Geometry dependence of wetting tension on charge-modified surfaces

Abstract

The electrostatic field around a wedge-shaped region of three-phase contact of a (electrolyte) liquid layer on a charged (or ionizable) substrate is analyzed to determine the Coulombic contribution to wetting tension. The linearized Poisson-Boltzmann equation is analyzed by introducing the Kantorovich-Lebedev transformation. The Maxwell stress acting on the droplet surface is integrated to obtain the wetting tension due to the Coulombic interaction. In addition, a numerical method based on the variational calculus is used to analyze the electrostatic field by solving the nonlinear Poisson-Boltzmann equation. The present theory clearly exhibits, although only the case of a straight profile is considered, that the Coulombic contribution to the wetting tension is dependent on the shape of the region of three-phase contact. It is also shown that the Coulombic wetting tension can be significantly greater than that predicted by the conventional theory of electrocapillarity.