Homogenization of the Poisson-Boltzmann Equation

Youcef Amirat (1) , Vladimir Shelukhin (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 LIH - Lavrentyev Institute of Hydrodynamics

By the homogenization approach we justify a two-scale model of ion equilibrium between solid layers. By up-scaling, the electric potential equation in nanoslits separated by thin solid layers is approximated by a homogenized macroscale equation in the form of the Poisson equation for an induced vertical electrical field.

Domaines: Equations aux dérivées partielles [math.AP]

Youcef Amirat, Vladimir Shelukhin. Homogenization of the Poisson-Boltzmann Equation. Book series: Advances in Mathematical Fluid Mechanics, New Directions in Mathematical Fluid Mechanics, Birkhäuser Basel, pp.23-40, 2009. ⟨hal-00477369⟩