ABSTRACT The anomalous diffusion and reaction process for Riemann-Liouville fractional differential equation is studied for heterogeneously isothermal nth-order reaction. The diffusion coefficient is regarded as a function of the position of the fractal porous catalyst. For a first-order irreversible reaction, new general analytical solutions of transient concentration profiles are derived with Mittag-Leffler function by taking into account of the intraparticle and external mass-transfer resistances. The numerical solution for anomalous diffusion-reaction is present for nth-order reaction; it is found that the results calculating by numerical solution are in satisfactory agreement with those by analytical solution for first-order reaction. The volume-averaged concentration and general expressions for effectiveness factor are present for first-order reaction. The effects of the order of the time fractional derivative, the fractal geometry of porous catalyst, diffusion coefficient, intraparticle and external mass-transfer resistances, and Thiele modulus on transient concentration profiles and catalytic efficiency are examined over a wide range of parameters by analytical solutions and numerical solution.

A predictive model based on Fick’s second law for radial diffusion is proposed and validated for modeling the diffusion of fragrances. A pure component, two binary systems, and a ternary system were used for validation. The model combines the prediction model to represent the liquid phase non-idealities, using the UNIFAC group contribution method, with the Fickian radial diffusion approach. The experimental headspace concentrations were measured in a diffusion chamber using the solid-phase microextraction (SPME) technique and quantified using gas chromatography with a flame ionization detector (GC-FID). The numerical solutions were obtained along with an analytical model considering constant surface concentration. The odor intensities of the studied systems were calculated using Stevens’ power law and the strongest component model, respectively. The numerical simulation presented good adherence to the experimental gas concentration data. The proposed methodology is an efficient and validated tool to assess the radial diffusion of fragrance and volatile systems.