Assessment of steady state diffusion of volatile organic compounds in unsaturated building materials based on fractal diffusion model

• Steady state diffusion of VOCs in unsaturated building materials is evaluated.
• Unsaturated building materials are the ones with time-dependent pore structure.
• A fractal diffusion model based on pore transportation mechanism is developed.
• Three phases (solid, liquid and gas) fractal carpet is proposed.
• The carpet is related to pore structure parameters and saturated degree.

This paper presents a preliminary work to evaluate the steady state diffusion of volatile organic compounds (VOCs) in unsaturated building materials based on a newly-proposed fractal diffusion model. This model studies the contributions of water and gas to the diffusion transportation in unsaturated building materials, involves geometry parameters of unsaturated building materials, fractal dimensions, minimal and maximal pore diameters. In this model, the derivation of some parameters is assisted by newly-established three phases fractal carpet consisting of middle and peripheral parts that represent gas and water occupied regions in the unsaturated building materials. The influences of some structural parameters (removed number, recursion number and size) of fractal carpet on diffusion performance have been discussed. Additionally, the effective diffusion coefficients of various kinds of volatile organic compounds (formaldehyde, methanol, 1,3,5-trimethylbenzene, Ethylbenzene, xylene isomers, benzene and toluene) are also compared based on this fractal model. Formaldehyde exhibits the largest value of effective diffusion coefficient among selected VOCs.