  Adsorption is a relevant process in many fields, such as product
manufacturing or pollution remediation in porous materials. Adsorption takes
place at the molecular scale, amenable to be modeled by Lagrangian numerical
methods. We have proposed a chemical diffusion-reaction model for the
simulation of adsorption, based on the combination of a random walk particle
tracking method involving the use of Gaussian Kernel Density Estimators. The
main feature of the proposed model is that it can effectively reproduce the
nonlinear behavior characteristic of the Langmuir and Freundlich isotherms. In
the former, it is enough to add a finite number of sorption sites of
homogeneous sorption properties, and to set the process as the combination of
the forward and the backward reactions, each one of them with a prespecified
reaction rate. To model the Freundlich isotherm instead, typical of low to
intermediate range of solute concentrations, there is a need to assign a
different equilibrium constant to each specific sorption site, provided they
are all drawn from a truncated power-law distribution. Both nonlinear models
can be combined in a single framework to obtain a typical observed behavior for
a wide range of concentration values.
