Diffusion-controlled emissions of volatile organic compounds (VOCs): Short-, mid-, and long-term emission profiles

This paper indicates that diffusion-controlled organic emissions can be identified as processes of three stages, i.e., short-, mid-, and long-term emissions. Based on two generalized mass-diffusion models, exact series and short-time solutions are derived and validated by using two reported environmental-chamber tests. Long-term emissions can be predicted by a new exponential-decay model, a simplified version of a series solution. Short-term emissions can be modeled efficiently by small-time solutions. Besides having simple forms, small-time solutions require no roots of transcendental equations and converge very fast for short times. They serve necessary complements to the exact series solutions. Especially interesting is the mid-stage emission between the very early and the late emission stages, which indicates that there is a straight-line relation between air-phase concentrations and 1/t (t is time). This simplest mathematical relation is the most desirable for engineering applications. Since all derivation has a solid mathematical–physics basis, the models presented in this paper may contribute to casting new light on the underlying mechanisms of diffusion-limited organic emissions.