Electric double layer structure close to the three-phase contact line in an electrolyte wetting a solid substrate

TL;DR

This paper models the electric double layer near a three-phase contact line in an electrolyte on a solid substrate using a linearized Poisson-Boltzmann approach, providing insights into the influence of the fluid interface.

Contribution

It introduces a simplified analytical model that characterizes the double layer structure and boundary influence length scale near the contact line, complementing existing solutions.

Findings

Model accurately predicts double layer structure for various contact angles.

The influence length scale is proportional to the Debye length and varies with contact angle.

Finite boundary influence occurs near 90° contact angles.

Abstract

The electric double layer structure in an electrolyte close to a solid substrate near the three-phase contact line is approximated by considering the linearized Poisson-Boltzmann equation in a wedge geometry. The mathematical approach complements the semi-analytical solutions reported in the literature by providing easily available characteristic information on the double layer structure. In particular, the model contains a length scale that quantifies the distance from the fluid-fluid interface over which this boundary influences the electric double layer. The analysis is based on an approximation for the equipotential lines. Excellent agreement between the model predictions and numerical results is achieved for a significant range of contact angles. The length scale quantifying the influence of the fluid-fluid interface is proportional to the Debye length and depends on the wall contact angle. It is shown that for contact angles approaching 90{\deg} there is a finite range of boundary influence.