A time-dependent diffusion coefficient and simulation of asphalt binder diffusion using ADI numerical scheme in asphalt recycling

Diffusion is one of the predominant processes occurring in asphalt pavement recycling. Past studies investigated diffusion on binders, recycling agents, or modifiers at variable recycling temperatures and times. Constant diffusion coefficients are estimated at different temperatures in past studies. Asphalt binder diffusion occurs continuously during the mixing, compaction, and cooling process due to the change in the temperature of the recycled mixture with time. Therefore, the time-dependent behaviour of asphalt diffusion should be investigated to observe the blending occurring due to diffusion. In this study, the time dependency of asphalt diffusion is investigated by solving for a time-dependent coefficient of diffusion. A novel solution considering the time-dependent behaviour is proposed, solving Fick's law of diffusion analytically with initial and boundary conditions. A numerical simulation of diffusion is performed on a two-dimensional scale to observe the asphalt diffusion on a recycled asphalt mixture. It is found that for an approximate mastic film thickness of 50 $\mu m$mu m, blending approaches completion, and for film thickness over 50 $\mu m$mu m, partial blending is observed between the binders or recycling agent. An optimum asphalt film thickness of 36 $\mu m$mu m is estimated numerically for asphalt diffusion.