Multiscale Modeling of Sorption Kinetics

TL;DR

This paper develops and validates a multiscale model for particle diffusion near trapping boundaries, incorporating short-range potentials and asymptotic analysis to derive boundary conditions, with validation across multiple geometries.

Contribution

It introduces a novel multiscale approach combining drift-diffusion equations with boundary conditions derived from asymptotic analysis of short-range potentials.

Findings

Model accurately predicts particle trapping behavior.

Boundary conditions derived from asymptotic analysis are validated.

Effective in multiple geometries and dimensions.

Abstract

In this paper we propose and validate a multiscale model for the description of particle diffusion in presence of trapping boundaries. We start from a drift-diffusion equation in which the drift term describes the effect of bubble traps, and is modeled by a short range potential with an attractive term and a repulsive core. The interaction of the particles attracted by the bubble surface is simulated by the Lennard-Jones potential that simplifies the capture due to the hydrophobic properties of the ions. In our model the effect of the potential is replaced by a suitable boundary condition derived by mass conservation and asymptotic analysis. The potential is assumed to have a range of small size $\varepsilon$. An asymptotic expansion in the $\varepsilon$ is considered, and the boundary conditions are obtained by retaining the lowest order terms in the expansion. Another aspect we investigate is saturation effect coming from high concentrations in the proximity of the bubble surface. The validity of the model is carefully checked with several tests in 1D, 2D and different geometries.