The influence of Coulombic interaction on wetting is elucidated within the framework of electromechanics. The Maxwell stress and osmotic pressure acting on a meniscus are integrated to obtain a concise analytical expression for the Coulombic contribution to wetting tension. The results are verified alternatively by using a thermodynamic approach. The method is applied to three important charge-related wetting configurations in which droplets are placed on a solid substrate. First, when the constant-potential boundary condition is applied at the substrate surface, only the electrocapillary term which represents the electrostatic free energy of the electrical double layer contributes to the wetting tension. Second, in the case of the constant-charge condition, the wetting tension includes an additional edge-effect term. It is found that the wetting tension in this case is dependent on the interface profile near the three-phase contact line. Third, in the case of electrowetting on dielectrics, the wetting tension also includes the edge-effect term. The wetting-tension term appearing in the Lippmann−Young equation is recovered as a special case of the third case.

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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.

In the wetting problems of very small scales, such as in nanotubes and nanoparticles, the contribution of line tension potentially becomes significant. In contrast to the molecular contribution, there rarely exists any literature that systematically considers the electrical contribution to the line tension in wetting. In this paper, the electrical double layer around a wedge-shaped confinement (which represents the region of the three-phase contact of an electrolyte droplet on a charged, or ionizable, substrate) is analyzed. An exact analytical solution for the linearized Poisson−Boltzmann equation is obtained for both the constant surface charge and the constant surface potential conditions. Comprehensive analytical formulas of the line tension are derived. An equation for predicting the contact angle is also shown, considering the dependence of the electrostatic line tension on the contact angle. It is exhibited that the line tension can have either a positive or a negative value depending on the sign of the surface charge density. It is demonstrated that the magnitude of the line tension is comparable or (potentially) greater than that of the molecular contribution. To corroborate the results of the linear theory, the nonlinear Poisson−Boltzmann equation is solved numerically. The results of the nonlinear theory show reasonable agreement with those of the linear theory.

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