Condensation corrosion: a theoretical approach

Condensation of water from warm, humid air to cold rock walls in caves is regarded to play a significant role in speleogenesis. The water condensing to the cave walls quickly attains equilibrium with the carbon dioxide in the surrounding air, and consequently dissolves limestone or gypsum forming various types of macro- ,meso-, and micromorphologies. In this paper we present the basic physical principles of condensation and give equations, which allow a satisfactory estimation of condensation rates. Water condensing to a cooler wall releases heat of condensation, which raises the temperature of the wall thus reducing the temperature difference ΔT between the warm air and the cave wall. Furthermore one has to take into account the heat flux from the air to the cave wall. This defines the boundary conditions for the equation of heat conduction. For a constant temperature of the air initial condensation rates are high but then drop down rapidly by orders of magnitude during the first few days. Finally constant condensation rates are attained, when the heat flux into the rock is fully transmitted to the surface of the karst plateau. For spherical and cylindrical conduits these can be obtained as a function of the depth Z below the surface. When diurnal or seasonal variations of the air temperature are active as is the case close to cave entrances, condensation rates can become quite significant, up to about 10-6 m/year. The theoretical results are applied also to corrosion of speleothems and the formation of r hrenkarren as described by Simms (2003). To convert condensation rates into retreat of bedrock the saturation state of the solution must be known. In the appendix we present experiments, which prove that in any case the solution flowing off the rock is saturated with respect to limestone or gypsum, respectively.