Simple Approximate Relations for van der Waals Interaction Energy Between Spherical Particles of Different Radii and Variable Distances

The van der Waals (vdW) interaction energy is a crucial factor in evaluating the potential destabilization of colloidal systems, such as those found in drinking-water treatment, where particles are often assumed to be spherical. Although the explicit dependence of the vdW interaction energy on the radii of spherical particles and their distances is known, a simple view is lacking due to the complexity of the relations. Here, we propose explicit, algebraically simple, approximate relations that provide insight into the fundamental influence of the input geometrical parameters. These relations, when combined with the exponentially decaying potential generated by the electrical double layer, can provide an approximate evaluation of the onset of raw water destabilization in drinking-water treatment, in other words, establishing the conditions under which pollutants in raw water begin to aggregate.