Diffusionadsorption

Diffusionadsorption refers to a coupled transport process in which molecules diffuse through a medium and simultaneously adsorb onto solid surfaces within that medium. This combination is important in porous materials, membranes, and thin films where the movement of species is hindered or stored by interactions with surfaces. Diffusionadsorption can slow diffusion, create concentration gradients between phases, and control overall transport rates in systems such as soils, clays, catalysts, and filtration media.

In modeling diffusionadsorption, a mass balance is typically written to account for diffusive transport and the amount of solute adsorbed on surfaces. Diffusion is described by Fick’s laws, while adsorption is represented by isotherms (equilibrium models) or kinetic expressions (rate laws). Instantaneous adsorption assumes equilibrium at every point, linking aqueous concentration to surface concentration via an isotherm (for example Langmuir or Freundlich). In noninstantaneous cases, adsorption follows kinetic forms such as pseudo-first or pseudo-second order, introducing a time-dependent exchange between phases. A common simplification introduces a retardation factor R, which captures the added storage due to sorption: R ∂C/∂t ≈ D ∂^2C/∂x^2 for simple one-dimensional diffusion with constant porosity and sorption parameters, where R = 1 + (rho_b / n) K_d in linear sorption.

Applications of diffusionadsorption include predicting contaminant transport in groundwater and soils, designing sorption-based filtration and remediation systems, and understanding catalytic surfaces where reactants diffuse to active sites and adsorb before reaction. The approach supports both linear and nonlinear sorption, single- and multicomponent systems, and is implemented with analytical or numerical methods depending on complexity.