Deformation of Fluid Interfaces Induced by Electrical Double-Layer Forces and Its Effect on Fluid−Solid Interactions

Abstract

The problem of determining the electrical double-layer interaction between a rigid planar surface and a deformable liquid droplet is formulated as a pair of coupled differential equations. The Young−Laplace equation, describing the shape of the droplet subject to double-layer pressures, is solved numerically, while the linearized Poisson−Boltzmann equation, which describes the double-layer interaction, is solved analytically. Results are provided for the three sets of boundary conditions of constant dissimilar surface potentials, constant dissimilar surface charges, and the mixed case of constant charge on one surface and constant potential on the other. Our principal object of interest is the net force between the surfaces evaluated as the integral of the normal stress tensor over the surfaces. We also provide information on the shape of the droplet interface and the distribution of the normal stress over that interface. Both of these items of information are vital for understanding the complex behavior of the net force. For constant charge surfaces of the same sign, as for the symmetric constant potential case, the results are qualitatively similar to those of our previously published work. For either constant dissimilar potential surfaces, for dissimilar constant charge surfaces, and/or the mixed case, however, we find greater diversity of qualitative features.