Development of a three-dimensional diffusion model for water vapor diffusing into asphalt mixtures

Abstract

Water vapor diffusion in asphalt mixtures has been investigated to develop water vapor diffusion models that predict the diffusivities of water vapor in asphalt mixtures. However, even the most comprehensive diffusion model available in the literature was not rigorously derived in the three-dimensional (3-D) coordinates but formulated by simply summing up the diffusion models for different directions. This study developed a closed-form 3-D diffusion model for Phase I water vapor diffusion in asphalt mixtures. The developed model was formulated through rigorous derivations originated from Fick’s second law in cylindrical coordinates. The final formulation was a discrete model with infinite terms.The developed model was applied to the data of Phase I water vapor diffusion tests performed on two types of asphalt mixtures at 20 °C using the Gravimetric Sorption Device. The initial relative humidity (RH) inside the test specimen was approximately 0% since the measuring cell where the specimen was placed was pre-vacuumed. The RH outside of the specimen was maintained at 51.51% throughout the test. The weight of the specimen was continuously measured to determine the mass of water molecules diffused into the specimen at different diffusion time points. The test data of every replicate specimen were fitted using the first 36 terms retained in the developed 3-D diffusion model in order to reduce computational efforts. A satisfied level of goodness of model fit was achieved with an R2 value larger than 0.97. The model parameters were determined during model fitting, including the diffusivities of the Phase I water vapor diffusion in asphalt mixtures and the moisture retention capability of each specimen per unit mass. These determined parameters of the hot mix asphalt specimens (HMA) were significantly larger than those of the fine aggregate mixture specimens, which should be attributed to the larger air void contents of the HMA specimens.