Abstract
A method is presented for modeling the unretarded van der Waals and the electric double layer interactions of two parallel flat plates of which one is smooth and the other is roughened, based on the methods of Hamaker and Derjaguin. The electric double layer interactions will be described for the cases of the constant surface charge and constant surface potential. The method consists of replacing the original system with flat plates which have an equivalent interaction energy. The configuration of the two flat plate system is determined by using the equivalent distance ratio. The equivalent distance ratio is the distance between the equivalent flat plates, divided by the actual plate separation. It is dependent on the nondimensional geometric parameters of the asperity system, the shape of the asperity and the type of interaction. The range of the ratio is from zero to unity for positive asperities, though for negative asperities they always exceed unity. Both positive and negative asperities are studied. In addition to presenting the equivalent distance ratio, the original model of Herman and Papadopoulos ( J. Colloid Interface Sci. 136, 385, 1990 ) is used for constant base area analysis as well as for a distribution of asperities on the surface.
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