The Properties of Titan’s Surface Liquids

• Introduction

Titan is the only extraterrestrial body known to have surface liquids with an associated hydrologic cycle, complete with rivers, lakes, seas, evaporation/condensation and precipitation; albeit with cycling mixtures of methane, ethane, and large, temperature-dependent quantities of dissolved atmospheric nitrogen [1–2]. Unlike water and its common solutes on Earth, however, the physical properties of methane–ethane–nitrogen mixtures are highly sensitive to composition, temperature, and pressure/depth. Understanding these variations is crucial for understanding the behavior of Titan’s surface liquids and its broader climate and weather patterns.

Deriving these properties, however, is not trivial. These three species can interfere with each other’s intermolecular bond strengths. As such, methane, ethane, and nitrogen don’t ideally mix; i.e., they differ significantly from Raoult’s Law [3]. As a result, the physical properties of methane–ethane–nitrogen mixtures under Titan-like conditions are much more complicated to compute accurately than if they could be treated as an ideal mixture.

 

• Methods

We use TITANPOOL [4], which computes the properties of liquid methane–ethane–nitrogen mixtures on Titan that are in vapor–liquid equilibrium (VLE) with the atmosphere. For a given temperature and relative methane–ethane ratio; TITANPOOL numerically determines the equilibrium nitrogen concentrations and then uses this composition to compute the physical properties of the liquid (e.g., density, surface, tension, viscosity, etc.). TITANPOOL integrates down the liquid column by adding the hydrostatic pressure from the liquid column overlying the material at the depth in question to compute the pressure from which equilibrium properties are derived.

TITANPOOL uses the GERG-2008 [5–6] equation of state (EOS) for methane–ethane–nitrogen mixtures, as published in REFPROP10 by NIST [7]. The GERG-2008 EOS has been benchmarked against laboratory studies under Titan-relevant conditions and is accurate to within a few percent [4]. As noted above, our results assume that the liquid is in VLE with the atmosphere, and that the liquid is saturated in nitrogen. The justification for this assumption is presented in this EPSC-DPS2025 session, in “Diffusing "Uphill" Against the Concentration Gradient and the Saturation of Stagnant Lakes on Titan” (Steckloff et al.).

 

• Results

We consider 90–94K isothermal 140m-deep lakes and a 1.47-bar surface pressure [6]. We use 2m integration steps for depth and parse the methane–ethane composition in 5% methane–alkane fraction steps (defined as the molar concentration of methane divided by the sum of the molar concentrations of methane and ethane). Nitrogen saturation includes dependencies on T, P (derived from the density of the overlying liquid column) and methane–alkane fraction.

The densities of the three liquids differ significantly, liquid nitrogen being the densest and methane the lightest. Nitrogen is significantly more soluble in methane-rich mixtures, however, leading to curious behavior at low temperatures (e.g., 90 K) where, at high pressure/depth, the liquid density is highest for methane-dominated and ethane-dominated mixture, and lower for more equal methane–ethane mixtures.

The viscosities of these liquids (which describe resistance to flow) also differ significantly, with liquid nitrogen having the lowest viscosity (REFPROP computes viscosities of hydrocarbon mixtures to within ~4% [9]). This leads to the strange behavior on Titan where, as depth increases (and thus nitrogen concentration), viscosity decreases.  The lower layers Titan’s lakes flow more readily than their surfaces, with viscosities at depth ~10–100% lower than at the surface—this is extremely foreign to us, as there are no common analogous lakes on Earth.

Surface tension (which measures how strongly liquids cohere) increases with ethane concentration. Like water, surface tension does not show much dependance on pressure, except at the coldest temperature considered. At 90K, surface tension increases with depth for ethane-dominated mixtures but decrease with depth/pressure for methane-dominated mixtures. We caution, however, as the surface tension of ethane is not as well studied as it is for methane and nitrogen [9].

 

• Discussion

These properties will influence the dynamics of Titan’s lakes. Methane-rich lakes exhibit larger density gradients than ethane-rich lakes and thus are more stable against overturn/mixing, and more resistant to non-density-driven circulation. If circulation were to begin in a methane-rich lake and push nitrogen-saturated materials to shallower depths, the liquid would exsolve nitrogen [10], reducing its density, further driving circulation.

Liquid properties influence the initiation and growth of wind-driven capillary-gravity waves on liquid bodies [11]. Our methane-rich liquid properties are similar to those used in pervious wave modeling [12] and thus support their conclusions. Our surface tension for ethane-rich liquids, however, are ~2X larger than those of [12], which would result in a greater restoring force that shifts the transition from capillary waves to capillary-gravity waves to larger wavelengths and result in waves most easily excited by wind that have higher phase speeds and longer wavelengths.

Fluid properties also influence how liquids interaction with landscapes. Surface tension governs capillary draw-up; lower surface tensions imply less groundwater supply into Titan’s rivers. Groundwater instead would be more readily sequestered, potentially following topography and affecting only locations of large liquid bodies. Density governs the dynamics of fluid runoff and sediment transport. As temperate may evolve within a Titan river [13], its ability to transport sediment may change as it traverses from Titan's highlands to its seas, influencing the formation and morphology of bedforms, and erosion of channel beds.

 

Acknowledgments: We acknowledge support from NASA grants NNX15AL48G and 80NSSC18K0967, and the Heising-Simons Foundation.

References: [1] Lunine et al. (1983) Science 222:1229–1230; [2] Mitri et al. (2007) Icarus 186:385–394; [3] Glein and Shock (2013) Geochimica Cosmochimica Acta 115, 217–240; [4] Steckloff et al. (2020) PSJ 1:26; [5] Kunz et al. (2007) European Gas Reserach Technical Monograph, 15; [6] Kunz & Wagner (2012) J. Chemical Engineering Data, 57:3032–3091; [7] Lemmon et al. (2010) REFPROP, V.9.0, Maryland; [8] Lindal et al. (1983) Icarus 53:348–363; [9] Huber et al. (2022) Industrial Engineering Chemistry Res. 61:15449–15472; [10] Cordier et al. (2017) Nature Astronomy 1:0102; [11] Kinsman (1984) ISBN 0486646521; [12] Hayes et al. (2013) Icarus 225:403–412; [13] Corlies et al. (2023) Titan Through Time VI, Paris, France.