Anomalous Sorption Kinetics of Self-Interacting Particles by a Spherical Trap (Communications in Computational Physics, 2022)
In this paper we propose a computational framework for the investigationof the correlated motion between positive and negative ions exposed to the attractionof a bubble surface that mimics the (oscillating) cell membrane. Specifically we aimto investigate the role of surface traps with substances freely diffusing around the cell.The physical system we want to model is an anchored gas drop submitted to a diffusive flow of charged surfactants (ions). When the diffusing surfactants meet the surfaceof the bubble, they are reversibly adsorbed and their local concentration is accuratelymeasured. The correlated diffusion of surfactants is described by a Poisson-Nernst-Planck (PNP) system, in which the drift term is given by the gradient of a potentialwhich includes both the effect of the bubble and the Coulomb interaction betweenthe carriers. The latter term is obtained from the solution of a self-consistent Poissonequation. For very short Debye lengths one can adopt the so called Quasi-Neutrallimit which drastically simplifies the system, thus allowing for much faster numericalsimulations. The paper has four main objectives. The first one is to present a PNPmodel that describes ion charges in presence of a trap. The second one is to providebenchmark tests for the validation of simplified multiscale models under current development [1]. The third one is to explore the relevance of the term describing theinteraction among the apolar tails of the anions. The last one is to quantitatively explore the validity of the Quasi-Neutral limit by comparison with detailed numericalsimulation for smaller and smaller Debye lengths. In order to reach these goals, wepropose a simple and efficient Alternate Direction Implicit method for the numericalsolution of the non-linear PNP system, which guarantees second order accuracy both in space and time, without requiring solution of nonlinear equation at each time step.New semi-implicit scheme for a simplified PNP system near quasi neutrality is alsoproposed.
Keywords: Spherycal trap; quasi-neutrality; finite differences; Coulomb potential; Poisson-Nernst-Planck system; ADI discretization; semi-implicit scheme.