DEFORMATION OF FLUID INTERFACES INDUCED BY ELECTRICAL DOUBLE-LAYER FORCES AND ITS EFFECT ON FLUID-SOLID INTERACTIONS

The problem of determining the electrical double-layer interaction bet ween a rigid planar surface and a deformable liquid droplet is formula ted as a pair of coupled differential equations. The Young-Laplace equ ation, describing the shape of the droplet subject to double-layer pre ssures, is solved numerically, while the linearized Poisson-Boltzmann equation, which describes the double-layer interaction, is solved anal ytically. Results are provided for the three sets of boundary conditio ns of constant dissimilar surface potentials, constant dissimilar surf ace charges, and the mixed case of constant charge on one surface and constant potential on the other. Our principal object of interest is t he net force between the surfaces evaluated as the integral of the nor mal stress tensor over the surfaces. We also provide information on th e shape of the droplet interface and the distribution of the normal st ress over that inter face: Both of these items of information are vita l for understanding the complex behavior of the net force. For constan t charge surfaces of the same sign, as for the symmetric constant pote ntial case, the results are qualitatively similar to those of our prev iously published work. For either constant dissimilar potential surfac es, for dissimilar constant charge surfaces, and/or the mixed case, ho wever, we find greater diversity of qualitative features.