2025/07/02 by Clarissa Astuto, Astuto, Clarissa, Giovanni Russo +1 · 1 citation
Chemistry · Computer Science · Physics and Astronomy · #65M06 65M55 76D07 76M20 76R50 #Advanced Mathematical Modeling in Engineering #Electrostatics and Colloid Interactions #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Micro and Nano Robotics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2507.01402
openalex publication_date 2025/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, we propose and validate a two-species Multiscale model for a Poisson-Nernst-Planck (PNP) system, focusing on the correlated motion of positive and negative ions under the influence of a trap. Specifically, we aim to model surface traps whose attraction range, of length δ, is much smaller then the scale of the problem. The physical setup we refer to is an anchored gas drop (bubble) surrounded by a flow of charged surfactants (composed by positive and negative ions) that diffuses in water. When the diffusing surfactants reach the surface of the trap, the negative ions are adsorbed because of their hydrophobic tail that is attracted by the air bubble. As in our previous works, the effect of the attractive potential is replaced by a suitable boundary condition derived by mass conservation and asymptotic analysis. The novelty of this work is the extension of the model proposed in \citeastuto2023multiscale, now incorporating the influence of both carriers -- positive and negative ions -- simultaneously, which is often neglected in traditional approaches that treat ion species independently. The two carriers interact through the Coulomb potential, that is computed by a Poisson equation. [...]