Fractal rate of adsorption and surface diffusivity of carbon dioxide across mesoporous adsorbents

The disordered nature of pore structures in adsorbents suggests the existence of a fractal structure formed by the pores. In this study, fractal theory has been employed to construct a rate and surface diffusivity model for these mesoporous adsorbents. The fractal dimensions for the adsorbent pore were obtained via the Dubinin-Astakhov equation and the Jaroniec equation. The model indicates the existence of three simultaneous gas-flow mechanisms. When the Reynolds number is less than 30, laminar flow is dominant; when the Reynolds number is greater than 1800, turbulent flow is dominant; and when the Reynolds number is in the range 30-1800, a transient region co-exists. Contact experiments employing CO₂ gas with mesoporous hydrotalcite adsorbents were conducted to validate the model. The calculated adsorption of CO ₂ from convective models was significantly higher in the turbulent regime. The adsorption rate increased with increasing values of ΔT (T _sub-T). The surface diffusivity also increased as ΔT increased, regardless of the flow regime.