Contributed Talk
Multi-scale modeling and numerics of Sorption Kinetics
King Abdullah University of Science & Technology, Saudi Arabia
Abstract
The trapping of diffusing particles by either a single or a distribution of moving traps is an interesting topic that has been employed to model a variety of
different real problems in chemistry, physics and biology [1]. Here we study the dynamics of diffusing particles in a domain with a spherical trap-bubble.
We investigate the correlated motion between positive and negative ions exposed to the attraction of a bubble surface that mimics the (oscillating) cell membrane [2].
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 potential
which includes both the effect of the bubble and the Coulomb interaction between the carriers. The latter term is obtained from the solution of
a self-consistent Poisson equation. For very short Debye lengths one can adopt the so called Quasi-Neutral limit which drastically simplifies the system,
thus allowing for much faster numerical simulations. We present a PNP model that describes ion charges in presence of a trap. Then we explore the validity
of the Quasi-Neutral limit by comparison with detailed numerical simulation for smaller and smaller Debye lengths. In order to reach these goals,
we propose a simple and efficient Alternate Direction Implicit method for the numerical solution 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. In the second part of the talk, we propose and validate
a multiscale model for the description of particle diffusion in presence of trapping boundaries [3].
We start from a drift-diffusion equation in which the drift term describes the effect of bubble traps. The interaction of the particles attracted by the bubble
surface is simulated by the Lennard-Jones potential. 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. The validity of the model is carefully checked with
several tests in 1D, 2D and different geometries.
References
[1] Oscillations of Bubble Shape Cause Raudino, A., Raciti, D., Grassi, A., Pannuzzo, M., Corti, M.,
Anomalous Surfactant Diffusion: Experiments, Theory, and Simulations, Langmuir, 2016, 32, 8574-8582.
[2] Anomalous sorption kinetics of self-interacting particles by a spherical trap, A. Raudino, G. Russo, C. Astuto,
Communication in Computational Physics, (accepted) arXiv:2202.01420
[3] Multiscale modeling of sorption kinetics, C. Astuto, A. Raudino, G. Russo, Multiscale Modeling and Simulation (SIAM), (submitted)
arXiv:2202.02552
[4] A. Jungel and Y. J. Peng, A Hierarchy of Hydrodynamic Models for Plasmas. Quasi-Neutral Limits in the Drift-Diffusion Equations, Asymptotic Analysis, 28, (2000)