Journal of Colloid and Interface Science, Vol.201, No.1, 48-58, 1998
Domain perturbation analysis of the interaction between a charged particle and a charged deformable interface
The interaction between a charged, spherical colloidal particle and a charged liquid/liquid interface is studied by domain perturbation analysis. A general solution for the potential near the nonplanar interface is derived in the form of a Hankel transform, and that solution is used in conjunction with the surface stress balance to find the interface shape and force on the particle to leading order. The range of accuracy of the asymptotic methods used are evaluated by direct comparison with corresponding numerical results obtained via a boundary integral method. In addition, analytic expressions for the interface shape at radial positions on the order of and much larger than a Debye length are given, and the scaling dependence of influences such as surface tension, surface charge density, gravity and separation distance are discussed. In particular, it is shown that under many conditions of interest the breadth of a perturbation in interface position (i.e., the distance over which the perturbation decays) can be many orders of magnitude larger than the depth of the perturbation, and scaling relationships illustrating this fact are derived.
Keywords:SPHERICAL COLLOIDAL PARTICLES;POISSON-BOLTZMANN THEORY;DOUBLE-LAYER INTERACTION;ELECTROSTATIC INTERACTION;HYPERNETTED CHAIN;PLANE SYSTEM;PLATE;EXTENSION