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 ε. An asymptotic expansion in the ε is considered, and the boundary conditions are obtained by retaining the lowest-order terms in the expansion. Another aspect we investigate is the 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 one and two dimensions and different geometries.
|Original language||English (US)|
|Number of pages||26|
|Journal||Multiscale Modeling & Simulation|
|State||Published - Mar 30 2023|
Bibliographical noteKAUST Repository Item: Exported on 2023-04-04
Acknowledgements: This work was supported by ITN-ETN Horizon 2020 Project ModCompShock, Modeling and Computation on Shocks and Interfaces, Project Reference 642768, and the Italian Ministry of Instruction, University and Research (MIUR), with funds coming from PRIN Project 2017(2017KKJP4X etitled ``Innovative Numerical Methods for Evolutionary Partial Differential Equations and Applications." The authors would like to thank the unknown referees forcarefully revising the manuscript and thus contributing to its improvement.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Modeling and Simulation
- Ecological Modeling
- Computer Science Applications