Mass Transfer Models in Adsorption Processes

Mass transfer models in adsorption processes describe the movement of solute molecules from the bulk fluid phase to and within the adsorbent material. The overall uptake rate is governed by a sequence of resistances, including external film diffusion through a boundary layer, intraparticle pore diffusion, and, in some cases, surface diffusion within adsorbent pores. Classical approaches adopt two‐resistance frameworks that combine a fluid–solid film mass transfer coefficient with an effective pore diffusion coefficient. More advanced descriptions incorporate homogeneous surface diffusion models or parallel diffusion models to account for simultaneous pore volume and surface transport. Dimensionless parameters such as the Biot number are used to identify rate‐limiting steps and guide the choice of simplified or detailed kinetic formulations. Recent advances have expanded one‐dimensional treatments into three‐dimensional simulations, capturing spatial variations in concentration within porous particles. These models have been applied to a wide range of systems, from activated carbons and biochars to modified minerals, and have underpinned the design of water treatment units, nutrient recovery processes and pollutant degradation schemes. By quantifying the relative contributions of external and internal resistances, mass transfer modelling enables optimisation of operating conditions and adsorbent architecture for global challenges such as removal of emerging contaminants and recovery of valuable resources from aqueous streams.

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Recent studies of emerging pollutant adsorption on activated carbon have combined chemical degradation kinetics with mass transfer modelling to predict both parent compounds and their labile derivatives. These works demonstrate that intraparticle pore diffusion often controls the overall rate, with effective pore diffusion coefficients spanning 10⁻⁸ to 10⁻¹⁰ cm² h⁻¹, and introduce coupled models that integrate reversible degradation steps and multilayer adsorption of degradation products. Advances in phosphate removal have employed dimensionless two‐phase homogeneous surface diffusion models, revealing that intraparticle diffusion dominates under typical wastewater concentrations. The homogeneous surface diffusion approach, paired with selectivity isotherms, yields surface diffusion coefficients in the 10⁻¹⁰ to 10⁻⁹ cm² s⁻¹ range and external mass transfer coefficients around 10⁻⁴ to 10⁻³ cm s⁻¹, with Biot numbers on the order of 10⁵ confirming pore diffusion control. Three‐dimensional mass transfer simulations of hydroquinone adsorption on biochar highlight the coexistence of pore‐volume and surface diffusion within porous particles. These models reveal that surface diffusion can contribute nearly 100 per cent of intraparticle transport under varied operating concentrations, with surface diffusion coefficients between 2.5 × 10⁻¹⁰ and 1.7 × 10⁻⁹ cm² s⁻¹. The combined modelling framework enhances predictive accuracy for kinetic design in emerging biochar‐based water treatment systems.

Mass Transfer Models in Adsorption Processes publication trend

The graph below shows the total number of articles in mass transfer models in adsorption processes across all publications each year (not limited to Nature Index journals).

Technical terms

Film diffusion: Movement of adsorbate molecules through the stagnant fluid layer enveloping the adsorbent particle.

Intraparticle diffusion: Transport of adsorbate molecules within the pore network of the adsorbent.

Surface diffusion: Migration of adsorbate species along the internal surfaces of pores.

Biot number (Bi): Dimensionless ratio of internal diffusion resistance to external film resistance, used to identify the rate‐controlling step.

Pore diffusion coefficient: Effective diffusivity representing intraparticle transport through the porous medium.

Homogeneous surface diffusion model: Theoretical framework that treats surface migration and pore diffusion as coupled resistances within a single transport equation.

References

1. Adsorption of stable and labile emerging pollutants on activated carbon: degradation and mass transfer kinetic study. Applied Water Science (2024).
2. Phosphate removal by Ca(OH)2-treated natural minerals: Experimental and modeling studies. Colloids and Surfaces A Physicochemical and Engineering Aspects (2023).
3. Three-Dimensional Mass Transfer Modeling of Hydroquinone Adsorption on Phragmites australis Biochar. Toxics (2023).