Diffuse-charge dynamics across a capacitive interface in a DC electric field

TL;DR

This paper models the charging dynamics of a capacitive membrane interface under a DC electric field using Poisson-Nernst-Planck equations, providing analytical solutions in specific limiting cases.

Contribution

It introduces a zero-thickness capacitive interface model and derives asymptotic solutions for ion and potential evolution under weak fields.

Findings

Analytical solutions for membrane charging dynamics

Characterization of ion distributions near the membrane

Insights into electric potential evolution across membranes

Abstract

Cells and cellular organelles are encapsulated by nanometrically thin membranes whose main component is a lipid bilayer. In the presence of electric fields, the ion-impermeable lipid bilayer acts as a capacitor and supports a potential difference across the membrane. We analyze the charging dynamics of a planar membrane separating bulk solutions with different electrolyte concentrations upon the application of an applied uniform DC electric field. The membrane is modeled as a zero-thickness capacitive interface. The evolution of the electric potential and ions distributions in the bulk are solved for using the Poisson-Nernst-Planck (PNP) equations. Asymptotic solutions are derived in the limit of thin Debye layers and weak fields (compared to the thermal electric potential).