁵. HCN is not the only species that can produce organic crystals in the atmosphere; among many others, molecules such as C₂H₂ and HC₃N also have a similar potential²⁶. Nonetheless, HCN appears to be the most abundant. The key point for our purpose is the potential propensity of these micrometre-sized crystals to aggregate with each other into micrometre- to millimetre-sized particles, analogues of terrestrial snowflakes²⁷. The physical properties of HCN do not preclude this type of process. In this perspective, Titan's troposphere could be the scene of 'exotic snowfalls' composed of 'HCN flakes' (or C₂H₂ flakes and so on). Even though CO₂ snowfalls were considered in the case of Mars²⁸, perhaps curiously this possibility has not been investigated from the point of view of microphysics in the context of Titan.

Finally, two Cassini instruments detected large molecules in Titan's thermosphere, with charge/mass ratios up to 10,000 (ref. ²⁹). In addition, the presence of polycyclic aromatic hydrocarbons above an altitude of ~900 km has also been suggested³⁰. These facts plead in favour of the presence of large molecules at ground level, analogues of terrestrial surfactants³¹.

In summary, we determined three sources of material that can settle at the surface of Titan's hydrocarbon seas: (1) the haze particles, (2) crystallized organics and (3) large molecules that harbour at least one 'liquidophobic' function.

## The floatability of Titan's aerosols

Two distinct effects may be invoked when the floatability of an object is questioned: (1) the Archimedes' buoyancy and (2) the effect of capillary processes.

**Archimedes' buoyancy.** In an idealized case, the only relevant parameter is the density of the monomer material ($ρ_{mono}$) compared to the density of the sea liquid. In the absence of any wetting effect, the liquid penetrates into the whole aerosol-free volume. In such a situation, the fractal structure of the aerosols cannot be invoked to introduce an 'effective density' lower than that of the monomer. This is why we focus on the density of the monomers. The monomers are recognized as formed by molecules that harbour a large number of carbon and nitrogen atoms³². As a first guess, we can adopt Earth fossil carbon forms, like oil or bitumen, as analogues for monomers of the organic matter. As these are made of complex mixtures of numerous species, their density is not unique, and for oil³³ ranges between 0.8 and 0.95 g cm⁻³.

During its descent to Titan's surface, the Huygens probe made many measurements, and the aerosol collector and pyrolyser with gas chromatography and mass spectrometry experiment analysed the chemical composition of the collected aerosols¹⁴. Their nuclei were found to be made up of nitrogen-rich organics, without information about the molecular structure. The best estimations of their composition and density are, to date, provided by Titan's aerosol laboratory analogues, named 'tholins'³⁴. The few available measurements may be classified into two categories: high-pressure experiments³⁵ that produce relatively light materials with a density of around ~0.8 g cm⁻³ and low-pressure simulations³⁶,³⁷ that lead to heavier products, with a mean density in the range 1.3–1.4 g cm⁻³. For low-pressure measurements, individual density determinations can be found down to 0.4 g cm⁻³ (ref. ³⁵). Concerning exotic snows, the densities of solid organics that could be common at the surface

<figure><img src="image_3.png" /><figcaption>**Fig. 1 | A monomer (symbolized by a shaded disk) in contact with a liquid, which is represented in blue. a, The ideal situation of perfect non-wettability of the monomer in which the capillarity force that sustains the monomer is the maximum. b, A wettable monomer 0° ≤ θc < 90°; in such a case the capillarity cannot produce a floatability effect by balancing the gravity.**</figcaption></figure>

of Titan are given in the literature³⁸; for the most abundant and less soluble HCN, the value should be ~1.03 g cm⁻³.

Even if the chemical composition of Titan's seas is not known in detail, there is a general consensus that the main components are methane, ethane and some nitrogen³⁹,⁴⁰. In Supplementary Table 1 we gather the densities of these species in conditions relevant to Titan's polar surface. A quick inspection of this table convinces that, as a general tendency, the monomer density should remain above the expected value for the liquid. In such circumstances, the majority of aerosol particles, or exotic snowflakes, should sink to the depths of the hydrocarbon seas. This does not exclude the formation of a floating deposit supported only by Archimedes' buoyancy and formed by the lightest elements in the mass spectrum.

## The effect of the interaction between the liquid and monomers.

We now turn our attention to capillary processes. It is well-known that small bodies heavier than the supporting liquid, including those made of iron, can float under the influence of the so-called capillary force. Even some animals, such as bugs of the family of the *Gerridae* (water striders), take advantage of this kind of force to survive at the surface of water⁴¹. As recorded in Methods, the action of a liquid on a tiny object is a function of two parameters: (1) the surface tension $σ$ (N m⁻¹), an intrinsic property of the liquid-air interface, and (2) the contact angle $θ_c$, which represents the interaction between the liquid and the material of the considered object (Fig. 1). For 0° ≤ $θ_c$ ≤ 90° the liquid is rather 'attracted' by the solid material, and thus called 'liquidophilic'. When 90° ≤ $θ_c$ ≤ 180°, the material is liquid repellent and is named 'liquidophobic'. Clearly, an aerosol monomer, seen as a small sphere, may be maintained at the surface solely if the monomer is made of liquidophobic matter. A simple derivation (Methods) based on a balance between the weight and capillarity forces leads to the layer thickness:

$$e \approx \frac{3\sigma|\cos \theta_c|}{rg_{TIT}\rho_{mono}} \quad (1)$$

where $g_{TIT}$ is the gravity on Titan. In the case of a perfect non-wetting liquid (that is, for $θ_c = 180°$), a numerical estimate can be obtained for e given the surface tension $σ$ is fixed at $2 \times 10^{-2}$ N m⁻¹ (Supplementary Table 2), the radius r is 50 nm and the density $ρ_{mono} = 800$ kg m⁻³; we found $e \approx 500$ m. Such an unrealistically large value is the signature of the existence of strong limiting factors. The
<figure><img src="image_4.png" /><figcaption>**Fig. 2** | Comparison of the wave damping efficiency due to a floating film in the Titan context and under Earth conditions. The wave relative damping ratio $y$ caused by a monomolecular film deposited over the surface of a liquid is a function of the wavelength $\lambda$. **a–c**, Different relaxation times for materials that form a slick, $\omega_d$=0.1 rad s$^{-1}$ (**a**), $\omega_d$=10 rad s$^{-1}$ (**b**) and $\omega_d$=1,000 rad s$^{-1}$ (**c**). In each panel, three values (that is, 36.5, 21.3 and 7.3 in $10^{-3}$ N m$^{-1}$ shown by solid, dashed and dot-dashed lines, respectively) are considered for the coefficient of elasticity in compression $E_o$ of the film. The parameters that concern Earth (blue lines) are gravity $g$=9.81 m s$^{-2}$, the surface tension $\sigma$=73 mN m$^{-1}$, the viscosity $\eta$=$10^{-3}$ Pa s and the density $\rho$=$10^3$ kg m$^{-3}$, a value relevant for liquid water. In the case of Titan (red lines), we took $g$=1.352 m s$^{-2}$ and the values expected for liquid methane: $\sigma$=2 $\times$ $10^{-2}$ N m$^{-1}$, $\eta$=2 $\times$ $10^{-4}$ Pa s and $\rho$=452 kg m$^{-3}$.</figcaption></figure>

most obvious limitations are the aerosol sedimentation rate, which represents a few nanometres per year, and the idealized poor wettability. This, then, leads naturally to a discussion of the expected contact angles.

On Titan, maritime surfaces are not the only place for possible interactions between liquids and solid particles. This kind of interaction is known to play a crucial role in the formation of cloud particles, which are generated by heterogeneous nucleation$^{42}$. On Earth, heterogeneous nucleation on micrometre and submicrometre aerosols is the dominant mechanism in forming liquid cloud droplets. In the context of Titan, given the large abundance of aerosols, a similar microphysics was proposed for the nucleation of liquid methane droplets or small ethane crystals$^{43}$. In these approaches, the contact angle plays a key role that can be easily understood: the more aerosols that are wettable, the more the liquid can spread over its surface and favour the formation of a liquid 'envelope'. Unfortunately, contact angles are very unconstrained parameters$^{44}$, and what is found in the literature is either not perfectly relevant$^{15,45}$ or is from informal personal communication$^{43}$. Except for the nucleation of solid butane, we did not find proper peer-reviewed publications that provide $\theta_c$ values for nucleation onto tholins. Also, cloud formation models include values close to $\theta_c \approx 0^\circ$ (ref. $^{43}$), which obviously favours the formation of droplets onto organic aerosol particles. In other words, microphysics models of clouds assume the existence of liquidophilic aerosols to play the role of condensation nuclei, whereas liquidophobic particles are required to form a floating layer over Titan lake surfaces.

We now examine if some clues can be found as to the wettability of the aerosols. The actual chemical composition of Titan's aerosols

is not known. Many teams published a global stoichiometry $C_xH_yN_z$ of tholins, which spectral signature is compatible with that observed at the Saturn moon. Nonetheless, spectroscopy is not sensitive to the detailed chemical composition or to the exact composition and physical state of the aerosol surface. These surface properties determine the liquidophilic or liquidophobic character of aerosols$^{46}$. During their fall to Titan's ground, particles may also undergo a variety of alterations due to charging, photolysis or radiolysis$^{26,47}$. This 'ageing' changes the surface properties of the aerosols. Thus, their wettability may evolve before they reach the sea surface. Laboratory measurements show a very low solubility of tholins in non-polar solvents$^{48}$. A high solubility is generally recognized as associated with a liquidophilic character. Thus, the low solubility of tholins may be regarded as an indication of liquidophobia. Similarly, HCN snow may also float due to the strong liquidophobic properties.

Given the very likely existence of a rich variety of aerosol surface properties, we propose the presence of both liquidophilic and liquidophobic aerosols in Titan's atmosphere. The first family of particles sink when they reach the maritime surface, even if they arrive in a 'dry state'. The particles that belong to the second category do not participate in the cloud formation and float when they touch the surface of the sea. These kinds of particles are good candidates for building up a more-or-less thick layer at the surface of hydrocarbon seas. In a sense, the surface of Titan's lakes and seas could retain liquidophobic material.

## The existence of a film and its persistence

As the precipitation rates of the atmospheric products are small, one might wonder how an organic microlayer can build up and be
<figure><img src="image_5.png" /><figcaption>**Fig. 3** | The relative damping ratio y as a function of the wavelength λ in the case of a thin finite thickness film deposited at the surface of water, that is, in the context of Earth. The red curves correspond to three different thicknesses using a 'standard' ratio for kinematic viscosities, $v_+/v_-=100$. The case where $d=0.01$ mm is approximately similar to the case of a monomolecular floating layer. The solid blue curve shows the influence of the film kinematic viscosity $v_+$.</figcaption></figure>

maintained, rather than being destroyed by weathering. Titan's surface is a dynamic environment: wind, rain, fluvial run off and/or tides could impede such a formation. It is well-known that the saltation of particles is much more difficult from a wet substrate than from a dry surface⁴⁹. Thus, if lands that surround seas are wet, the wind should let organic dusty material settle over these terrains, and similarly should not rip the marine floating film. On the contrary, if polar lands are dry, the saltation should be easy and the wind could transport material to the sea surface, which could behave as a 'wet trap' and lead to an accumulation process. Methane rain droplets or nitrogen bubbles that come from the sea bed³⁹,⁵⁰ may locally disrupt the layer. From basic physics, the momenta associated with the impact of such objects can be estimated, respectively, as $5 \times 10^{-2} \text{ kg m s}^{-1}$ or $1 \text{ kg m s}^{-1}$, which reveals that bubbles could be more efficient than rain droplets. Nevertheless, a more specific conclusion cannot be drawn because the mechanical properties of the films are not known. However, bubbles and droplets have a significant difference: droplets bring to the seas material washed up along their fall. Indeed, droplets transport solid particles on which they have nucleated. If the rainfall is heavy enough, fluvial run off can also favour the appearance of surface layers by transporting material from the land to the seas. Finally, according to numerical simulations⁵¹, Titan's seas undergo a moderate tidal activity. Except along the shores, where material could be periodically deposited and returned to the liquid, the tides should not alter any large film due to their large 'wavelength'. Nevertheless, relatively strong tidal currents through the straits may generate some wave fields⁵².

If lakes behave like a trap, an almost continuous shore-to-shore deposit can be expected. On the contrary, where only a partial coverage is at work, this aspect could introduce some temporal and spatial variabilities in the surface properties. Even if it seems difficult to destroy floating layers by wind, rain, run off or tides, these effects could induce migration or fragmentation of the slicks. The intrinsic properties of the floating material could also induce some evolution. Floating small objects⁵³ can make large structures by self-assembly processes driven by lateral capillary interactions. Finally, we stress that the observations of specular reflections⁵⁴ over lakes is consistent with a partial and evolving film coverage. In the case of a shore-to-shore slick, a large range of refractive index values is compatible with glint observations, for which the photon fluxes are

uncertain due to the lack of knowledge about the optical thickness of the hazy cap.

## Damping of sea waves by surface films

The first fully satisfying theoretical explanation of such damping was published in the 1960s⁵⁵. For a monomolecular film, the damping of a wave of initial amplitude $a_0$ after a propagation along a distance $x$ can be written as:

$$a(x) = a_0 \exp -\Delta x \quad (2)$$

where $\Delta$ (m⁻¹) is the damping coefficient, which depends on the wavelength $\lambda$. A 'clean surface', that is, free of slick, has the damping coefficient $\Delta_0$ (Methods). To characterize the damping effect of a supernatant film, it is usual to introduce the relative damping ratio defined as⁴:

$$y(\lambda) = \Delta / \Delta_0 \quad (3)$$

This ratio depends on the intrinsic mechanical properties of the surface slick, which are represented by $E_0$ (N m⁻¹), the modulus of its coefficient of elasticity, and $\omega_d$ (rad s⁻¹), a parameter that accounts for the relaxation time of the layer (Methods gives details). In Fig. 2, we report the variations of $y(\lambda)$ with values representative for monomolecular films (for example, for hexadecanoic acid methyl ester $E_0 = 4.5 \times 10^{-2} \text{ N m}^{-1}$ and $\omega_d = 22 \text{ rad s}^{-1}$, whereas for oleic acid $E_0 = 1.4 \times 10^{-2} \text{ N m}^{-1}$ and $\omega_d = 38 \text{ rad s}^{-1}$). Not surprisingly, large viscoelastic moduli $E_0$ produce a strong damping effect, whereas long relaxation times (that is, low frequency $\omega_d$) lead to efficient damping. If we compare Earth and Titan, the general tendency is at least a similar damping effect at short wavelengths, and Titan has a much stronger effect at longer wavelengths. The properties of the sea liquid also influence wave formation. Except for the surface tension $\sigma$ (Supplementary Fig. 2), which has a minor influence, all the other parameters tend to enhance the wave damping on Titan. Undoubtedly, the sea viscosity $\nu$ has the strongest effect by, in our example, multiplying the value of $y$ by a factor of ~4, which corresponds to a factor of ~exp 4 ≈ 55 on the wave amplitude. According to this first approach, Titan seems to be more favourable than Earth for wave damping caused by a monomolecular film, because liquid hydrocarbons have a density and a viscosity smaller than that of liquid water. A monomolecular film is the thinnest blanket that one can imagine, but thicker deposits are also conceivable. A formalism specifically adapted to these finite-thickness layers has also been developed (Methods). In this more general frame, the relative damping ratio $y$ depends explicitly on the slick thickness $d$, and it firmly increases when $d$ becomes larger. Essentially, the results obtained with monomolecular films remain valid with thicker ones.

Common observations, and numerous academic studies, show that winds blowing over water are found to result in the birth and growth of waves on the sea surface⁵⁶. The global picture of wave generation can be divided into three physical processes. First, turbulence in the wind produces random stress variations on the surface. These pressure and tangential shear fluctuations give rise to small wavelets due to resonances in the wind-sea coupling⁵⁷,⁵⁸. Second, the wave amplitude is reinforced by the air flow, the pressure being maximum on the windward side of the crest and minimum on the leeward side⁵⁸. Finally, the waves start to interact with each other, which excites longer wavelength modes²⁶. Many effects conspire to limit the wave growth in height and wavelength. For instance, the fetch length over which the wind blows and the so-called 'whitecapping' affect the final spectrum of the waves⁵⁶.

Note that without the generation of the very first ripples, due to air turbulent eddies near the surface, large waves cannot be produced, and the surface of the ocean would remain mirror smooth.
An estimation, for the wavelength $\lambda_r$ of these initial wavelets caused by resonances is given by⁵⁷:

$$ \lambda_r = 2\pi \sqrt{\frac{\sigma}{\rho g}} \qquad (4) $$

with the notation already adopted in previous paragraphs. In the context of Earth, this equation leads to $\lambda_r \approx 1.7$ cm, whereas a trans-position to Titan yields a similar value $\lambda_r \approx 3.4$ cm. Our discussion of the damping rate of waves indicates that a very strong damping could occur at Titan mares, with a maximum efficiency around a wavelength of a few centimetres (Fig. 3), depending on the nature and actual properties of the floating deposit. Therefore, if the surface of a Titan sea was covered, at least partially, by such a film or slick, the onset of wave formation could be impeded and lead to the non-existence of waves at all larger wavelengths in the corresponding regions.

## Compatibility of a strong wave damping with observations

In this paper, we consider the massive presence of aerosols and other organic products (large molecules, HCN crystals and snow flakes, and so on) in the atmosphere of Titan that sediment to the ground, with hydrocarbon seas and lakes are observed in polar regions. The formation of a more-or-less thin deposit at the sea surface appears to be plausible. As already mentioned, the off-specular infrared observations may not be in conflict with this scenario: (1) the deposit may be patchy, which lets free liquid be wavy, and/or (2) the floating layer may itself produce these reflections if the local deposit has a kind of 'roughness' at infrared wavelengths. Recently, a mechanism was proposed to explain the occurrence of efficient RADAR reflectors at Ligeia Mare, one of the main Titan seas⁵⁹,⁶⁰. These so-called Magic Islands could be produced by streams of nitrogen bubbles that rise from the sea depths³⁹,⁵⁰. This scenario is not in conflict with the existence of a thin film at the sea surface: bubbles that arrive at the surface could locally break the layer and, at the same time, the RADAR wave transparency of that slick could not prevent the observation of bubbles still in the volume of the sea liquid, as is proposed.

## Conclusion

This work strongly highlights the need for laboratory studies of interactions between the cryogenic liquids relevant to Titan and tholins. Particularly, reliable contact angle determinations are fundamental for the behaviour of hydrocarbon seas together with the nucleation of liquid droplets within atmospheric microphysics processes. This new class of experiments includes studies of surfaces states and compositions of tholin particles. As an extension of preliminary work⁶¹, wind tunnels may also be used, at room temperature, with liquids and fine particles or floating films analogous to those expected on Titan.

Given their potentially crucial role in the carbon cycle, floating films and slicks could be an important target for possible future in situ explorations⁶². And, much more speculatively, they could harbour an original 'exobiological' activity.

## Online content

Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41561-019-0344-4.

Received: 15 February 2018; Accepted: 11 March 2019; Published online: 22 April 2019

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## Acknowledgements

N.C. thanks the European Research Council for funding via the ERC PrimChem project (grant agreement no. 636829). This work was also supported by the Programme National de Planétologie (PNP) of CNRS-INSU co-funded by CNES. The authors thank S. Lebonnois, J. Vatant d’Ollone, T. Tokano and B. Charnay for fruitful scientific discussions.

## Author contributions

D.C. wrote the paper and performed numerical simulations. N.C. provided expertise concerning the properties of Titan’s aerosols.

## Competing interests

The authors declare no competing interests.

## Additional information

*Supplementary information* is available for this paper at https://doi.org/10.1038/s41561-019-0344-4.

*Reprints and permissions information* is available at www.nature.com/reprints.

*Correspondence and requests for materials* should be addressed to D.C.

*Publisher’s note:* Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

© The Author(s), under exclusive licence to Springer Nature Limited 2019
Methods

**Interaction between a monomer and the sea liquid.** In Fig. 1 we recall some basics about the capillarity forces that act on a tiny object. If the latter is assimilated to a partially immersed sphere, each elementary portion dl (m) of the float line undergoes an elementary force, the vertical component of which is given by:

$$df_{\text{cap}} = \sigma \cos \theta_c dl \quad (5)$$

The surface tension is an intrinsic property of the liquid and depends on the thermodynamic conditions together with the chemical composition of the liquid. The contact angle accounts for the interactions between the liquid and the solid substrate. The range $0^\circ \le \theta_c \le 90^\circ$ corresponds to high wettabilities—the solid is liquidophilic. For a perfect wetting, $\theta_c = 0^\circ$, the liquid has the tendency to spread out over the entire surface of the solid. A liquidophobic liquid, that is, presenting a low wettability, leads to $90^\circ \le \theta_c \le 180^\circ$. The perfectly non-wetting case occurs when $\theta_c = 180^\circ$. On a flat surface the liquid tends to form spherical droplets. Figure 1 describes the interaction between an idealized spherical monomer and the liquid phase of a Titan sea. Clearly, when $0^\circ \le \theta_c < 90^\circ$ the monomer is attracted by the liquid and consequently sinks into the liquid (Fig. 1b). On the contrary, if $90^\circ < \theta_c \le 180^\circ$ a vertical force can balance the effect of gravity—this force is at a maximum when the monomer is perfectly non-wettable (Fig. 1a, $\theta_c = 180^\circ$). The contact angles are very unconstrained parameters, as discussed in the main text.

For a single monomer, the resulting vertical force $f_{\text{cap}}(N)$, produced by capillarity, may be approximated by:

$$f_{\text{cap}} \approx 2\pi\sigma\cos\theta_c \quad (6)$$

This expression assumes that the plane of flotation contains the centre of the monomer, which is not necessarily the case. Furthermore, real monomers are built from clusters of large organic molecules and their shapes are certainly not perfectly spherical; therefore, equation (6) has to be understood as an approximation. Unambiguously, the floatability of the considered monomer is governed by the value of the angle of contact: if the wettability of the monomer is high (that is, $0^\circ \le \theta_c \le 90^\circ$), the capillarity force is downwards and the monomer sinks. Oppositely, for a low wettability (that is, $90^\circ \le \theta_c \le 180^\circ$), the capillarity force has a vertical ascending component that can counterbalance the weight of the object.

**Maximum thickness of a slick supported by capillarity.** By definition, the first layer of aerosols deposited at the surface of a Titan sea is in contact with the liquid by the monomers at the lowest positions. We denote $N^*(\text{N m}^{-2})$ as the number per unit of surface of these monomers located on the surface of the liquid. If $p$ is the 'porosity' of the aerosols, then $N^*$ can be estimated by:

$$N^* \approx (1-p) \times \frac{1}{s} \quad (7)$$

where $s (\text{m}^2)$ is the cross-section of an individual monomer, specifically $s \approx \pi r^2$. Thus, the force $F_{\text{cap}}^*(\text{N m}^{-2})$ per unit of surface due to the effect of surface tension and acting on the aerosol layer that covers the sea can be derived by:

$$F_{\text{cap}}^* \approx \frac{2(1-p)\sigma \cos \theta_c}{r} \quad (8)$$

$M_{\text{aero}}^*(\text{kg m}^{-2})$ is the mass per unit of surface of the aerosols deposited at the surface of the liquid. It can be expressed as:

$$M_{\text{aero}}^* \approx N^* n^{\frac{4}{3}} \pi r^3 \rho_{\text{mono}} \quad (9)$$

with $n^*(\text{m}^{-1})$ the mean number of monomers per unit length along the vertical axis. An estimation of $n^*$ can be made by adopting $n^* \approx e/2\pi$ with $e$ (m) the total thickness of the aerosol slick. The weight per unit of surface supported by the liquid is then $P_{\text{aero}}^* = M_{\text{aero}}^* g_{\text{Tit}} (\text{N m}^{-2})$. With some algebra, we get:

$$P_{\text{aero}}^* \approx \frac{2}{3}(1-p)\epsilon\rho_{\text{mono}}g_{\text{Tit}} \quad (10)$$

By equalizing equations (8) and (10), we can extract the thickness:

$$e \approx \frac{3\sigma|\cos \theta_c|}{rg_{\text{Tit}}\rho_{\text{mono}}} \quad (11)$$

As can be expected, a high surface tension and small monomers favour thick aerosol deposits, whereas a high gravity together with large densities decrease the value of $e$. Perhaps more surprisingly, this result does not depend on the porosity of the aerosols. This behaviour is easily explained as both the layer weight and the surface capillary force are proportional to $(1-p)$.

**The wave relative damping ratio.** For a surface free of floating material, the damping coefficient $\Delta_0$ is given by the Stokes' equation¹:

$$\Delta_0 = \frac{4k^2\eta\omega}{\rho g + 3\sigma k^2} \quad (12)$$

where $k (\text{m}^{-1})$ is the wavenumber related to the wavelength $\lambda$ by the well-known equation $k = 2\pi/\lambda$ and $\omega$ (rad s$^{-1}$) is the angular frequency. In the present context, all these quantities are also constrained by the dispersion relation for gravity-capillary waves:

$$\omega^2 = gk + \frac{\sigma k^3}{\rho} \quad (13)$$

Together with $\Delta$, the actual damping coefficient of the considered sea surface, $\Delta_0$, appears in the relative damping ratio defined as in equation (3)¹:

$$y(\lambda) = \Delta/\Delta_0 \quad (14)$$

The proper mechanical properties of a surface film are a function of its complex viscoelastic modulus $E$ (N m$^{-1}$). Its real and imaginary parts, respectively denoted $E_r$ and $E_i$, as a function of $\omega$ (rad s$^{-1}$) are given by⁶,⁶⁴:

$$E_r = E_0 \frac{1 + (\omega_d/2\omega)^{1/2}}{1 + \omega_d/\omega + (2\omega_d/\omega)^{1/2}} \quad (15)$$

and

$$E_i = E_0 \frac{(\omega_d/2\omega)^{1/2}}{1 + \omega_d/\omega + (2\omega_d/\omega)^{1/2}} \quad (16)$$

The relative damping ratio is finally expressed as⁶³:

$$y = \frac{1 - \frac{E_r - E_i}{2^{1/2}}ak + \frac{E_r^2 + E_i^2}{4(2^{1/2})}a^2k^3 + \frac{E_i}{4}ak^2}{1 + (E_r^2 + E_i^2)a^2k^2 - (2^{1/2})(E_r - E_i)ak} \quad (17)$$

$$a = k^3/\rho\omega^2$$

The effect of a finite thickness, that is, a non-monomolecular surface deposit, has been investigated in the context of heavy fuel slicks and grease ice⁶⁵,⁶⁶. Up to a thickness of ~10 µm, the computed damping rate does not differ essentially from that with zero thickness. In the frame of the formalism relevant for finite-thickness film, the properties of such a film are no longer represented by only two parameters. Instead, more specific quantities are introduced: the kinematic viscosities of the film $\nu_+$ and that of the bulk liquid $\nu_-$ (m$^2$s$^{-1}$), their respective densities $\rho_+$ and $\rho_-$ (kg m$^{-3}$) together with surface and interfacial tensions. The thickness $d$ (m) is also taken into account. The model parametrization is summarized in Supplementary Fig. 3. The behaviour of an oil film over water at Earth's surface is illustrated by the damping ratio $y$ for $d=0.01$ mm (that is, 10 µm) in Fig. 3. This curve has to be understood as the reference for that produced by a quasi-monomolecular film⁶⁶. At all wavelengths, an increase of $d$ leads to a substantially larger relative damping ratio $y$. The conclusions of our previous discussion, developed using the simple monomolecular formalism, remain valid and the increased factor of $y$, found in this frame, must be taken as a minimum value.

Although totally unknown, the intrinsic properties of a possible slick deposited at a Titan sea surface should play an important role. For instance, a high value for the kinematic viscosity $\nu_+$ naturally yields a much more efficient damping. In Fig. 3, the consequences of a ten times more viscous 'oil' can be seen for a $d=5$ mm thick layer. As could be expected, the wave damping appears much stronger, particularly at long wavelengths.

## Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## Code availability

The codes used to generate the plots in this paper are available from the corresponding author upon reasonable request.

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