The interaction between closely spaced conducting spheres is fundamental to aerosol coagulation because any variation of surface charge between interacting aerosols will directly affect coagulation rates. The solution to the general Coulomb force equation for the electrostatic force between two unlike sized spheres held at a constant, but not necessarily equal, charge is constructed via the Fredholm integral equation. The electrostatic force is either attractive, null, or repulsive depending on sphere charge, size, and separation distance and thus modifies the stability of aerosols. The evaluation also yields an exact description of the surface charge distribution as a function of separation distance important to the study of liquid droplet stability, deformation, and breakup. It is found that the difference between the simple dipole approximation and the general Coulomb force equation is significant when both particle size and charge are taken into account. Scavenging of small particles by coarse particles can be explained in part from electrostatic considerations.
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