UBC Theses and Dissertations
Electrostatic interactions between interfacial particles Lyne, Michael Peter
The Finite Element Method (FEM) is employed, using Galerkin weighted residuals, to simulate the electrostatic interactions between interfacial particles in two separate models. The three phase problem of two identical, parallel, infinitely long, solid cylinders at a given separation and each embedded to the same extent in an oil/water interface is considered. It is revealed that due to the asymmetric charge distribution surrounding an interfacial particle, a force (normal to the interface) acts on the particle in the direction of the electrolyte phase. The electrostatic forces acting on the particles normal and parallel to the oil/water interface are calculated and it is found that under certain conditions they may be of comparable magnitude. The Debye-Hiickel form of the Derjaguin method is also applied to this model; this method showed good agreement with the low potential numerical results for the parallel force when the oil/water interface is assumed to be uncharged. Interactions between the cylinders on a constant potential interface are also considered and it is revealed that for some circumstances the magnitude of these interactions will be significantly different from the corresponding interactions on an uncharged interface. For practical situations, however, increases in the interaction force were not large enough to account for a 10⁶kT change in the free energy associated with the interaction. The more complex interaction between particles in a dense, two-dimensional structure on an oil/water interface is simulated using a cell model approach. The normal forces acting on the spheres and the electrostatic free energy change associated with forming the structure are calculated. The normal force per unit of particle perimeter in contact with the oil/water interface is shown to be comparable to that acting on cylinders while the free energy calculations are only accurate enough for order of magnitude estimations. Additionally, to test the effectiveness of the numerical approach, the familiar case of two identical interacting spheres completely immersed in a single electrolyte is modeled for both constant potential and constant charge boundary conditions on the sphere surfaces. The implicit assumption inherent in the Derjaguin method when it is applied to constant charge interactions (i.e. zero potential gradient inside the particle) is examined and found to cause errors of > 10% in cases of low ka and large particle dielectric constants.
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