Thermodynamic non-equilibrium theory of the condensational growth of atmospheric water drops

Summary

The application of the theory of non-equilibrium thermodynamics to phenomena of cloud micro-physics has been examined for the example of mass growth of atmospheric water drops due to vapour diffusion and condensation. A materially and energetically closed heterogeneous system composed of a drop phase and a surrounding dry air-water vapour mixture is assumed as appropriate basic model in order to treat the concomitant theoretical aspects (comprising description of the individual growth rate, variation of moist air temperature, and drop surface conditions) in dependency on the central criteria of irreversibility. Owing to this, a main object of our theory is the thorough derivation of the budget equations of thermal energy and entropy representing, respectively, the first and second law of thermodynamics. Physically, these principles, associated with the peculiar thermodynamic behaviour of coexisting atmospheric drops and vapour, embody a suitable theoretical frame for the line of reasoning. The dominant position is owned by the production rate of entropy, a bilinear form of thermodynamic forces and fluxes. The occasion arises to postulate adequate non-equilibrium laws for the irreversible transport of matter and heat. With regard to the entropy rate of change and the thermodynamic situation in the drop-moist air model, one is left with the option to consider several alternative postulates for the fluxes and, hence, several equivalent parameterizations of the growth rate of drops. Four such approaches in accord with the thermodynamic context are discussed. As each of them depends on the surface temperatures of drops, it is expedient to complete the growth equations by a separate treatment of these micro-state variables. Practical scaling arguments for these internal thermodynamic parameters reveal that a suitable reduced form of the energy budget for the isolated drop-moist air-model system can be assumed. As a consequence, the droplet surface temperature becomes a diagnostic parameter which can be eliminated from the growth equation.