Kinetics of Capillary Condensation in Wedge-Shaped Pores

Abstract

The kinetics of capillary condensation into an initially dry pore is treated as an unsteady diffusion problem with a moving boundary at which the vapor concentration satisfies the Kelvin equation. The (justifiable) approximation that the phenomenon is radial leads to important simplifications. An exact similarity solution is found which is valid for the early stages of the condensation process. An approximate method of analysis is developed, using the class of similarity solutions of the two-dimensional radial diffusion problem with a constant concentration condition at an appropriately moving boundary. The method has some analogies to the Pohlhausen method in fluid mechanics in that the initial and boundary conditions are satisfied exactly, and the diffusion equation is satisfied in an integral sense. The method depends on numerical methods of integration, but approximate analytical solutions are available when the time is sufficiently large. Numerical solutions are given for the capillary condensation of water. The characteristic equilibration time is highly sensitive to h0, the relative saturation of the atmosphere to which the dry pore is exposed, varying approximately as (1—h0)—3. The initial condensation rate is a constant, largely independent of h0 when this is close to one. The kinetics of capillary condensation is highly sensitive to temperature, equilibration times for water at 80°C being only 1/233 as great as at 0°C. The major influence of temperature on kinetics is due to the temperature dependence of the saturated vapor density. A limitation to this approach is that the treatment is essentially macroscopic, although the early stages of condensation may involve relatively few molecules.