Mechanistic Insights into Phenol Adsorption and Mass Transport on Multi-Walled Carbon Nanotubes

Phenol remediation from contaminated effluents presents a critical industrial challenge due to its acute toxicity even at trace concentrations [1-3]. Multi-walled carbon nanotubes (MWCNTs) are promising adsorbents for this purpose, given their high adsorption capacity and ease of separation [4]. This work presents a phenomenological and numerical analysis of mass transport coupled to phenol adsorption on MWCNTs (d_ext = 50 nm) parameterized with published experimental equilibrium data under neutral pH conditions at 298 K [1,4, 5]. The mathematical model incorporates effective pore diffusivity (D_e = 4.82 × 10⁻¹⁰ m²/s) derived from pore structure parameters and describes three distinct scenarios: (1) pure physical adsorption via modified Fick's Second Law, (2) kinetics incorporating 0.5-order reaction kinetics, and (3) parametric analysis of particle size (1–100 nm) and concentration sensitivity (1–5 mg/L). Numerical solutions establish a Thiele modulus of ϕ ≪ 1 across the tested range, indicating kinetically controlled mass transfer with effectiveness factor η = 1.0, and validate the theoretical dependence ϕ ∝ Cs⁻⁰·²⁵. During effluent polishing operations (reduction from 5 to 1 mg/L), relative diffusive resistance increases by 49.5%, necessitating proportional increases in contact time or adsorbent dosage. The nanoscale architecture of MWCNTs reduces diffusional limitations by approximately 10⁶ compared to macroscopic granular adsorbents, enabling significantly reduced contact times. This phenomenological analysis provides fundamental mass transport insights for optimizing phenol remediation systems using nano-adsorbents.

References

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