Development of Two-Phase Diffusion Model Consisting of Free and Bound Water Molecules for Water Vapor Diffusing into Asphalt Mixtures

Water vapor diffusing inside asphalt mixtures is one of the most important ways for water molecules accessing asphalt mixtures to trigger moisture damage. Several diffusion models have been constructed to describe the water vapor diffusion in asphalt mixtures based on Fick’s second law, with the assumption that all water molecules are free. However, when water vapor diffuses in asphalt mixtures, there exists free and bound water molecules simultaneously. Most of the current diffusion models ignore the bound phase of water molecules during the diffusion process. This study developed a three-dimensional (3D) two-phase diffusion model in cylindrical coordinates. Fick’s second law was used to describe the free phase of water molecules, and the relationship between free and bound water molecules was formulated to establish the model. The accumulative water vapor diffusion test was conducted on two types of asphalt mixtures at three relative humidity (RH) levels (17.17%, 51.51%, and 90.14%) at 20°C using the gravimetric sorption analyzer (GSA). The initial RH of the test specimens was set to 0% by evacuating the specimens, and then a steady level of water vapor pressure was applied to achieve the specific RH. The mass of diffused water vapor in the specimens was weighed every 5 s by the magnetic suspension balance of GSA. The raw data, consisting of diffused mass of water vapor versus diffusing time, were obtained. The developed 3D two-phase diffusion model with the first 36 terms was used to fit the diffusion data. Four model parameters—diffusivity of water vapor in asphalt mixtures ($D$), maximum mass of diffused water vapor [$M(\infty )$], probability of free water molecules becoming bound ($y$), and probability of bound water molecules becoming free ($\beta$)—were determined after model fitting. Furthermore, the maximum mass of bound water molecules [$M_1(\infty )$] and the maximum mass of free water molecules [$M_2(\infty )$] could be calculated after determination of these model parameters.