Moisture sorption kinetics for water-soluble substances. I: Theoretical considerations of heat transport control

A model based on heat transport control was developed to describe the uptake of water on a deliquescent solid in an atmosphere of pure water vapor. The model assumes the presence of a saturated liquid film on the surface of the solid. The decrease in the vapor pressure of water over the surface, brought about by the colligative effect of solid dissolved in the liquid film, is effectively offset by the increase in temperature of the film (and the solid) caused by the heat released on condensation of the water vapor. The thermal transients die out quickly and a steady-state analysis is valid. At steady state the temperature of the liquid film (and solid) is that temperature at which the vapor pressure of water above the saturated solution is equal to the chamber pressure. Consequently, water uptake occurs at a rate that depends on the heat flux away from the surface. The water uptake rate, W'h, is constant at a given relative humidity and is described by an equation of the form W'h = (C + F) . ln (RHi/RHo), where C and F are conductive and radiative coefficients, RHi the chamber relative humidity, and RHo the relative humidity at and above which continuous water uptake (deliquescence) occurs. The model contains no adjustable parameters and can thus be directly tested against experimental results.