Colloidal interaction between a rigid solid and a fluid drop

We present results of a theoretical study of the effect of surface deformation on a macroscopic system composed of a solid surface interacting with a fluid drop through electrostatic double-layer forces. The analysis involves numerically solving a Laplace equation suitably modified to describe the shape of a liquid drop subjected to a repulsive double-layer force. The latter is evaluated in nonlinear mean-field theory. Some analytical results are also given. The results indicate that although deformation need not be significant on the macroscopic scale, its effect on the interaction is significant and modifies the picture usually presented in DLVO theory. The decay length of the exponential repulsion deviates marginally from the Debye length, dependent on the interfacial tension of the drop. More significantly, at separations where the double-layer force becomes comparable to the internal pressure of the drop, the net force between the two bodies, the local radius of curvature of the drop, and the amount of deformation grow abruptly. The results of this work are relevant to emulsion stability, micelle, vesicle, and cell interactions, and recent experiments on bubble-particle interaction.