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Modélisation des changements de phase dans la basse atmosphère de Titan

Abstract : I -- Importance of phase changes and nucleation in Titan's lower Atmosphere -- We have pointed out the interactions between phase changes in the lower atmosphere and other processes which occur on Titan. Phase change processes can affect photo-chemistry, the nature of Titan's exposed surface and hence its spectral properties, and the atmospheric thermal profile. We have critically reviewed clues that suggest that nucleation is difficult in Titan's atmosphere and we have tried to make clear why the description of nucleation is a priority in modeling phase changes. The results of the analysis of IRIS spectra and the low temperatures that imply solid rather than liquid phases are the main arguments for nucleation modeling. In the frame of the classical theory of nucleation, we have proposed a definition and a value of the critical nucleation rate which are adapted to the study of Titan's atmosphere. From this critical rate, we have computed the contact angle of methane on aerosols that is needed if the inhibition of methane nucleation is the reason for the super-saturation suggested by IRIS observations. -- II -- Estimation of contact angles and surface free enthalpies of solids -- Those parameters are essential for the description of nucleation. As experimental data for the solid phases of the species we are interested in are unavailable, we have selected and pieced together estimation methods for contact angles and surface free enthalpies of solids, from the existing literature. The surface free enthalpy of a solid may be linked to the surface tension of the liquid and the latent heats of vaporization and sublimation. However, a few variations on this idea have been proposed. In order to choose the adequate correlation for solid hydrocarbons and nitriles, the solid surface free enthalpy for a few selected reference species may also be estimated from the Hamaker constant. The Hamaker constant is itself linked to the dielectric permittivity, hence to the absorption spectra of the solid phase. Thus, we have opened up a way between ongoing laboratory investigations on the spectra of solid hydrocarbons and nitriles, and the computations of surface free enthalpies and contact angles. -- III -- Building models for the description of phase changes in Titan's lower atmosphere -- Essential phenomena to be described in a model of phase changes, beside condensation and evaporation, are nucleation, aerosol settling and gas transport by eddy diffusion. Nucleation is described with the classical theory. The contact angle is not assumed to be zero, it is a free parameter. We have managed to bring together these phenomena in the equations, addressing such problems as the volume of the aerosols just after nucleation and the treatment of aerosols with size smaller than the Kelvin equilibrium size. As we expect non-stationary evolution for some values of the contact angle, we have made the model time-dependent. Therefore, the model (numbered 3) consists of a set of partial differential equations. In order to check the validity of the model itself (the way nucleation is built into the equations) and the validity of the numerical resolution to come, we have considered a simpler model (numbered 2) with instantaneous nucleation, and we have demonstrated that the solutions of model 3 should tend toward a solution of model 2 when the contact angle and the surface free enthalpy of the condensed phase tend toward zero. -- IV -- We have studied two more simple models. One model (numbered 1) assumes negligible super-saturation of all species. This very easy-to-use model provides insight into the influence of such parameters as the eddy diffusion coefficient, the mass flux of tholins falling from the upper atmosphere, the radius of tholin particles, the gas mole fractions at the surface. In particular, for plausible values of those parameters (as found in the literature), by studying the self-consistency of the model, we have shown that methane super-saturation would rather be due to nucleation inhibition or coagulation than the dynamics of gas transport and condensation (after nucleation). Thus, small super-saturation is really not a hypothesis, and model 1 gives correct results in the event of easy nucleation and unimportant coagulation. Then the evaporation-condensation cycle of methane in the troposphere involves the evaporation of typically a few centimeters, up to fifty centimeters, of methane per year, and the concomitant exchange of latent heat may be on the order of 0.1 W m-2, up to 3 W m-2. Condensation of acetylene starts at about 61 km, and condensation of ethane at 51 km. At the tropopause, the radius of aerosols reaches approximately 3 times the radius of tholin nuclei. At 20 km, the radius has increased to typically 200 times the radius of tholin nuclei due to methane condensation. Finally, a model is specifically set up to demonstrate the potential periodic behavior associated to some values of the contact angle. As opposed to the other models mentioned above, it does not aim at providing values for properties of Titan's atmosphere, and gives a qualitative information. Periodicity is expected when the abundance from the instantaneous nucleation model is distinctly lower than the critical abundance (obtained from the critical nucleation rate), and the critical abundance itself is distinctly lower than the abundance without condensation. The period then diminishes with the critical abundance.
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Lionel Guez. Modélisation des changements de phase dans la basse atmosphère de Titan. Astrophysique [astro-ph]. Université Paris-Diderot - Paris VII, 1997. Français. ⟨tel-00007042⟩

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