4.1. Evaporation Theory and Effect of Buoyancy
 Since methane is lighter than molecular N2, buoyancy is expected to affect evaporation. This appears to be the case for both our experimental setup and the atmosphere of Titan where the average weight is 28 g mol−1 compared to CH4's 16 g mol−1. Buoyancy-driven evaporation is estimated by a modified mass flux equation originally developed for martian ice [Ingersoll, 1970]:
where DCH4/N2 is the diffusion coefficient of CH4 gas in N2 [Elliott and Watts, 1972] , is the difference between the density of CH4 above the liquid layer and the density of CH4 in the ambient atmosphere, Δρ = ρatm − ρsurf is the difference between the density of the ambient gas and the gas at the surface, g is the gravitational acceleration on Titan, and ν is the kinematic viscosity of CH4 [Crane Co., 1982]. These parameters and their values are summarized in Table 1 (for additional information on the used parameters, see auxiliary material). Buoyancy-driven evaporation rates on Earth are expected to be larger relative to those in Titan's gravity field with a factor of = 0.516. Thus, the average evaporation rate from our simulations, corrected for the gravity field of Titan is (1.6 ± 0.3) × 10−4 kgs−1m−2.
Table 1. Measured and Calculated Parameters in methane Evaporation Experimentsa
|(2.2 ± 0.02) × 10−4||94.0||1.5||N/A|
|(3.4 ± 0.01) × 10−4||95.0||1.5||2.3 × 10−2|
|(3.3 ± 0.01) × 10−4||93.7||1.5||1.9 × 10−2|
|(3.2 ± 0.02) × 10−4||93.7||1.5||2.2 × 10−2|
|<Eexp> = (3.1 ± 0.6)× 10−4||94.1 ± 0.6||1.5||2.1 × 10−2|
|<Ecorr> = (1.6 ± 0.3) × 10−4||94.1 ± 0.6||1.5||2.1 × 10−2|
4.2. Liquid Composition
 Considering the solubility of N2 in CH4, we suggest a binary mixture of CH4-N2 for the composition of the evaporating liquid in the chamber. Assuming N2 is only mixed when the CH4 is in contact with the chamber atmosphere, the time it takes for the mixture to equilibrate is only 10 seconds. This is due to the high diffusion coefficient of N2 into liquid CH4. We calculate that the mole fractions of N2 and CH4 in the condensed liquid is 0.16 and 0.84 respectively (see auxiliary material). Using Ingersoll's equation (equation (1)) and dividing it by the density of the binary mixture (Table 2), we derive an evaporation rate of 1.52 × 10−4 kgs−1m−2. This value is in excellent agreement with the gravity-corrected experimental value of (1.58 ± 0.3) × 10−4 kg s−1m−2.
Table 2. Parameters and Their Values Used in Equation (1) for a CH4-N2 Liquid
|Surface temperature||T||94 K|
|Surface pressure||Ptot||1.5 bar|
|Saturation density of CH4 vapor||ρsurfCH4,gas||0.37 kg m−3|
|Initial atmospheric CH4 density||ρatmCH4,gas||0.15 kg m−3|
|Liquid density||ρliq||501.32 kg m−3|
|Mole fraction of CH4 in liquid||XCH4||0.84|
|Density of liquid CH4||ρCH4||442.8 kg m−3|
|Density of N2||ρN2||808.6 kg m−3|
|Molecular mass of CH4||MCH4||0.016 kg mol−1|
|Saturation mole fraction of CH4||YCH4||0.119|
|Diffusion coefficient||DCH4/N2||1.89 × 10−6 m2 s−1|
|Density of ambient gas||ρatm||5.26|
|Density of gas at the surface||ρsurf||5.09|
|Gravitational acceleration||g||1.35 m s−2|
|Kinematic viscosity||ν||1.16 × 10−6 m2 s−1|
 To examine the possibility of a pure CH4 liquid evaporating in the chamber, we performed the same calculations from equation (1) for a CH4 mole fraction of 1. The resulting evaporation rate of 2.31 × 10−4 kgs−1m−2 largely overestimates the experimentally measured rate, with an error of 31.5%.
 We conclude that based on the good agreement of the experimentally determined and gravity corrected evaporation rate and the theoretical approach, the composition of the evaporating liquid in the chamber is a CH4-N2binary mixture with mole fractions of 0.84 and 0.16 respectively. The fact that Ingersoll's equation predicts the evaporation rate in the chamber demonstrates that mass transfer in our experiments is largely controlled by the concentration difference in the simulated atmosphere and buoyancy-driven diffusion.
4.3. Implications for Titan
 Although lakes are not observed at the low latitude regions of Titan, transient liquids may still exist for limited periods of time [Griffith et al., 2012]. Recent observations of a low-latitude storm and accompanied surface darkening may indicate temporal liquid CH4 accumulation [Turtle et al., 2011]. Assuming the reported surface changes are in fact due to CH4 precipitation and possibly standing liquid on the surface, rough quantitative estimates on the depth of evaporated CH4 and the total mass of precipitation can be made based on the experimental evaporation rates presented here. The storm onset was reported to be around 27 September 2010, accompanying surface changes were observed through October 2010, and most changes reverted by 15 January 2011 [Turtle et al., 2011]. The area subject to albedo changes seen by ISS until 29 October 2010 was 510,000 ± 20,000 km2 [Turtle et al., 2011]. Assuming that all the CH4 precipitated between the onset and 29 October 2010, in order for the darkened terrain to reverse to normal, all the accumulated CH4 had to evaporate by 15 January 2011.
 Using our experimentally determined evaporation rate and the time between 29 October, 2010 and 15 January 2011, the maximum depth of the evaporated liquid resulting from the storm is 2.4 ± 0.5 m. Once multiplied by the area of observed changes (510,000 km2) and the density of the CH4-N2 mixture at 94 K, this corresponds to a maximum total mass of (5.4 ± 1.2) × 1010 kg of evaporated/precipitated CH4.
 It is important to note that our mass and depth estimates are an upper limit, because the evaporation of the CH4-N2mixture is predominantly diffusion-driven in our experiments, while numerical models and GCMs predict heat balance driven evaporation [Schneider et al., 2012; Williams et al., 2012; Mitchell, 2008]. Indeed, energy transfer is limited on Titan as shown by McKay et al.  and more recently by Williams et al. , and thus leads to significantly lower evaporation rates. Alternatively, our results indicate that the main driver for CH4evaporation under Titan conditions is buoyancy-driven, although an energy source is still required for the phase change to occur. Considering the extremely low temperatures during our experiments, radiation from the chamber walls is negligible; however, additional energy sources could arise from the cooling of the liquid during diffusion and heat conduction from the bottom of the liquid to the colder top layer. A detailed heat transfer study will be presented in a future paper, nonetheless the results of our experiments suggest that even in an energy-limited environment, the evaporation process can still be controlled by mass transfer.
 On Titan, according to the model of Williams et al. , the daily average non-radiative fluxes are 20 times higher than previously thought [McKay et al., 1991], and are theoretically available for convective energy. At the same time, we do not see any evidence for active convection in the chamber, only for passive convection in the form of buoyancy. Indeed, as shown in Figures 1d and 1c, the temperature close to the pan remains cooler than in the ambient atmosphere of the chamber during both the steady-state and the plateau periods. Moreover, the temperature profiles remain very parallel and show an overall decreasing trend (Figure 1c). These observations are indicative of heat conduction from the warmer upper gas downward into the liquid. The biggest temperature difference occurs between the uppermost and lowermost positioned thermocouples (TC #3 and TC #2 in Figure S1). Considering that the error for the K type thermocouples used is about 1°C, the thermocouples may hint at a statistically significant thermal gradient between these two thermocouples, though, if so, the gradient is very small. For the other thermocouples, the uncertainties resulting from the temperature readings makes these temperature gradients statistically not unique. By the onset of the steady-state section, where the evaporation rates were determined, sufficient time has elapsed such that the system reaches similar temperatures within error (standard deviations of 0.75, 0.96, 0.48 and 0.18 K for thermocouple #s 2, 3, 4 and 6, respectively).
 Additionally, since the exact onset and offset of precipitation over the course of the low latitude storm is unknown, we may be overestimating the depth and mass. The differences in topography will cause a non-uniform distribution of liquid due to runoff with deeper and shallower areas. Processes other than evaporation, such as infiltration are important as well (as indicated by the presence of subsurface CH4 moisture detected by the Huygens GCMS [Niemann et al., 2005]), but are not within the scope of the present work.
4.4. Effect of Wind
 Wind speeds at the surface of Titan are generally weak with speeds of 0.2–1 m s−1 [Lorenz, 2006]. Based on the model of Mitri et al. , evaporation, or rather the flux, is linearly proportional to wind speed. To examine the maximum effect of wind, we assume the highest wind speeds of 1 m s−1 and calculate the mass flux from the equation of Mitri et al.  E = ρatmK(q* − q)ur, where K is the transfer coefficient (0.0013 [Mitri et al., 2007]), q* and q are the saturation specific humidity and specific humidity of CH4, respectively, and ur is the horizontal wind speed. Dividing by the density of the binary mixture we get a value of 1.65 mm hr−1. The corrected evaporation rate in our experiments - as mentioned before - is 1.13 ± 0.3 mm hr−1. Since wind removes humidity over the liquid, we are taking the effect of wind into consideration by assuming a dry N2 atmosphere in our calculations. Considering the excellent agreement of our experimental results with Ingersoll's equation (equation (1)), we used that in our calculations. Assuming a dry Titanian atmosphere of 1.5 bar of N2, the evaporation rate of the mixture would be 2.6 mm hr−1, almost 2.5 times faster than in a humid atmosphere. That would result in an evaporated liquid of 1.2 × 1011 kg over the low latitude storm reported by Turtle et al.  under windy Titan conditions. This again is an upper bound, considering the overestimation of the mass and depth of evaporated liquid from our evaporation rates and a completely dry atmosphere.