Surface Element Integration: A Novel Technique for Evaluation of DLVO Interaction between a Particle and a Flat Plate

Abstract

A novel method, the surface element integration (SEI), is developed to determine the van der Waals and electrostatic double layer interactions between a particle and an infinite flat plate from the corresponding interactions per unit area between two infinite flat plates. Comparison with the Hamaker expression for nonretarded van der Waals interaction reveals that the new technique gives the exact interaction energy between a spherical particle and a flat plate. Available analytical expressions for the electrostatic double layer interaction energy between two infinite flat plates, based on the linearized Poisson–Boltzmann equation, are used in SEI to obtain the sphere–flat plate interaction energy. These sphere–flat plate interaction energies determined using SEI are compared with the corresponding interaction energies obtained from a detailed numerical solution of the Poisson–Boltzmann equation based on finite element analysis. The comparisons reveal that SEI scales the flat plate interaction to the corresponding sphere–flat plate geometry exactly, while the scaling based on the conventional Derjaguin approximation technique grossly overpredicts the interaction energy for small particles and low electrolyte concentrations.