  The qualitative behavior of charged particles in a vacuum is given by
Earnshaw's Theorem which states that there is no steady configuration of
charged particles in a vacuum which is asymptotically stable to perturbations.
In a viscous fluid, examples of stationary configurations of sedimenting
uncharged particles are known, but they are unstable or neutrally stable - they
are not attractors. In this paper, it is shown by example that two charged
particles settling in a fluid may have a configuration which is asymptotically
stable to perturbations, for a wide range of charges, radii and densities. The
existence of such "bound states" is essential from a fundamental point of view
and it can be significant for dilute charged particulate systems in various
biological, medical and industrial contexts.
